A) \[A\frac{1}{2}q\omega {{r}^{2}}\]
B) \[\frac{4}{3}q\omega {{r}^{2}}\]
C) \[\frac{3}{2}q\omega {{r}^{2}}\]
D) \[q\omega {{r}^{2}}\]
Correct Answer: A
Solution :
Let us take an element at an angle \[\theta \] subtending an angle \[d\theta \] The charge the element has can be written as \[dq=\frac{q}{2\pi }d\theta \] We know that\[i=\frac{dq}{dt}=\frac{q}{2\pi }\times \frac{d\theta }{dt}\] The time dt can be written as \[dt=\frac{d\theta }{w}\] Hence\[i=\frac{qw}{2\pi }\] magnetic moment = iA Hence Magnetic moment\[M=\frac{qw}{2\pi }\times \pi {{r}^{2}}=\frac{qw{{r}^{2}}}{2}\]
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