Question

A circular loop of radius R carries a current I. Another circular loop of radius r(<

Answer 1

Explanation:

To find: The torque acting on the smaller loop.

Given data in the question  :

To the outer loop,

Current Magnitude = I

Loop Radius = R

The magnetic field at the center is thus supplied by the larger loop

$B=\frac{\mu_{0} I}{2 R}$

Let A be the smaller loop field, and let current pass through it.

Angle between the smaller loop area vector and the magnetic field due to the larger loop = 90°

The required torque is therefore given by the

$\Gamma=i(\vec{A} \times \vec{B})$

$=\mathrm{i} \mathrm{AB} \sin 90^{\circ}$

we know that $|A|=\pi r^{2},|B|=\frac{\mu_{0} l}{2 R}$

$=i \pi r^{2} \frac{\mu_{0} I}{2 R}$

=$=\frac{\mu_{0} I i \pi r^{2}}{2 R}$