N equally spaced charges each of value q , are placed on a circle of radius R. The circle rotates about its…

N equally spaced charges each of value q , are placed on a circle of radius R. The circle rotates about its axis with an angular velocity $\omega$ as shown in the figure. A bigger Amperian loop B encloses the whole circle where as a smaller Amperian loop A encloses a small segment. The difference between enclosed currents, $I_A-I_B$, for the given Amperian loops is

1. $\frac{2 \pi}{N} q \omega$
2. $\frac{\mathrm{N}^2}{2 \pi} \mathrm{q} \omega$
3. $\frac{\mathrm{N}}{\pi} \mathrm{q} \omega$
4. $\frac{\mathrm{N}}{2 \pi} \mathrm{q} \omega$

Solution

$\begin{aligned} & I_A=\frac{N q}{\frac{2 \pi}{\omega}} \\ & I_A=\frac{N q \omega}{2 \pi}, I_B=0 \\ & I_A=I_B=\frac{N q \omega}{2 \pi}\end{aligned}$

Asked in: JEE Main 2025 (24 Jan Shift 2)

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