Question

A conducting ring of radius r and resistance R is
placed in a region of uniform time varying magnetic
field B which is perpendicular to the plane of the
ring. If the magnetic field is changing at a rate a,
then the current induced in the ring is​

Answer 1

The current induced in the ring is $\boxed{\frac{\pi r^2a}{R}}$

Explanation:

Given:

magnetic field = B

Radius of the ring = r

Rate of change of magnetic field = a

Resistance of the ring = R

To find out:

Current induced in the ring

Solution:

The total flux passing

$\phi=\pi r^2B$

Therefore, emf induced in the ring

$e=\frac{d\phi}{dt}=\pir^2\frac{dB}{dt}=\pi r^2a$

Therefore, current in the ring

$i=\frac{e}{R}$

$\implies i=\frac{\pi r^2a}{R}$

Hope this answer is helpful.

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