Question

A non-conducting ring of radius $R$ has charge $Q$ distributed unevenly over it. If it rotates with an angular velocity $\omega$, the equivalent current will be

• A. zero
• B. Q$\omega$
• C. $Q\frac{\omega }{2\pi }$
• D. $Q\frac{\omega }{2\pi R}$

Answer 1

The correct option is C $Q\frac{\omega }{2\pi }$

With each rotation, charge $Q$ crosses any fixed point near the ring.
Number of rotations per second $=$ frequency $\left(f\right)=\frac{\omega }{2\pi }$
Thus, charge cross the point per second $=$current $=Qf=\frac{Q\omega }{2\pi }$