A circular loop of radius R carries a current I . A second circular loop of radius r ( R ) carrying a current i is positioned at the centre of the larger loop. The planes of the two circles are at right angles to one another. Determine the torque acting on the smaller loop.

Step-by-step solution

The magnetic field produced by the larger loop at its centre is given by B = ₀ I 2R . The magnetic dipole moment of the smaller loop is m = iA = i( r^2) . Since the planes of the two loops are at right angles, the angle between the magnetic field vector B and the magnetic dipole moment vector m is 90^ . The torque acting on the smaller loop is = mB 90^ . Substituting the values of m and B , we get = (i r^2) ( ₀ I 2R ) = ₀ i I r^2 2R .