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 `vecB` at `(0, 0, z), zgt gt R` increases
D. The magnitude of `vecB` at `(0,0,z), z gt gt R` is unchanged

Answer

A

Explanation

For a circular loop of radius R, carrying current I in x-y plane, the magnetic moment `M=Ixxpir^2`. It atcs perpendicular to the loop along z-direction. When half of the current loop is bent in y-z plane, then magnetic moment due to half current loop in x-y plane, `M_1=I(piR^2//2)` acting along z-direction. Magnetic moment due to half current loop in y-z plane, `M_2=I(piR^2//2)` along x-direction.
Effective magnetic moment due to entire bent current loop,
`M^'=sqrt(M_1^2+M_2^2)=sqrt((IpiR^2//2)^2+(IpiR^2//2)^2)=(IpirR^2)/(2)sqrt2 lt M`
i.e., magnetic moment diminishes.
The magnitude of `vecB` at a point on the axis of loop, distance z from hte centre of current loop in x-y plane is
`B=(mu_0)/(4pi)(2piIR^2)/((R^2+z^2)^(3//2))`
The magnitude of `vecB` at a point distance z from the centre of bent current loop, whose half part is in x-y plane and half part is in y-z plane, is
`B^'=sqrt([(mu_0)/(4pi)(piIR^2)/((R^2+z^2)^(3//2))]^2+[(mu_0)/(4pi)(piIR^2)/((R^2+z^2)^(3//2))]^2)=(mu_0)/(4pi)(piIR^2)/((R^2+z^2)^(3//2))sqrt2 lt B`.