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 `xgt0` is now bent so that it now lies in the y-z plane.

Options

A. The magnitude of magnetic moment now diminishes.
B. The magnetic moment does not change.
C. The magnitude of `vec(B)` at `(0,0,z),zgtgtR` increases.
D. The magnitude of `vec(B)` at `(0,0,z), zgtgtR` is unchanged.

Answer

A

Explanation

For a circular loop of a radius R carrying current I placed in x-y plance, the magnetic moment `M=I xx piR^(2)`. It acts perpendicular to the loop i.e., along z-direction. When half of the current loop is bent n y-z plane, then magnetic moment due to half current loop in x-y plan, `M_(1) =I(pi R^(2)//2)` acting along z-direction. Magnetic moment due to half current loop in y-z plane, `M_(2) = I(pi R^(2)//2)` along x-direction.
Effective magnetic moment due to entire bent current loop,
`M' = sqrt(M_(1)^(2) + M_(2)^(2)) = sqrt((Ipi R^(2)//2)^(2) + (Ipi R^(2)//2)^(2))`
`(I pi R^(2))/(2) sqrt(2) lt M`
i.e., magnetic moment diminishes.