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.

• A. The magnitude of magnetic moment now diminishes.
• B. The magnetic moment does not change.
• C. The magnitude of $\overline{B}$ at $(0,0,z),z$>>R increases.
• D. The magnitude of $\overline{B}$ at $(0,0,z),z$>>R is unchanged.

Answer 1

The correct option is A The magnitude of magnetic moment now diminishes.

For a circular loop of radius R carrying current, I placed in $x-y$ plane, the magnetic moment $M=I\pi R^2$. It acts perpendicular to the loop i.e., along with the z-direction. When half of the current loop is bent in y-z plane, the magnetic moment due to half current loop in x-y plane,$M_1=I\left(\frac{\pi R^2}{2}\right)$ acting along z-direction.
Magnetic moment due to half current loop in y-z plane,$M_2=I\left(\frac{\pi R^2}{2}\right)$ along x-direction.
Effective magnetic moment due to entire bent current loop,
$M^{\prime }$ =$\sqrt{M_1^2+M_2^2}$=$\sqrt{{\left(\frac{I\pi R^2}{2}\right)}^2+{\left(\frac{I\pi R^2}{2}\right)}^2}$
$M^{\prime }=\frac{I\pi R^2}{2}\sqrt{2}<M$
i.e., magnetic moment diminishes.