Question

A circular loop of wire of radius R is bent about its diameter along two mutually perpendicular planes as shown in Fig. If the loop carries a current I, then determine its magnetic moment.

Answer 1

The given loop may be obtained by the superposition of two
semicircular loops as shown in the figure.
The magnetic moment of the semicircle in the y-z plane is along
the x-axis and that in the x-z plane is along the y-axis.
`M_x=(piR^2I)/2, M_y=(piR^2I)/(2)`
The total magnetic moment is `vecM=M_xhati+M_y hatj`
or `M=(piR^2I)/2(hati+hatj)`