question_answer

If a steel wire of length I and magnetic moment \[M\] is bent into a semi-circular arc, then the new magnetic moment is

A) \[M\times l\]                    

B) \[\frac{M}{l}\]

C)  \[\frac{2M}{\pi }\]                                         

D)  \[M\]

Correct Answer: C

Solution :

When wire is bent in the form of semi circular arc then,\[l=\pi r\] \[\therefore \]The radius of semi-circular arc\[,\]\[r=l/\pi \]. Distance between two end points of semi-circular wire\[=2\pi =\frac{2l}{\pi }\] \[\therefore \]Magnetic moment of semi-circular wire                 \[=m\times 2\pi \]                 \[=m\times \frac{2l}{\pi }=\frac{2}{\pi }ml\] But \[ml\] is the magnetic moment of straight wire \[i.e.,\] \[ml=M\] \[\therefore \]New magnetic moment\[=\frac{2}{\pi }M\]