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.

विकल्प

• 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.

Answer 1

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, M_net < M or M diminishes.