N equally spaced charges, each of value q, ar | vedclass

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(C) The current $I$ produced by a rotating charge $q$ is $I = \frac{q}{T}$, where $T = \frac{2\pi}{\omega}$ is the time period of rotation.For loop $A

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(C) The current $I$ produced by a rotating charge $q$ is $I = \frac{q}{T}$, where $T = \frac{2\pi}{\omega}$ is the time period of rotation.For loop $A$, it encloses one charge $q$. The current passing through loop $A$ is $I_A = \frac{q}{T} = \frac{q\omega}{2\pi}$.For loop $B$, it encloses all $N$ charges. The total charge passing through the cross-section of the loop $B$ in one time period $T$ is $Nq$. Thus, the current $I_B = \frac{Nq}{T} = \frac{Nq\omega}{2\pi}$.However, in the context of an Amperian loop enclosing a rotating ring of charges, the net current $I_{net}$ through the loop is the total charge passing through the loop's cross-section per unit time. Since the ring is continuous, the current $I_B$ through loop $B$ is the same as the current $I_A$ through loop $A$ because both loops effectively capture the same rate of charge flow $(I = \frac{Nq}{T_{total}} = \frac{q}{T_{individual}})$. Thus, $I_A = I_B$, and the difference $I_A - I_B = 0$.

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