question_answer

    A charge\[4\mu C\]is placed on a small conducting sphere that is located at the end of thin insulating rod of length 0.5 m. The rod rotates in horizontal plane with a constant angular velocity of\[100\text{ }rad{{s}^{-1}}\]about a vertical axis that passes through its other end. The magnetic moment of the rotating charge is

A)  zero

B)  \[0.5\times {{10}^{-4}}A{{m}^{2}}\]

C)  \[1.25\times {{10}^{-4}}A{{m}^{2}}\]

D)  magnetic moment is not defined for this case

Correct Answer: B

Solution :

                A moving charge along a circle is equivalent to a current carrying ring, whose current is given by, \[I=\frac{q}{T}=\frac{q}{2\pi /\omega }\] \[\Rightarrow \]               \[I=\frac{4\times {{10}^{-6}}}{2\pi }\times 100\]                 \[=0.64\times {{10}^{-4}}A\] Magnetic moment of rotating charge is \[M=IA\] \[\Rightarrow \]               \[M=0.64\times {{10}^{-4}}\times \pi \times {{0.5}^{2}}\] \[=0.5\times {{10}^{-4}}A-{{m}^{2}}\]