Charge q is uniformly spread on a thin ring of radius R. The ring rotates about its axis with a uniform freque

Question

Charge q is uniformly spread on a thin ring of radius R. The ring rotates about its axis with a uniform frequency f Hz. The magnitude of magnetic induction at the center of the ring is :

Accepted Answer

1. **Current Equivalent:** A charge $q$ rotating with frequency $f$ constitutes an equivalent electric current $I$. Since current is the rate of flow of charge ($I = q/t$) and the time period of rotation is $T = 1/f$, the effective current is given by:
   $$I = \frac{q}{T} = qf$$ .
2. **Magnetic Field Formula:** The magnetic field ($B$) at the center of a circular current-carrying loop of radius $R$ is given by the formula:
   $$B = \frac{\mu_0 I}{2R}$$ .
3. **Substitution:** Substituting the expression for equivalent current ($I = qf$) into the magnetic field formula:
   $$B = \frac{\mu_0 (qf)}{2R}$$
   This matches Option 1.

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