JEE Advance - Physics (2020 - Paper 1 Offline - No. 16)
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 Bo parallel to the plane of the coil. When the switch is closed, the capacitor
gets discharged through the coil in a very short time. By the time the capacitor is discharged fully,
magnitude of the angular momentum gained by the coil will be (assume that the discharge time is so
short that the coil has hardly rotated during this time)
$${\pi \over 2}NQ{B_0}{R^2}$$
$$\pi NQ{B_0}{R^2}$$
$$2\pi NQ{B_0}{R^2}$$
$$4\pi NQ{B_0}{R^2}$$
Explanation
Torque experienced by circular loop = M $$ \times $$ B
where, M is magnetic moment and B is magnetic field.
$$ \therefore $$ $$\tau $$ = i$$\pi $$R2NB0
(at the instant shown $$\theta $$ = $$\pi $$/2)
$$ \therefore $$ $$\tau $$dt = dL = i$$\pi $$R2NB0dt
= Q$$\pi $$R2NB0 ($$ \because $$ idt = Q)
where, M is magnetic moment and B is magnetic field.
$$ \therefore $$ $$\tau $$ = i$$\pi $$R2NB0
(at the instant shown $$\theta $$ = $$\pi $$/2)
$$ \therefore $$ $$\tau $$dt = dL = i$$\pi $$R2NB0dt
= Q$$\pi $$R2NB0 ($$ \because $$ idt = Q)
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