Question

Two co-planar, concentric circular coils of radii a and b are placed in the y-z plane such that the common center of the coils is origin (a >> b). A current i flows in the outer coil. Now the inner coil is moved along the x-axis with a constant speed v keeping its plane unchanged. The emf induced in the inner coil is maximum at:

Answer 1

Given that,

Radius of circular coils is a and b.

Current = i

Constant speed = v

We know that,

Magnetic field in the inside region of outer coil due to current I in the coil is

$B=\dfrac{\mu_{0}I}{2b}$

The flux passing through the coil is

We need to calculate the flux

Using formula of flux

$\phi=BA$

Put the value into the formula

$\phi=\dfrac{\mu_{0}i}{2b}\times\pi a^2$

$\phi=\dfrac{\mu_{0}i\pi a^2}{2b}$

We need to calculate the emf induced in the inner coil

Using formula of induced emf

$e=\dfrac{d\phi}{dt}$

Put the value into the formula

$e=\dfrac{d}{dt}(\dfrac{\mu_{0}i\pi a^2}{2b})$

$e=\dfrac{\mu_{0}\pi\ a^2}{2b}\dfrac{di}{dt}$

Hence, The emf induced in the inner coil is $\dfrac{\mu_{0}\pi\ a^2}{2b}\dfrac{di}{dt}$

Answer 2

Answer:

Emf induced is maximum at t= a/ 2v

Explanation: