A circular wire-loop of radius a , carrying a current i , is placed in a perpendicular magnetic field B . Determine the force of compression in the wire.

Step-by-step solution

Consider a small element of the circular wire subtending an angle d at the center. The length of this element is dl = a d . The magnetic force on this element is dF = i(dl)B = i(a d )B . By the right-hand rule for d l B , this force is directed radially inwards, causing a compressive force T in the wire. The compressive forces act tangentially at the ends of the small element. The radial component of these forces balances the inward magnetic force. The net inward radial force due to compression is 2T ( d 2 ) . For