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NCERT Solutions for Class 12 Physics I Chapter 1 to 8

Exercise

28 Qs

Related questions

A circular coil of wire consisting of turns, each of radius  carries a current of . What is the magnitude of the magnetic field at the centre of the coil?

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A long straight wire carries a current of 35 A. What is the magnitude of the field B at a point 20 cm from the wire?

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A long straight wire in the horizontal plane carries a current of 50 A in north to south direction. Give the magnitude and direction of B at a point 2.5 m east of the wire.

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A horizontal overhead power line carries a current of 90 A in east to west direction. What is the magnitude and direction of the magnetic field due to the current 1.5 m below the line?

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What is the magnitude of magnetic force per unit length on a wire carrying a current of 8 A and making an angle of with the direction of a uniform magnetic field of 0.15 T?

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A 3.0 cm wire carrying a current of 10 A is placed inside a solenoid perpendicular to its axis. The magnetic field inside the solenoid is given to be 0.27 T. What is the magnetic force on the wire?

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Two long and parallel straight wires A and B carrying currents of 8.0 A and 5.0 A in the same direction are separated by a distance of 4.0 cm. Estimate the force on a 10 cm section of wire A.

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A closely wound solenoid 80 cm long has 5 layers of windings of 400 turns each. The diameter of the solenoid is 1.8 cm. If the current carried is 8.0 A, estimate the magnitude of B inside the solenoid near its centre.

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A square coil of side 10 cm consists of 20 turns and carries a current of 12 A. The coil is suspended vertically and the normal to the plane of the coil makes an angle of with the direction of a uniform horizontal magnetic field of magnitude 0.80 T. What is the magnitude of torque experienced by the coil?

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Two moving coil meters, and have the following particulars:




(The spring constants are identical for the two meters).Determine the ratio of (a) current sensitivity and (b) voltage sensitivity of and .

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In a chamber, a uniform magnetic field of 6.5 G is maintained. An electron is shot into the field with a speed of normal to the field. Explain why the path of the electron is a circle. Determine the radius of the circular orbit.

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In a chamber, a uniform magnetic field of is maintained. An electron is shot into the field with a speed of normal to the field. Explain why the path of the electron is a circle? 
Determine the radius of the circular orbit. .

Also obtain the frequency of revolution of the electron in its circular orbit. Does the answer depend on the speed of the electron? Explain.

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(a) A circular coil of 30 turns and radius 8.0 cm carrying a current of 6.0 A is suspended vertically in a uniform horizontal magnetic field of magnitude 1.0 T. The field lines make an angle of with the normal of the coil. Calculate the magnitude of the counter torque that must be applied to prevent the coil from turning.
(b) Would your answer change, if the circular coil in (a) were replaced by a planar coil of some irregular shape that encloses the same area? (All other particulars are also unaltered.)

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What was Vijay Singh’s weakness? Which awkward situation did it push him into?

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A magnetic field of 100 G (1 G = 10 T) is required which is uniform in a region of linear dimension about 10 cm and area of cross-section about . The maximum current-carrying capacity of a given coil of wire is 15 A and the number of turns per unit length that can be wound round a core is at most 1000 turns . Suggest some appropriate design particulars of a solenoid for the required purpose. Assume the core is not ferromagnetic. 

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For a circular coil of radius R and N turns carrying current I, the magnitude of the magnetic field at a point on its axis at a distance x from its centre is given by,

(a) Show that this reduces to the familiar result for field at the centre of the coil.
(b) Consider two parallel co-axial circular coils of equal radius R,and number of turns N, carrying equal currents in the same direction, and separated by a distance R. Show that the field on the axis around the mid-point between the coils is uniform over a distance that is small as compared to R, and is given by.

[Such an arrangement to produce a nearly uniform magnetic field over a small region is known as Helmholtz coils.]

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A toroid has a core (non -ferromagnetic) of inner radius 25 cm and outer radius 26 cm, around which 3500 turns of a wire are wound. If the current in the wire is 11 A, what is the magnetic field (a) outside the toroid, (b) inside the core of the toroid, and (c) in the empty space surrounded by the toroid.

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Answer the following questions:
(a) A magnetic field that varies in magnitude from point to point but has a constant direction (east to west) is set up in a chamber. A charged particle enters the chamber and travels undeflected along a straight path with constant speed. What can you say about the initial velocity of the particle?
(b) A charged particle enters an environment of a strong and non-uniform magnetic field varying from point to point both in magnitude and direction and comes out of it following a complicated trajectory. Would its final speed equal the initial speed if it suffered no collisions with the environment?
(c) An electron travelling west to east enters a chamber having a uniform electrostatic field in north to south direction. Specify the direction in which a uniform magnetic field should be setup to prevent the electron from deflecting from its straight line path.

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An electron emitted by a heated cathode and accelerated through a potential difference of 2.0 kV, enters a region with uniform magnetic field of 0.15 T. Determine the trajectory of the electron if the field (a) is transverse to its initial velocity, (b)
makes an angle of with the initial velocity.

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A magnetic field set up using Helmholtz coils (described below) is uniform in a small region and has a magnitude of . In the same region, a uniform electrostatic field is maintained in a direction normal to the common axis of the coils. A narrow beam of (single species) charged particles all accelerated through enters this region in a direction perpendicular to both the axis of the coils and the electrostatic field. If the beam remains undeflected when the electrostatic field is , make a simple guess as to what the beam contains. Why is the answer not unique?

Consider two parallel co-axial circular coils of equal radius , and number of turns , carrying equal currents in the same direction, and separated by a distance . Show that the field on the axis around the mid-point between the coils is uniform over a distance that is small as compared to , and is given by, .
[Such an arrangement to produce a nearly uniform magnetic field over a small region is known as Helmholtz coils].

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A straight horizontal conducting rod of length 0.45 m and mass 60 g is suspended by two vertical wires at its ends. A current of 5.0 A is set up in the rod through the wires.
(a) What magnetic field should be set up normal to the conductor in order that the tension in the wires is zero?

(b) What will be the total tension in the wires if the direction of current is reversed keeping the magnetic field same as before?(Ignore the mass of the wires.)  .

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The wires which connect the battery of an automobile to its starting motor carry a current of 300 A (for a short time). What is the force per unit length between the wires if they are 70 cm long and 1.5 cm apart? Is the force attractive or repulsive?

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A uniform magnetic field of 1.5 T exists in a cylindrical region of radius 10.0 cm, its direction parallel to the axis along east to west. A wire carrying current of 7.0 A in the north to south direction passes through this region. What is the magnitude and direction of the force on the wire if,(a) the wire intersects the axis,(b) the wire is turned from N-S to northeast-northwest direction,(c) the wire in the N-S direction is lowered from the axis by a distance of 6.0 cm?

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A uniform magnetic field of 3000 G is established along the positive z-direction. A rectangular loop of sides 10 cm and 5 cm carries a current of 12 A. What is the torque on the loop in the different cases shown in Fig.? What is the force in each case? Which case corresponds to stable equilibrium?

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A circular coil of 20 turns and radius 10 cm is placed in a uniform magnetic field of 0.10 T normal to the plane of the coil. If the current in the coil is 5.0 A, what is the(a) total torque on the coil,(b) the total force on the coil,(c) average force on each electron in the coil due to the magnetic field?
(The coil is made of copper wire of cross-sectional area , and the free electron density in copper is given to be about )

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A solenoid 60 cm long and of radius 4.0 cm has 3 layers of windings of 300 turns each. A 2.0 cm long wire of mass 2.5 g lies inside the solenoid (near its centre) normal to its axis; both the wire and the axis of the solenoid are in the horizontal plane. The wire is connected through two leads parallel to the axis of the solenoid to an external battery which supplies a current of 6.0 A in the wire. What value of current (with appropriate sense of circulation) in the windings of the solenoid can support the weight of the wire? .

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A galvanometer coil has a resistance of 12 and the metre shows full scale deflection for a current of 3 mA. How will you convert the metre into a voltmeter of range 0 to 18 V?

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A galvanometer coil has a resistance of and the metre shows full scale deflection for a current of . How will you convert the metre into an ammeter of range to ?

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Exercise

26 Qs

Related questions

A 100  resistor is connected to a 220 V, 50 Hz ac supply.(a) What is the rms value of current in the circuit?

(b) What is the net
power consumed over a full cycle?

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(a) The peak voltage of an ac supply is 300 V. What is the rms voltage?

(b) The rms value of
current in an ac circuit is 10 A. What is the peak current?

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A 44 mH inductor is connected to 220 V, 50 Hz ac supply. Determine the rms value of the current in the circuit.

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A capacitor is connected to a 110 V, 60 Hz ac supply. Determine the rms value of the current in the circuit.

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In question and what is the net power absorbed by each circuit over a complete cycle. Explain your answer.

. A inductor is connected to ac supply. Determine the rms value of the current in the circuit.

. A capacitor is connected to a ac supply. Determine the rms value of the current in the circuit.

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Obtain the resonant frequency  of a series LCR circuit with L = 2.0 H, C = 32 F and R = 10 . What is the Q-value of this circuit?

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A charged 30 F capacitor is connected to a 27 mH inductor. What is the angular frequency of free oscillations of the circuit?

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Do you agree that it is difficult not to go along with someone who is very strong and powerful? Express your views frankly and clearly

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A series LCR circuit with R = 20  , L = 1.5 H and C = 35 F is connected to a variable-frequency 200 V ac supply. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one complete cycle?

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A radio can tune over the frequency range of a portion of MW broadcast band: (800 kHz to 1200 kHz). If its LC circuit has an effective inductance of 200 H, what must be the range of its variable capacitor?
[Hint: For tuning, the natural frequency i.e., the frequency of free oscillations of the LC circuit should be equal to the frequency of the radiowave.

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Figure shows a series LCR circuit connected to a variable frequency 230 V source. L = 5.0 H, C = 80 F, R = 40.
(a) Determine the source frequency which drives the circuit in resonance.

(b) Obtain the impedance of the circuit and the amplitude of current at the resonating frequency.

(c) Determine the rms potential drops across the three elements of the circuit. Show that the potential drop across the LC combination is zero at the resonating frequency.

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An LC circuit contains a 20 mH inductor and a 50 F capacitor with an initial charge of 10 mC. The resistance of the circuit is negligible. Let the instant the circuit is closed be t = 0.(a) What is the total energy stored initially? Is it conserved during LC oscillations?

(b) What is the natural frequency of the
circuit?

(c) At what time is  the energy stored 

     (i) completely electrical (i.e., stored in the capacitor)? 

     (ii) completely magnetic (i.e. stored in the inductor)?

(d) At what times is the total energy shared
equally between the inductor and the capacitor?

(e) If a resistor is inserted in the circuit,

how much energy is eventually dissipated as heat?

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A coil of inductance 0.50 H and resistance is connected to a 240 V, 50 Hz ac supply.
(a) What is the maximum current in the coil?

(b) What is the time lag between the voltage maximum and the current maximum?

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A 100 F capacitor in series with a 40 resistance is connected to a 110 V, 60 Hz supply.
(a) What is the maximum current in the circuit?

(b) What is the time lag between the current maximum and the voltage maximum?

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A series LCR circuit with L = 0.12 H. C = 480 nF, R = 23 is connected to a 230 V variable frequency supply.
(a) What is the source frequency for which current amplitude is maximum. Obtain this maximum value.

(b) What is the source frequency for which average power absorbed by the circuit is maximum. Obtain the value of this maximum power.

(c) For which frequencies of the source is the power transferred to the circuit half the power at resonant frequency? What is the current amplitude at these frequencies?

(d) What is the Q-factor of the given circuit?

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A coil of inductance 0.50 H and resistance is connected to a 240 V, 50 Hz ac supply.
(a) What is the maximum current in the coil?

(b) What is the time lag between the voltage maximum and the current maximum?

Hence, explain the statement that at very high frequency, an inductor in a circuit nearly amounts to an open circuit. How does an inductor behave in a dc circuit after the steady state?


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Obtain the answers to (a) and (b) in given question, if the circuit is connected to a supply? Hence, explain the statement that a capacitor is a conductor at very high frequencies. Compare this behavior with that of a capacitor in a dc circuit after the steady-state.

 capacitor in series with a resistance is connected to a supply. What is the maximum current in the circuit?

What is the time lag between the current maximum and the voltage maximum?

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Keeping the source frequency equal to the resonating frequency of the series LCR circuit, if the three elements, L, C, and R are arranged in parallel, show that the total current in the parallel LCR circuit is minimum at this frequency. Obtain the current RMS value in each branch of the circuit for the elements and source specified as below for this frequency.

The figure shows a series LCR circuit connected to a variable frequency source. , , .

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A circuit containing a 80 mH inductor and a capacitor in series is connected to a 230 V, 50 Hz supply. The resistance of the circuit is negligible.(a) Obtain the current amplitude and rms values.

(b) Obtain the rms values of potential drops across each element.

(c) What is the average power transferred to

(d) What is the average power transferred to
the capacitor?

(e) What is the total average power absorbed by the circuit? [Average implies average value over one cycle.]

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A circuit containing an 80 mH inductor and a 60 F capacitor in series connected to a 230 V, 50 Hz supply. The resistance of the circuit is negligible.
what is the average power consumed by inductor ,capacitor and the total power absorbed by the circuit?

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Obtain the resonant frequency and Q-factor of a series LCR circuit with L = 3.0 H, , and . It is desired to improve the sharpness of the resonance of the circuit by reducing its 'full width at half maximum' by a factor of 2. Suggest a suitable way.

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Answer the following questions::
(a) In any ac circuit, is the applied instantaneous voltage equal to the algebraic sum of the instantaneous voltages across the series elements of the circuit? Is the same true for rms voltage?

(b) A capacitor is used in the primary circuit of an induction coil.

(c) An applied voltage signal consists of a superposition of a dc voltage and an ac voltage of high frequency. The circuit consists of an inductor and a capacitor in series. Show that the dc signal will appear across C and the ac signal across L.

(d) A choke coil in series with a lamp is connected to a dc line. The lamp is seen to shine brightly. Insertion of an iron core in the choke causes no change in the lamps brightness. Predict the corresponding observations if the connection is to an ac line.

(e) Why is choke coil needed in the use of fluorescent tubes with ac mains? Why can we not use an ordinary resistor instead of the choke coil?

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A power transmission line feeds input power at 2300 V to a step down transformer with its primary windings having 4000 turns. What should be the number of turns in the secondary in order to get output power at 230 V?

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At a hydroelectric power plant, the water pressure head is at a height of 300 m and the water flow available is 100 . If the turbine generator efficiency is 60%, estimate the electric power available from the plant (g = 9.8 ).

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A small town with a demand of 800 kW of electric power at 220 V is situated 15 km away from an electric plant generating power at 440 V.The resistance of the two wire line carrying power is 0.5 per km.The town gets power from the line through a 4000-220 V step-down transformer at a sub-station in the town.

(a) Estimate the line power loss in the form of heat.

(b) How much power must the plant supply, assuming there is negligible power loss due to leakage?

(c) Characterise the step up transformer at the plant.

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Do the same exercise as above with the replacement of the earlier transformer by a 40,000-220 V step-down transformer (Neglect, as before, leakage losses though this may not be a good assumption any longer because of the very high voltage transmission involved).Hence, explain why high voltage transmission is preferred?

Exercise:
[
A small town with a demand of 800 kW of electric power at 220 V is situated 15 km away from an electric plant generating power at 440 V.The resistance of the two wire line carrying power is 0.5 per km.The town gets power from the line through a 4000-220 V step-down transformer at a sub-station in the town.
]

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Exercise

17 Qs

Related questions

Predict the direction of induced current in the situations described by the following Figs. (a) to (f ).

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Use Lenz's law to determine the direction of induced current in the situations described by Fig.(a) A wire of irregular shape turning into a circular shape;(b) A circular loop being deformed into a narrow straight wire.

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A long solenoid with turns per has a small loop of area placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from to in , calculate the induced in the loop while the current is changing.

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A rectangular wire loop of sides 8 cm and 2 cm with a small cut is moving out of a region of uniform magnetic field of magnitude 0.3 T directed normal to the loop. What is the emf developed across the cut if the velocity of the loop is 1 cm in a direction normal to the (a) longer side, (b) shorter side of the loop? For how long does the induced voltage last in each case?

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A 1.0 m long metallic rod is rotated with an angular frequency of 400 rad about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field of 0.5 T parallel to the axis exists everywhere. Calculate the emf developed between the centre and the ring.

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A circular coil of radius and turns is rotated about its vertical diameter with an angular speed of in a uniform horizontal magnetic field of magnitude . Obtain the maximum and average emf induced in the coil. If the coil forms a closed loop of resistance   , calculate the maximum value of current in the coil. Calculate the average power loss due to Joule heating. Where does this power come from?

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A horizontal straight wire 10 m long extending from east to west is falling with a speed of , at right angles to the horizontal component of the earth's magnetic field 0.30.(a) What is the instantaneous value of the emf induced in the wire?(b) What is the direction of the emf?(c) Which end of the wire is at the higher electrical potential?

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Current in a circuit falls from to  in . If an average emf of  induced, find an estimate of the self-inductance of the circuit.

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A pair of adjacent coil has a mutual inductance of . If the current in one coil changes from to   in sec, what is the change of flux linkage with the other coil?

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A jet plane is travelling towards west at a speed of 1600 km/h. What is the voltage difference developed between the ends of the wing having a span of 25 m, if the Earths magnetic field at the location has a magnitude of 5 T and the dip angle is .

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Suppose the loop in Exercise is stationary but the current feeding the electromagnet that produces the magnetic field is gradually reduced so that the field decreases from its initial value of 0.3 T at the rate of 0.02 T . If the cut is joined and the loop has a resistance of 1.6 ohm , how much power is dissipated by the loop as heat? What is the source of this power?

Exercise :
A rectangular wire loop of sides 8 cm and 2 cm with a small cut is moving out of a region of uniform magnetic field of magnitude 0.3 T directed normal to the loop. What is the emf developed across the cut if the velocity of the loop is 1 cm in a direction normal to the (a) longer side, (b) shorter side of the loop? For how long does the induced voltage last in each case? ]

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A square loop of side 12 cm with its sides parallel to X and Y axes is moved with a velocity of in the positive x-direction in an environment containing a magnetic field in the positive z-direction. The field is neither uniform in space nor constant in time. It has a gradient of  along the negative x-direction (that is it increases by  as one moves in the negative x-direction), and it is decreasing in time at the rate of . Determine the direction and magnitude of the induced current in the loop if its resistance is 4.50 m.

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It is desired to measure the magnitude of field between the poles of a powerful loud speaker magnet. A small flat search coil of area  with 25 closely wound turns, is positioned normal to the field direction, and then quickly snatched out of the field region. Equivalently, one can give it a quick turn to bring its plane parallel to the field direction). The total charge flown in the coil (measured by a ballistic galvanometer connected to coil) is 7.5 mC. The combined resistance of the coil and the galvanometer is 0.50 . Estimate the field strength of magnet.

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Figure shows a metal rod PQ resting on the smooth rails AB and positioned between the poles of a permanent magnet. The rails,the rod, and the magnetic field are in three mutual perpendicular directions. A galvanometer G connects the rails through a switch K. Length of the rod = 15 cm, B = 0.50 T, resistance of the closed loop containing the rod = 9.0 m. Assume the field to be uniform.

(a) Suppose K is open and the rod is moved with a speed of in the direction shown. Give the polarity and magnitude of the induced emf.

(b) Is there an excess charge built up at the ends of the rods when K is open? What if K is closed?

(c) With K open and the rod moving uniformly, there is no net force on the electrons in the rod PQ even though they do experience magnetic force due to the motion of the rod. Explain.

(d) What is the retarding force on the rod when K is closed?

(e) How much power is required (by an external agent) to keep the rod moving at the same speed when K is closed? How much power is required when K is open?

(f) How much power is dissipated as heat in the closed circuit? What is the source of this power?

(g) What is the induced emf in the moving rod if the magnetic field is parallel to the rails instead of being perpendicular?

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An air-cored solenoid with length 30 cm, area of cross-section  and number of turns 500, carries a current of 2.5 A. The current is suddenly switched off in a brief time of . How much is the average back emf induced across the ends of the open switch in the circuit? Ignore the variation in magnetic field near the ends of the solenoid.

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(a) Obtain an expression for the mutual inductance between a long straight wire and a square loop of side a as shown in Fig.
(b) Now assume that the straight wire carries a current of 50 A and the loop is moved to the right with a constant velocity, v = 10 m/s. Calculate the induced emf in the loop at the instant when x = 0.2 m. Take a = 0.1 m and assume that the loop has a large resistance.

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A line charge per unit length is lodged uniformly onto the rim of a wheel of mass and radius . The wheel has light non-conducting spokes and is free to rotate without friction about its axis as shown in above figure. A uniform magnetic field extends over a circular region within the rim. It is given by,
, or (otherwise).
What is the angular velocity of the wheel after the field is suddenly switched off?

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Exercise

17 Qs

Related questions

Figure shows a capacitor made of two circular plates each of radius 12 cm, and separated by 5.0 cm. The capacitor is being charged by an external source (not shown in the figure). The charging current is constant and equal to 0.15A.
(a) Calculate the capacitance and the rate of change of potential difference between the plates.
(b)
Obtain the displacement current across the plates.
(c)
Is
Kirchhoffs first rule (junction rule) valid at each plate of
the capacitor Explain.

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A parallel plate capacitor (Fig.) made of circular plates each of radius R = 6.0 cm has a capacitance C = 100 pF. The capacitor is connected to a 230 V ac supply with a (angular) frequency of 300 rad .
(a) What is the rms value of the conduction current?

(b) Is the conduction current equal to the displacement current?

(c) Determine the amplitude of B at a point 3.0 cm from the axis between the plates.

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What physical quantity is the same for X-rays of wavelength , red light of wavelength 6800 and radiowaves of wavelength 500m?

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A plane electromagnetic wave travels in vacuum along z-direction. What can you say about the directions of its electric and magnetic field vectors? If the frequency of the wave is 30 MHz, what is its wavelength?

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A radio can tune in to any station in the 7.5 MHz to 12 MHz band. What is the corresponding wavelength band?

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A charged particle oscillates about its mean (equilibrium) position with a frequency of . What is the frequency of the electromagnetic waves produced by the oscillator?

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The amplitude of the magnetic field part of a harmonic electromagnetic wave in vacuum is . What is the amplitude of the electric field part of the wave?

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Suppose that the electric field amplitude of an electromagnetic wave is and that its frequency is .
(a) Determine,  
(b) Find the expression for E and B.

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The terminology of different parts of the electromagnetic spectrum is given in the text. Use the formula (for energy of a quantum of radiation: photon) and obtain the photon energy in units of eV for different parts of the electromagnetic spectrum. In what way are the different scales of photon energies that you obtain related to the sources of electromagnetic radiation?

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In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of and amplitude .
(a) What is the wavelength of the wave?
(b) What is the amplitude of the oscillating magnetic field?
(c) Show that the average energy density of the E field equals the average energy density of the B field. [c = 3 ]

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Suppose that the electric field part of an electromagnetic wave in vacuum is (a) What is the direction of propagation?
(b) What is the wavelength ?
(c) What is the frequency v?
(d) What is the amplitude of the magnetic field part of the wave?
(e) Write an expression for the magnetic field part of the wave.

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About 5% of the power of a 100 W light bulb is converted to visible radiation. What is the average intensity of visible radiation
(a) at a distance of 1m from the bulb?
(b) at a distance of 10 m?

Assume that the radiation is emitted isotropically and neglect reflection.

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Use the formula T = 0.29 cm K to obtain the characteristic temperature ranges for different parts of the electromagnetic spectrum. What do the numbers that you obtain tell you?

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Given below are some famous numbers associated with electromagnetic radiations in different contexts in physics. State the part of the electromagnetic spectrum to which each belongs.
(a) 21 cm (wavelength emitted by atomic hydrogen in interstellar space).

(b) 1057 MHz (frequency of radiation arising from two close energy levels in hydrogen; known as Lamb shift).

(c) 2.7 K [temperature associated with the isotropic radiation filling all space thought to be a relic of the big-bang origin of the universe].

(d) [double lines of sodium]

(e) 14.4 ke V [energy of a particular transition in Fe nucleus associated with a famous high resolution spectroscopic method ()].

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Answer the following questions:
(a) Long distance radio broadcasts use short-wave bands. Why?
(b) It is necessary to use satellites for long distance TV transmission.Why?

(c) Optical and radiotelescopes are built on the ground but X-ray astronomy is possible only from satellites orbiting the earth.Why?

(d) The small ozone layer on top of the stratosphere is crucial for human survival. Why?

(e) If the earth did not have an atmosphere, would its average surface temperature be higher or lower than what it is now?

(f) Some scientists have predicted that a global nuclear war on the earth would be followed by a severe nuclear winter with a devastating effect on life on earth. What might be the basis of this prediction?

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Exercise

25 Qs

Related questions

The storage battery of a car has an emf of 12 V. If the internal resistance of the battery is 0.4 , what is the maximum current that can be drawn from the battery?

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A battery of emf 10 V and internal resistance 3 W is connected to a resistor. If the current in the circuit is 0.5 A, what is the resistance of the resistor? What is the terminal voltage of the battery when the circuit is closed?

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(a) Three resistors  and are combined in series. What is the total resistance of the combination?
(b) If the combination is connected to a battery of emf 12 V and negligible internal resistance, obtain the potential drop across each resistor.

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(a) Three resistors and are combined in parallel. What is the total resistance of the combination?
(b) If the combination is connected to a battery of emf 20 V and negligible internal resistance, determine the current through each resistor, and the total current drawn from the battery.

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At room temperature the resistance of a heating element is . What is the temperature of the element if the resistance is found to be , given that the temperature coefficient of the material of the resistor is .

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A negligibly small current is passed through a wire of length 15 m and uniform cross-section , and  its  resistance is  measured  to  be  .  What is the resistivity of the material at the temperature of the experiment?

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A silver wire has a resistance of  at , and a resistance of   at . Determine the temperature coefficient of resistivity of silver.

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A heating element using nichrome connected to a 230 V supply draws an initial current of 3.2 A which settles after a few seconds to a steady value of 2.8 A. What is the steady temperature of the heating element if the room temperature is ? Temperature coefficient of resistance of nichrome averaged over the temperature range involved is .

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Determine the current in each branch of the network shown in Fig.

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(a) In a metre bridge [Fig.], the balance point is found to be at 39.5 cm from the end A, when the resistor Y is of 12.5 . Determine the resistance of X. Why are the connections between resistors in a Wheat stone or meter bridge made of thick copper strips?(b) Determine the balance point of the bridge above if X and Y are interchanged.(c) What happens if the galvanometer and cell are interchanged at the balance point of the bridge? Would the galvanometer show any current?

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A storage battery of emf 8.0 V and internal resistance is being charged by a 120 V dc supply using a series resistor of . What is the terminal voltage of the battery during charging? What is the purpose of having a series resistor in the charging circuit?

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In a potentiometer arrangement, a cell of emf 1.25 V gives a balance point at 35.0 cm length of the wire. If the cell is replaced by another cell and the balance point shifts to 63.0 cm, what is the emf of the second cell?

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The earths surface has a negative surface charge density of . The potential difference of 400 kV between the top of the atmosphere and the surface results (due to the low conductivity of the lower atmosphere) in a current of only 1800 A over the entire globe. If there were no mechanism of sustaining atmospheric electric field, how much time (roughly) would be required to neutralise the earths surface? (This never happens in practice because there is a mechanism to replenish electric charges, namely the continual thunderstorms and lightning in different parts of the globe). (Radius of earth = m.)

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(a) Six lead-acid type of secondary cells each of emf 2.0 V and internal resistance  are joined in series to provide a supply to a resistance of  . What are the current drawn from the supply and its terminal voltage?
(b) A secondary cell after long use has an emf of 1.9 V and a large internal resistance of  . What maximum current can be drawn from the cell? Could the cell drive the starting motor of a car?

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Two wires of equal length, one of aluminium and the other of copper have the same resistance. Which of the two wires is lighter? Hence explain why aluminium wires are preferred for overhead power cables. , Relative density of Al = 2.7, of Cu = 8.9.)

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What conclusion can you draw from the following observations on a resistor made of alloy manganin? 
 Current  A Voltage VCurrent A Voltage V 
 0.2 3.94 3.0 59.2
 0.4
 7.87 4.078.8
  0.6 11.8 5.0  98.6
  0.8 15.7 6.0  118.5
  1.0 19.7 7.0  138.2
  2.0 39.4 8.0 158.0

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Answer the following question:
(a) A steady current flows in a metallic conductor of non-uniform cross-section. Which of these quantities is constant along the conductor: current, current density, electric field, drift speed?
(b) Is Ohms law universally applicable for all conducting elements?If not, give examples of elements which do not obey Ohms law.
(c) A low voltage supply from which one needs high currents must have very low internal resistance. Why?
(d) A high tension (HT) supply of, say, 6 kV must have a very large internal resistance. Why?

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Choose the correct alternative:
(a) Alloys of metals usually have (greater/less) resistivity than that of their constituent metals.
(b) Alloys usually have much (lower/higher) temperature coefficients of resistance than pure metals.
(c) The resistivity of the alloy manganin is nearly independent of / increases rapidly with increase of temperature.
(d) The resistivity of a typical insulator (e.g., amber) is greater than that of a metal by a factor of the order of ().

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(a) Given n resistors each of resistance R, how will you combine them to get the (i) maximum (ii) minimum effective resistance?What is the ratio of the maximum to minimum resistance?
(b) Given the resistances of 1 how  will be  combine  them  to  get  an  equivalent  resistance  of  (i) (11/3)   (ii) (11/5),   (iii) 6,   (iv) (6/11) ?
(c) Determine the equivalent resistance of networks shown in Fig. (a) and (b)

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Determine the current drawn from a 12V supply with internal resistance by the infinite network shown  in Fig. Each resistor has resistance.

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Figure shows a potentiometer with a cell of 2.0 V and internal resistance maintaining  a  potential  drop  across  the  resistor  wire AB. A  standard  cell  which  maintains  a constant  emf  of  1.02  V (for  very moderate  currents  up to a  few mA) gives  a balance  point  at 67.3 cm length of the wire. To ensure very low currents drawn from the standard cell, a very high resistance of 600 k is put in series with it, which is shorted close to the balance point. The standard cell is then replaced by a cell of unknown emf and the balance point found similarly, turns out to be at 82.3 cm length of the wire.(a) What is the value ?(b) What purpose does the high resistance of 600 k  have?(c) Is the balance point affected by this high resistance? (d) Is the balance point affected by the internal resistance of the driver cell?(e) Would the method work in the above situation if the driver cell of the potentiometer had an emf of 1.0 V instead of 2.0 V?(f) Would the circuit work well for determining an extremely small emf, say of the order of a few mV (such as the typical emf of a thermo-couple)? If not, how will you modify the circuit?

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Figure shows a potentiometer circuit for comparison of two resistances. The balance point with a standard resistor is found to be 58.3 cm, while that with the unknown resistance X is 68.5 cm. Determine the value of X. What might you do if you failed to find a balance point with the given cell of emf ?

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Figure shows a 2.0 V potentiometer used for the determination of internal resistance of a 1.5 V cell. The balance point of the cell in open circuit is 76.3 cm. When a resistor of 9.5 is used in the external circuit of the cell, the balance point shifts to 64.8 cm of the potentiometer wire. Determine the internal resistance of the cell.

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Exercise

34 Qs

Related questions

What is the force between two small charged spheres having charges of C and C placed 30 cm apart in air?

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The electrostatic force on a small sphere of charge due to another small sphere of charge in air is 0.2 N.
(a) What is the distance between the two spheres? 
(b) What is the force on the second sphere due to the first? 

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Check that the ratio  /G is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?

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(a) Explain the meaning of the statement 'electric charge of a body is quantised'.
(b) Why can one ignore quantisation of electric charge when dealing with macroscopic i.e., large scale charges?

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When a glass rod is rubbed with a silk cloth, charges appear on both. A similar phenomenon is observed with many other pairs of bodies. Explain how this observation is consistent with the law of conservation of charge.

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Four point charges , and are located at the corners of a square of side . What is the force on a charge of placed at the centre of the square?

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Answer the following questions.
(i) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why is it so?
(ii) Explain why two field lines never cross each other at any point.

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Two point charges and are located apart in vacuum
(a) What is the electric field at the midpoint O of the line joining the two charges?
(b) If a negative test charge of magnitude is placed at this point, what is the force experienced by the test charge?

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A system has two charges and located at points and , respectively. What are the total charge and electric dipole moment of the system?

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An electric dipole with dipole moment C m is aligned at with the direction of a uniform electric field of magnitude . Calculate the magnitude of the torque acting on the dipole.

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A polythene piece rubbed with wool is found to have a negative charge of C.
(a) Estimate the number of electrons transferred (from which to which?)
(b) Is there a transfer of mass from wool to polythene?

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(a) Two insulated charged copper spheres A and B have their centres separated by a distance of 50 cm. What is the mutual force of electrostatic repulsion if the charge on each is C? The radii of A and B are negligible compared to the distance of separation.
(b) What is the force of repulsion if each sphere is charged double the above amount, and the distance between them is halved?

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Exercise:
[
Two insulated charged copper spheres A and B have their centres separated by a distance of 50 cm. The charge on each is C? The radii of A and B are negligible compared to the distance of separation.
]
Suppose the spheres A and B in Exercise have identical sizes. A third sphere of the same size but uncharged is brought in contact with the first, then brought in contact with the second, and finally removed from both. What is the new force of repulsion between A and B?

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Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

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Consider a uniform electric field . (a) What is the flux of this field through a square of 10 cm on a side whose plane is parallel to the yz plane? (b) What is the flux through the same square if the normal to its plane makes a angle with the x-axis? 

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Consider a uniform electric field What is the net flux of the uniform electric field through a cube of side 20 cm oriented so that its faces are parallel to the coordinate planes?

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Careful measurement of the electric field at the surface of a black box indicates that the net outward flux through the surface of the box is
(a) What is the net charge inside the box?(b) If the net outward flux through the surface of the box were zero, could you conclude that there were no charges inside the box? Why or Why not?

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A point charge is a distance directly above the center of a square of side as shown in fig. What is the magnitude of the electric flux through the square? (Hint: Think of the square as one face of a cube with edge )

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A point charge of is at the centre of a cubic Gaussian surface on edge. What is the net electric flux through the surface?

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A point charge causes an electric flux of N/C to pass through a spherical Gaussian surface of 10.0 cm radius centred on the charge. (a) If the radius of the Gaussian surface were doubled,how much flux would pass through the surface? (b) What is the value of the point charge?

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A conducting sphere of radius  has an unknown charge. If the electric field  from the centre of the sphere is   and points radially inward, what is the net charge on the sphere?

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A uniformly charged conducting sphere of 2.4 m diameter has a surface charge density of .
(a) Find the charge on the sphere.
(b) What is the total electric flux leaving the surface of the sphere?

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An infinite line charge produces a field of N/C at a distance of 2 cm. Calculate the linear charge density.

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Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude  . What is E: (a) in the outer region of the first plate. (b) in the outer region of the second plate, and (c) between the plates?

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An oil drop of 12 excess electrons is held stationary under a constant electric field of in Millikans oil drop experiment. The density of the oil is . Estimate the radius of the drop. [g = 1.60 C].

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Which among the curves shown cannot possibly represent electrostatic field lines?

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In a certain region of space, electric field is along the z-direction throughout. The magnitude of electric field is, however, not constant but increases uniformly along the positive z-direction, at the rate of  per metre. What are the force and torque experienced by a system having a total dipole moment equal to  Cm in the negative z-direction ?

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(a) A conductor with a cavity as shown in Fig. (a) is given a charge . Show that the entire charge must appear on the outer surface of the conductor. 
(b) Another conductor with charge is inserted into the cavity keeping insulated from . Show that the total charge on the outside surface of is
(c) A sensitive instrument is to be shielded from the strong electrostatic fields in its environment. Suggest a possible way.

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A hollow charged conductor has a tiny hole cut into its surface. Show that the electric field in the hole is where is the unit vector in the outward normal direction, and is the surface charge density near the hole.

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Obtain the formula for the electric field due to a long thin wire of uniform linear charge density without using Gauss's law.
 [Hint: Use Coulombs law directly and evaluate the necessary integral.]

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It is now believed that protons and neutrons (which constitute nuclei of ordinary matter) are themselves built out of more elementary units called quarks. A proton and a neutron consist of three quarks each. Two types of quarks, the so-called 'up' quark (denoted by u) of charge + (2/3) e, and the 'down' quark (denoted by d) of charge (-1/3) e, together with electrons build up ordinary matter. (Quarks of other types have also been found which give rise to different unusual varieties of matter.) Suggest a possible quark composition of a proton and neutron.

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(a) Consider an arbitrary electrostatic field configuration. A small test charge is placed at a null point (i.e., where E = 0) of the configuration. Show that the equilibrium of the test charge is necessarily unstable.
(b) Verify this result for the simple configuration of two charges of the same magnitude and sign placed a certain distance apart.

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A particle of mass m and charge (-q) enters the region between the two charged plates initially moving along x-axis with speed (like particle 1 in Fig.). The length of plate is L and an uniform electric field E is maintained between the plates. Show that the vertical deflection of the particle at the far edge of the plate is  ).
Compare this motion with motion of a projectile in gravitational field.

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A particle of mass m and charge (-q) enters the region between the two charged plates initially moving along x-axis with speed (like particle 1 in Fig.). The length of plate is L and an uniform electric field E is maintained between the plates.
Suppose that the particle in Exercise is an electron projected with velocity . If E between the plates separated  by 0.5 cm is N/C, where will the electron strike the upper plate?

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Exercise

38 Qs

Related questions

Two charges and are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.

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A regular hexagon of side 10 cm has a charge at each of its vertices. Calculate the potential at the centre of the hexagon.

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Two charges and are placed at points A and B 6 cm apart.
(a) Identify an equipotential surface of the system.
(b) What is the direction of the electric field at every point on this surface?

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A spherical conductor of radius 12 cm has a charge of C distributed uniformly on its surface. What is the electric field
(a) inside the sphere
(b) just outside the sphere
(c) at a point 18 cm from the centre of the sphere?

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A parallel plate capacitor with air between the plates has a capacitance of 8 pF (1pF = F). What will be the capacitance if the distance between the plates is reduced by half, and the space between them is filled with a substance of dielectric constant 6?

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Three capacitors each of capacitance are connected in series.
(a) What is the total capacitance of the combination?
(b) What is the potential difference across each capacitor if the combination is connected to a supply?

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Three capacitors of capacitances 2 pF, 3 pF and 4 pF are connected in parallel.
(a) What is the total capacitance of the combination?
(b) Determine the charge on each capacitor if the combination is connected to a 100 V supply.

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Was the old woman’s gift to Vijay Singh eccentric? Why?

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Exercise: 
In a parallel plate capacitor with air between the plates, each plate has an area of and the distance between the plates is 3 mm. Calculate the capacitance of the capacitor. If this capacitor is connected to a 100 V supply, what is the charge on each plate of the capacitor?

Explain what would happen if in the capacitor given in Exercise a  thick mica sheet (of dielectric constant = 6) were inserted between the plates,
(a) While the voltage supply remained connected.
(b) After the supply was disconnected.

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A 12pF capacitor is connected to a 50V battery. How much electrostatic energy is stored in the capacitor?

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A 600 pF capacitor is charged by a 200V supply. It is then disconnected from the supply and is connected to another uncharged 600 pF capacitor. How much electrostatic energy is lost in the process?

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A cube of side b has a charge q at each of its vertices. Determine the potential and electric field due to this charge array at the centre of the cube.

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Two tiny spheres carrying charges and are located 30 cm apart. Find the potential and electric field:
(a) at the mid-point of the line joining the two charges, and
(b) at a point 10 cm from this midpoint in a plane normal to the line and passing through the mid-point.

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A spherical conducting shell of inner radius and outer radius  has a charge Q.
(a) A charge q is placed at the centre of the shell. What is the surface charge density on the inner and outer surfaces of the shell?
(b) Is the electric field inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape? Explain.

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(a) Show that the normal component of electrostatic field has a discontinuity from one side of a charged surface to another given by 
$$(E_2\,-\, E_1)\, \dot\, \hat{n}\,\displaystyle \frac{\sigma }{\varepsilon _0}$$
where  is a unit vector normal to the surface at a point and is the surface charge density at that point. (The direction of  is from side 1 to side 2.) Hence show that just outside a conductor, the electric field is
(b) Show that the tangential component of electrostatic field is continuous from one side of a charged surface to another.  [Hint: For (a), use Gauss's law. For, (b) use the fact that work done by electrostatic field on a closed loop is zero.]

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A long charged cylinder of linear charged density   is surrounded by a hollow co-axial conducting cylinder. What is the electric field in the space between the two cylinders?

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In a hydrogen atom, the electron and proton are bound at a distance of about :

(a) Estimate the potential energy of the system in eV, taking the zero of the potential energy at infinite separation of the electron from the proton.

(b) What is the minimum work required to free the electron, given that its kinetic energy in the orbit is half the magnitude of potential energy obtained in (a)?

(c) What are the answers to (a) and (b) above if the zero of potential energy is taken at separation?

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If one of the two electrons of a molecule is removed, we get a hydrogen molecular ion . In the ground state of an , the two protons are separated by roughly , and the electron is roughly from each proton. Determine the potential energy of the system. Specify your choice of the zero of potential energy.

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Two charged conducting spheres of radii a and b are connected to each other by a wire. What is the ratio of electric fields at the surfaces of the two spheres? Use the result obtained to explain why charge density on the sharp and pointed ends of a conductor is higher than on its flatter portions.

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Two charges -q and +q are located at points (0, 0, -a) and (0, 0, a), respectively. 
(a) What is the electrostatic potential at the points (0, 0, z) and (x, y, 0) ?
(b) Obtain the dependence of potential on the distance r of a point from the origin when r/a >> 1
(c) How much work is done in moving a small test charge from the point (5,0,0) to (-7,0,0) along the x-axis? Does the answer change if the path of the test charge between the same points is not along the x-axis?

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Figure shows a charge array known as an electric quadrupole. For a point on the axis of the quadrupole, obtain the dependence of potential on r for r/a >> 1, and contrast your results with that due to an electric dipole, and an electric monopole (i.e., a single charge).

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An electrical technician requires a capacitance of in a circuit across a potential difference of 1 kV. A large number of capacitors are available to him each of which can withstand a potential difference of not more than 400 V. Suggest a possible arrangement that requires the minimum number of capacitors.

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What is the area of the plates of a 2 F parallel plate capacitor, given that the separation between the plates is 0.5 cm? [You will realise from your answer why ordinary capacitors are in the range of F or less. However, electrolytic capacitors do have a much larger capacitance (0.1 F) because of very minute separation between the conductors.]

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Obtain the equivalent capacitance of the network shown in the figure. For a 300 V supply, determine the charge and voltage across each capacitor.

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The plates of a parallel plate capacitor have an area of  each and are separated by 2.5 mm. The capacitor is charged by connecting it to a 400 V supply.
(a) How much electrostatic energy is stored by the capacitor?
(b) View this energy as stored in the electrostatic field between the plates, and obtain the energy per unit volume u. Hence arrive at a relation between u and the magnitude of electric field E between the plates.

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A capacitor is charged by a 200 V supply. It is then disconnected from the supply, and is connected to another uncharged capacitor. How much electrostatic energy of the first capacitor is lost in the form of heat and electromagnetic radiation?

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Show that the force on each plate of a parallel plate capacitor has a magnitude equal to QE, where Q is the charge on the capacitor, and E is the magnitude of electric field between the plates. Explain the origin of the factor .

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A spherical capacitor consists of two concentric spherical conductors, held in position by suitable insulating supports (Fig.). Show that the capacitance of a spherical capacitor is given by 

where and are the radii of outer and inner spheres, respectively.

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A spherical capacitor has an inner sphere of radius 12 cm and an outer sphere of radius 13 cm. The outer sphere is earthed and the inner sphere is given a charge of . The space between the concentric spheres is filled with a liquid of dielectric constant 32.
(a) Determine the capacitance of the capacitor.
(b) What is the potential of the inner sphere?
(c) Compare the capacitance of this capacitor with that of an isolated sphere of radius 12 cm. Explain why the latter is much smaller.

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Answer carefully:

(a) Two large conducting spheres carrying charges and are brought close to each other. Is the magnitude of electrostatic force between them exactly given by , where is the distance between their centres?

(b) If Coulomb's law involved 1/ dependence (instead of 1/),would Gauss' law be still true ?

(c) A small test charge is released at rest at a point in an electrostatic field configuration. Will it travel along the field line passing through that point?

(d) What is the work done by the field of a nucleus in a complete circular orbit of the electron? What if the orbit is elliptical?

(e) We know that electric field is discontinuous across the surface of a charged conductor. Is electric potential also discontinuous there?

(f) What meaning would you give to the capacitance of a single conductor?

(g) Guess a possible reason why water has a much greater dielectric constant (= 80) than say, mica (= 6).

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A cylindrical capacitor has two co-axial cylinders of length 15 cm and radii 1.5 cm and 1.4 cm. The outer cylinder is earthed and the inner cylinder is given a charge of . Determine the capacitance of the system and the potential of the inner cylinder. Neglect end effects (i.e., bending of field lines at the ends).

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A parallel plate capacitor is to be designed with a voltage rating  1 kV, using a material of dielectric constant 3 and dielectric strength about . (Dielectric strength is the maximum electric field a material can tolerate without breakdown, i.e., without starting to conduct electricity through partial ionisation.) For safety, we should like the field never to exceed, say 10% of the dielectric strength.What minimum area of the plates is required to have a capacitance of 50 pF ?

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Describe schematically the equipotential surfaces corresponding to
(a) a constant electric field in the z-direction,
(b) a field that uniformly increases in magnitude but remains in a constant (say, z) direction,

(c) a single positive charge at the origin, and

(d) a uniform grid consisting of long equally spaced parallel charged wires in a plane.

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If you were a baby crocodile, would you tell Makara that he was wrong? What would you say to convince him?

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A small sphere of radius and charge is enclosed by a spherical shell of radius and charge . Show that if is positive, charge will necessarily flow from the sphere to the shell (when the two are connected by a wire) no matter what the charge on the shell is.

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Answer the following:
(a) The top of the atmosphere is at about 400 kV with respect to the surface of the earth, corresponding to an electric field that decreases with altitude. Near the surface of the earth, the field is about . Why then do we not get an electric shock as we step out of our house into the open? (Assume the house to be a steel cage so there is no field inside!)

(b) A man fixes outside his house one evening a two metre high insulating slab carrying on its top a large aluminium sheet of area . Will he get an electric shock if he touches the metal sheet next morning?

(c) The discharging current in the atmosphere due to the small conductivity of air is known to be 1800 A on an average over the globe. Why then does the atmosphere not discharge itself completely in due course and become electrically neutral? In other words, what keeps the atmosphere charged?

(d) What are the forms of energy into which the electrical energy of the atmosphere is dissipated during a lightning?
(Hint: The earth has an electric field of about 100 V at its surface in the downward direction, corresponding to a surface charge density = C. Due to the slight conductivity of the atmosphere up to about 50 km (beyond which it is good conductor), about + 1800 C is pumped every second into the earth as a whole. The earth, however, does not get discharged since thunderstorms and lightning occurring continually allover the globe pump an equal amount of negative charge on the earth.)

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