Question

A wire of length \(L\) is bent round into (i) a square coil having \(N\) turns and (ii) a circular coil having \(N\) turns. The coil in both cases is free to turn about a vertical axis coinciding with the plane of the coil, in a uniform, horizontal magnetic field and carry the same currents. Find the ratio of the maximum value of the torque acting on the square coil to that on the circular coil.

Hint:

For a current-carrying coil, \[ \tau_{\max}=NIAB. \] If \(N\), \(I\), and \(B\) are the same for different shapes of coils, then \[ \tau_{\max}\propto A. \] Also, among all plane figures with the same perimeter, the circle encloses the maximum area. Therefore, the circular coil always experiences a larger maximum torque than the square coil.

Answer 1