A current carrying circular loop of radius R is placed in the x-y plane with centre at the origin. Half of the loop with x 0 is now bent so that it now lies in the y-z plane.

Question

A current carrying circular loop of radius R is placed in the x-y plane with centre at the origin. Half of the loop with x > 0 is now bent so that it now lies in the y-z plane.

KollegeApply · Accepted Answer

The magnitude of magnetic moment now diminishes. Explanation: Direction of magnetic moment (M = 14) of the circular loop (in figure) is perpendicular to the loop by the right-hand thumb rule. So to compare these magnetic moments, we have to analyse them vectorically. Now let us first analyse the situation: The direction of the magnetic moment of circular loop of radius R is placed in the x-y plane along the z-direction and given by M = InR, (as shown in above figure). When half of the loop with x > 0 is now bent so that it now lies in the y-z plane as shown in the figure below. The magnitudes of the magnetic moment of each semicircular loop of radius R lie in the x-y plane and the y-z plane is M1 = M2 = I (piR^2)/2 and the direction of magnetic moments are along the z-direction and x-direction respectively. Their resultant `M_("net") = sqrt(M_1^2 + M_2^2) = sqrt(2I) (piR^2)/2 = M/sqrt(2)` So, Mnet < M or M diminishes. [Solution diagram: 252570_solution_1.png] [Solution diagram: 252570_solution_2.png]

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