question_answer

A wire of length 6.28 m is bent into a circular coil of 2 turns. If a current of 0.5 A exists in the coil, the magnetic moment of the coil is, in\[~A-{{m}^{2}}\]

A)                  \[\frac{\pi }{4}\]                                             

B)                  \[\frac{1}{4}\]

C)                  \[\pi \]                                

D)                  4\[\pi \]

Correct Answer: A

Solution :

                 Given, N = 2                 \[i=0.5A\]                 When a wire is bent into a circular coil of 2 turns then                                 \[4\pi r=6.28\]                 \[r=\frac{6.28}{4\times \pi }\]                 \[=\frac{6.28}{4\times 3.14}\]                 \[r=\frac{1}{2}\]                 Area,     \[A=\pi {{r}^{2}}=\frac{\pi }{4}\]                 Magnetic moment = NiA                 \[=2\times 0.5\times \frac{\pi }{4}\]                 \[=\frac{\pi }{4}\]