## The Inductors of two LR circuits are placed next to each other , as shown in the figure . The values of the self-Inductance ….

Q: 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 voltage 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 …..

Click to See Solution :
Ans: (55)
Sol: Mutual inductance is producing flux in same direction as self inductance

$\displaystyle U = \frac{1}{2}L_1 I_1^2 + \frac{1}{2}L_2 I_2^2 + M I_1 I_2$

$\displaystyle U = \frac{1}{2}(10\times 10^{-3})1^2 + \frac{1}{2}(20\times 10^{-3})2^2 + (5 \times 10^{-3})\times 1 \times 2$

= 55

## A circular coil of radius R and N turns has negligible resistance . As shown in the schematic figure , its two ends are ….

Q: A circular coil of radius R and N turns has negligible resistance . As shown in the schematic figure , its two ends are connected to two wires and it is hanging by those wires with its plane being vertical . The wires are connected to a capacitor with charge Q through a switch . The coil is in a horizontal uniform magnetic field B_0 parallel to the plane of coil . When the switch is closed , the capacitor gets discharged through the coil in very short time . By the time the capacitor discharged fully , magnitude of angular momentum gained by the coil will be (assume that discharge time is so short that the coil has hardly rotated during this time )

(a) $\frac{\pi}{2}N Q B_0 R^2$

(b) π NQB0 R2

(c) 2π NQB0 R2

(d) 4π NQB0 R2

Click to See Solution :
Ans: (b)
Sol: Torque experienced by circular loop is

$\vec{\tau} = \vec{M} \times \vec{B}$ ; Where M = magnetic moment and B = magnetic field

τ = N I A B0 ; (As θ = π/2 at the instant shown )

τ = N I (π R2) B0

τ dt = dL = N I (π R2) B0 dt

= Q π R2 B0 N ; (Since I dt = Q )

## A light disc made of aluminium (a non-magnetic material) is kept horizontally and is free to rotate ….

Q: A light disc made of aluminium (a non-magnetic 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

(a) rotate in the direction opposite to the direction of magnet’s motion

(b) rotate in the same direction as the direction of magnet’s motion

(c) not rotate and its temperature will remain unchanged

(d) not rotate but its temperature will slowly rise

Click to See Solution :
Ans: (b)
Sol:When magnet is moved , it creates a state such that where plate moves through the magnetic flux , due to which an electromotive force generated in the plate and eddy currents are induced . These currents are such that it opposes the relative motion .

## A long solenoid S has n turns per meter, with diameter a. At the centre of this coil, we place a smaller coil of N turns and diameter b (where b < a).

Q: A long solenoid S has n turns per meter, with diameter a. At the centre of this coil, we place a smaller coil of N turns and diameter b (where b < a). If the current in the solenoid increases linearly, with time what is the induced emf appearing in the smaller coil. Plot graph showing nature of variation in emf, if current varies as a function of m t2 + C.