Electromagnetic Induction

Q: A spatially uniform magnetic field of 0.080 T is directed into the plane of the page and perpendicular to it, as shown in the accompanying figure. A wire loop in the plane of the page has constant area 0.010 m ^2 . The magnitude of the magnetic field decreases at a constant rate of 3.0\times 10^{-4} T/s. The magnitude and direction of the induced emf is:

\dfrac{dB}{dt}=-3\times 10^{-4}T/s e=-\dfrac{d\phi}{dt} e=-A\dfrac{d\phi}{do} =-0.010\times(-3\times 10^{-4}) =3\times 10^{-6}V As flux is decreasing in-ward the plane, \therefore Direction of induced emf will be clockwise

Q: A rectangular coil of n turns is perpendicular to a uniform magnetic field. If the field is reversed in a short time interval of t, then find the value of n given the charge flowing through the wire is independent of time.

Emf=\dfrac { 2nBA }{ t } i=\dfrac { Emf }{ R } =\dfrac { 2nBA }{ Rt } q=it=\dfrac { 2nBA }{ R } So,Charge is independent of time and hence , n= 0Where, n is number of turns in coil, B is magnetic field. A area of rectangular coil, R is resistance of coil and t is time

Q: A coil of 1200 turns and mean area of 500 cm^{2} is held perpendicular to a uniform magnetic field of induction 4 \times10^{-4} T. The resistance of the coil is 20 ohms. When the coil is rotated through 180^{0} in the magnetic field in 0.1 s, the average electric current (in mA) induced is :

Magnetic flux through the loop is given by \phi = nB.A Change in flux when it is rotated by 180^o is given by: \Delta \phi = nBA cos (\pi) -nBA cos(0)=-2nBA Emf=\dfrac { -\Delta \phi }{ dt } =\dfrac { 1200\times { 4\times 10 }^{ -4 }\times 2\times 500\times { 10 }^{ -4 } }{ 0.1 } =12\times { 4\times 10 }^{ -2 }V i=\dfrac { emf }{ R } =\dfrac { 12\times 4\times { 10 }^{ -2 } }{ 20 } =12\times 2\times { 10 }^{ -3 }A= 24mA

Q: A magnetic flux of 500\mu Wb passing through a 200 turns coil is reversed in 20\times 10^{-3} seconds. The average emf per unit area induced in the coil in V/m^2 is

Emf=N\dfrac { \triangle \phi }{ \triangle t } \displaystyle =\dfrac { 2 \times 500\times { 10 }^{ -6 }\times 200 }{ 20\times { 10 }^{ -3 } } =10V/m^2

Q: In a coil of area 10 cm^{2} and 10 turns with magnetic field directed perpendicular to the plane and is changing at the rate of 10^{4} gauss/ second. The resistance of the coil is 20 \Omega . The current in the coil will be

Induced current in the coil will be i=\dfrac { emf }{ R } =\dfrac { dB }{ dt } \times \dfrac { A\times n }{ R } =\dfrac { { 10 }^{ 4 } }{ 10^{ 4 } } \times \dfrac { 10\times 10 }{ 20 } = 5 A.

Q: The e.m.f. induced in a secondary coil is 20000 V when the current breaks in the primary coil. The mutual inductance is 5H and the current reaches to zero in 10^{-4} sec in the primary.The maximum current in the primary before it breaks is

\phi =mi emf=\dfrac { \triangle \phi }{ \triangle t } =M\dfrac { \triangle i }{ \triangle t } 20000=5\dfrac { \triangle i }{ { 10 }^{ -4 } } \triangle i=0.4A So, maximum current is 0.4A

Q: A solenoid (air core) ahs 400 turns, is 20 cm long and has a cross section of 4 cm^2 . Then the coefficient of self induction is approximately

n=400 turns, l=20 cm, A=4 cm^2 L=? L=\frac {1\cdot 25\times 10^{-6}Hm^{-1}\times 400\times 400\times 4\times 100}{100\times 100\times 20} =4\times 10^{-4}H

Q: In the circuit shown the capacitor and an ideal inductor do not have energy initially and key is switch on at t = 0 . Then which of the following options is/are true:

key : As we know that at t = 0 capacitor offers zero resistance and at t = infinity capacitors get fully charged and offers infinite resistance (in another term we assume break in circuit ).While inductor offers infinite resistance at t = 0 and zero resistance at t = infinite (in fully charged condition).So According to above concept we draw the circuit diagram at t = 0 and t = infinity as shown.so at t = 0Resistance of capacitor = 0, so potential difference = 0resistance of 10 \Omega is out of circuit because current choose to follow the path having less resistance and capacitor has zero resistance at t=0. So current will follow this path only.So according to image (i), at t = 0Total resistance of circuit (R) = 20 + 20 = 40 \Omega Total potential difference (V) = 20\ V Current I = \dfrac { V }{ R } ,Therefore I= \dfrac { 20 }{ 40 } = 0.5\ A At t = \infty Resistance due to inductor is zero so potential difference across inductor at t = \infty is zero.according to image (ii) solving circuit. Last two 10 \Omega and 20 \Omega resistances are in parallel, so its resultant resistance (R1) = \dfrac { 20\times 10 }{ 20+10 } = \dfrac { 20 }{ 3 } \Omega \quad First two resistances 10, 20 and resultant R1 are in series.So total resistance of circuit ( R_2 ) = 10+20 + \dfrac { 20 }{ 3 } =\dfrac { 110 }{ 3 } \Omega \quad Current at t = \infty , I = \dfrac { V }{ R2 } I = \dfrac { 20 }{ \dfrac { 110 }{ 3 } } \quad =\quad \dfrac { 6 }{ 11 }\ A. All options are true.

Q: A flat coil ABCD is freely suspended between the pole pieces of a U-shaped permanent magnet with the plane of coil parallel to the magnetic field. Name an instrument which makes use of the principle stated above.

The direct current (DC) motor is one of the first machines devised to converts electrical power into mechanical power. Permanent magnet (PM) direct current converts electrical energy into mechanical energy through the interaction of two magnetic fields. One field is produced by a permanent magnet assembly; the other field is produced by an electrical current flowing in the rectangular coil ABCD, through the brushes and split-ring commutators. These two fields result in a torque which tends to rotate the coil. As the coil turns, the current in the winding is commutated to produce a continuous torque output. Hence, the DC motor is a device which works on the above principle.

Solve Study Textbooks Guides

Use app

Hots Questions

7 min read

- Want to initiate thinking skills? Practice Higher Order Thinking Questions

This question explains how a current carrying conductor produces a magnetic field in its surrounding space.

An equilateral triangle of side a is formed from a piece of uniform resistance wire. The current enters in one corner and leaves out of the other as shown in Figure. What is the flux density of magnetic field at the centre O?

\frac{3 μ _{0} i}{4 π a}

\frac{μ _{o} i}{2 π a}

Zero

\frac{3 μ _{o} i}{2 π a}

View solution

Concept of electromagnetic induction is the basic principle of working of generators and motors. How emf is induced in the coil of generator or motor and how it produce the required torque to move the rotor. This question explain its working.

A spatially uniform magnetic field of

0.080

T

is directed into the plane of the page and perpendicular to it, as shown in the accompanying figure. A wire loop in the plane of the page has constant area

0.010

^{2}

. The magnitude of the magnetic field decreases at a constant rate of

3.0 \times 1 0^{- 4}

T/s. The magnitude and direction of the induced emf is:

3.0 \times 1 0^{- 6}

V clockwise

3.0 \times 1 0^{- 6}

V anticlockwise

2.4 \times 1 0^{- 5}

V anticlockwise

8.0 \times 1 0^{- 4}

V clockwise

View solution

A rectangular coil of

n

turns is perpendicular to a uniform magnetic field. If the field is reversed in a short time interval of t, then find the value of

n

given the charge flowing through the wire is independent of time.

- 1

zero

View solution

There are three ways to change the magnetic flux through a loop:
Change the magnetic field strength (increase, decrease) over the surface area.
Change the area of the loop (increase by expanding the loop, decrease by shrinking the loop).
Change the angle between the surface defined by the loop and the magnetic field vector. Remember that flux is the integral of the dot product between B and dA.
Solve problems where circuit is rotating in the plane of magnetic field.

A coil of 1200 turns and mean area of 500

c m^{2}

is held perpendicular to a uniform magnetic field of induction

4 \times 1 0^{- 4}

T. The resistance of the coil is 20 ohms. When the coil is rotated through

18 0^{0}

in the magnetic field in 0.1 s, the average electric current (in mA) induced is :

View solution

A magnetic flux of

500 μ W b

passing through a

200

turns coil is reversed in

20 \times 1 0^{- 3}

seconds. The average emf per unit area induced in the coil in

V / m^{2}

2.5

5.0

7.5

10.0

View solution

In a coil of area

10

c m^{2}

and

10

turns with magnetic field directed perpendicular to the plane and is changing at the rate of

1 0^{4}

gauss/ second. The resistance of the coil is

20

Ω

. The current in the coil will be

0.5 A

5 A

50 A

5 \times 1 0^{8} A

View solution

Self inductance is the characteristic of the coil itself. Mutual inductance is the characteristic of a pair of coils. The induced current opposes the decay of current in the coil when the main current in the coil decreases. Charging of capacitor and inductive circuit work on the principle.

The e.m.f. induced in a secondary coil is

20000 V

when the current breaks in the primary coil. The mutual inductance is

5 H

and the current reaches to zero in

1 0^{- 4}

sec in the primary.The maximum current in the primary before it breaks is

0.1 A

0.4 A

0.6 A

0.8 A

View solution

A solenoid (air core) ahs 400 turns, is 20 cm long and has a cross section of

4 c m^{2}

. Then the coefficient of self induction is approximately

4 \times 1 0^{- 5} H

4 \times 1 0^{1} H

4 \times 1 0^{- 4} H

4 H

View solution

Series having capacitor and an ideal inductor has applications in radio and communication engineering. They can be used to select a certain narrow range of frequencies from the total spectrum of ambient radio waves. It consists of an inductor (L), capacitor (C) and resistor (R) connected in series or parallel. Let's see a problem to understand how it works.

In the circuit shown the capacitor and an ideal inductor do not have energy initially and key is switch on at

t = 0

. Then which of the following options is/are true:

This question has multiple correct options

Potential difference across the capacitor at

t = 0

is zero

The current flowing through the battery at

t = 0

0.5 A

Potential difference across the inductor at

t = \infty

is zero

The current flowing through the battery at

t = \infty

\frac{6}{1 1}

View solution

DC motors are common in small household appliances such as vacuum cleaners, cordless power tools, and food mixers. We will see how it works.

A flat coil ABCD is freely suspended between the pole pieces of a U-shaped permanent magnet with the plane of coil parallel to the magnetic field. Name an instrument which makes use of the principle stated above.

a.c. motor

d.c. motor

m.c. motor

None of the above

View solution

AC generators power home electrical appliances and small motors such as water pump etc. in households. Describe the principal, construction and working of a single-phase AC generator.

Describe the principal, construction and working of a single-phase AC generator

View solution