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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.
Options
The magnitude of magnetic moment now diminishes.
The magnetic moment does not change.
The magnitude of B at (0, 0, z), z > R increases.
The magnitude of B at (0, 0, z), z >> R is unchanged.
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Solution
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.
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