A long solenoid of radius $R$ carries a time (t)-dependent current $I(t)=I_{0}t(1-t)$. A ring of radius $2R$ is placed coaxially near its middle. During the time interval $0\le t\le 1$, the induced current $(I_R)$ and the induced $EMF(V_R)$ in the ring change as:

A conducting circular loop made of a thin wire, has area $3.5\times 10^{-3}{m}^2$ and resistance $10\Omega$. It is placed perpendicular to a time dependent magnetic field $B(t)=(0.4T)\sin (50\pi t)$. The field is uniform in space. Then the net charge flowing through the loop during $t=0s$ and $t=10ms$ is close to:

The figure shows a square loop $L$ of side $5cm$ which is connected to a network of resistances. The whole setup is moving towards right with a constant speed of $1cm{s}^{-1}$. At some instant, a part of L is in a uniform magnetic field of $1T$, perpendicular to the plane of the loop. If the resistance of $L$ is $1.7\Omega$, the current in the loop at that instant will be close to : 

A power transmission line feeds input power at $2300V$ to a step down transformer with its primary windings having $4000$ turns, giving the output power at $230V$. If the current in the primary of the transformer is $5A$, and its efficiency is $90\%$, the output current would be:

A coil of cross-sectional area $A$ having $n$ turns is placed in a uniform magnetic field $B$. When it is rotated with an angular velocity $\omega$, the maximum e.m.f. induced in the coil will be

A small circle loop of wire of radius a is located at the centre of a much larger circular wire loop of radius $b$. The two loops are in the same plane. The outer loop of radius $b$ carries an alternating current $I+I_{o}cos(\omega t)$ . The emf induced in the smaller inner loop is nearly :

Consider a thin metallic sheet perpendicular to the plane of the paper moving with speed ${}^{\prime }{v}^{\prime }$ in a uniform magnetic field B going into the plane of the paper (See figure). If charge densities ${\sigma }_1$ and ${\sigma }_2$ are induced on the left and right surfaces, respectively, of the sheet then (ignore fringe effects) : 

A fighter plane of length 20 m, wing span (distance from tip of one wing to the tip of the other wing) of 15 m and height 5 m is flying towards east over Delhi. Its speed is $240m{s}^{-1}$. The earth's magnetic field over Delhi is $5\times 10^{-5}$ T with the declination angle $\sim 0^o$ and dip of $\theta$ such that $sin\theta =\frac{2}{3}$. If the voltage developed is $V_B$ between the lower and upper side of the plane and $V_W$ between the tips of the wings then $V_B$ and $V_W$ are close to 

A conducting metal circular-wire-loop of radius r is placed perpendicular to a magnetic field which varies with time as $B=B_0{e}^{-t/\tau }$, where $B_0$ and $\tau$ are constants, at time t = 0. If the resistance of the loop is R then the heat generated in the loop after a long time $(t\to \infty )$ is

A light disc made of aluminium (a nonmagnetic material) is kept horizontally and is free to rotate about its axis as shown in the figure. A strong magnet is held vertically at a point above the disc away from its axis. On revolving the magnet about the axis of the disc, the disc will (figure is schematic and not drawn to scale) 

The inductors of two LR circuits are placed next to each other, as shown in the figure. The values of the self-inductance of the inductors, resistances, mutual-inductance and applied voltages are specified in the given circuit. After both the switches are closed simultaneously, the total work done by the batteries against the induced EMF in the inductors by the time the currents reach their steady state values is ______ mJ.

A conducting wire of parabolic shape, $y=x^2$, is moving with velocity $\vec{V}=V_0\hat{i}$ in a non-uniform magnetic field $\vec{B}=B_0\left(1+{\left(\frac{y}{L}\right)}^{\beta }\right)\hat{k}$, as shown in figure. If $V_0$, $B_0$, L and $\beta$ are positive constants and $\Delta \varphi$ is the potential difference developed between the ends of the wire, then the correct statement(s) is/are?

A $10$ cm long perfectly conducting wire PQ is moving with a velocity 1 cm/s on a pair of horizontal rails of zero resistance. One side of the rails is connected to an inductor $L=1$ mH and a resistance $R=1\Omega$ as shown in figure. The horizontal rail, L and R lie in the same plane with a uniform magnetic field $B=1T$ perpendicular to the plane. If the key S is closed at certain instant , the current in the circuit after 1 millisecond is $x\times 10^{-3}A$, where the value of x is ____ .
[Assume  the velocity of wire PQ remains constant (1 cm/s) after key S is closed. Given : $e^{-1}=0.37$, where e is base of the natural logarithm]

A circular insulated copper wire loop is twisted to form two loops of area $A$ and $2A$ as shown in the figure. At the point of crossing the wires remain electrically insulated from each other. The entire loop lies in the plane (of the paper). A uniform magnetic field $B$ point into the plane of the paper. At $t=0$, the loop starts rotating about the common diameter as axis with a constant angular velocity $\omega$ in the magnetic field. Which of the following options is/are correct? 

A conducting loop in the shape of a right angled isosceles triangle of height $10$ cm is kept such that the ${90}^{\circ }$ vertex is very close to an infinitely long conducting wire (see the figure). The wire is electrically insulated from the loop. The hypotenuse of the triangle is parallel to the wire. The current in the triangular loop is in counter clockwise direction and increased at a constant rate of 10 ${As}^{-1}$. Which of the following statement (s) is (are) true?

A rigid wire loop of square shape having side of length L and resistance R is moving along the x-axis with a constant velocity $v_0$ in the plane of the paper. At t=0, the right edge of the loop enters a region of length 3L where there is a uniform magnetic field $B_0$ into the plane of the paper, as shown in the figure. For sufficient large $v_0$, the loop eventually crosses the region. Let x be the location of the right edge of the loop. Let $v(x),I(x)$ and $F(x)$ represent the velocity of the loop, current in the loop, and force on the loop, respectively, as a function of x. Counter-clockwise current is taken as positive.
Which of the following schematic plot(s) is (are) correct? (Ignore gravity)