A circular and a square coil is prepared from two identical metal wires and a current is passed through them. Ratio of magnetic dipole moment associated with circular coil to that with square coil is

Step-by-step solution

Let I be the length of metal wire. When wire is bent into a circular coil of radius (r ), then (r= l 2 ) ( ) Area, ( A = ( l 2 )²= l² 4 ² ) ( ) Magnetic dipole moment associated with circular coil, ( _ c - iA = i ( l² 4 ² ) ) ( _ c = i i ^ 2 4 . .( i ) ) When metal wire Is bent into a square coil then side of square ( a = l 4 ) ( ) Area, ( A = a ²= l² 16 ) ( ) Magnetic dipole moment associated with square coil, ( _ s = i A = i l² 16 ) ( aligned & _ c _ s = i l² 4 i l² 16 &= 16 4 = 4 aligned ) Hence, the ratio of ma