MHT CET · Physics · Magnetic Effects of Current

A thin ring of radius ' \(R\) ' carries a uniformly distributed charge. The ring rotates at constant speed ' \(N\) ' r.p.s. about its axis perpendicular to the plane. If ' \(B\) ' is the magnetic field at the centre, the charge on the ring is ( \(\mu_0=\) permeability of free space)

A \(\frac{\mu_0 \mathrm{~N}}{2 \mathrm{RB}}\)
B \(\frac{\mathrm{RB}}{2 \mu_0^{\prime} \mathrm{N}}\)
C \(\frac{\mu_0 \mathrm{~N}}{\mathrm{RB}}\)
D \(\frac{2 R B}{\mu_0 \mathrm{~N}}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{2 R B}{\mu_0 \mathrm{~N}}\)

Step-by-step Solution

Detailed explanation

A thin uniformly charged rotating ring acts like a current carrying coil.
Magnetic field at the centre of current carrying coil,
\(B=\frac{\mu_0 I}{2 R}\)
Current is given by, \(\mathrm{I}=\mathrm{qN} \quad\) where N is revolutions per second.
\(\begin{array}{ll}
\therefore & B=\frac{\mu_0 q N}{2 R} \\
\therefore & q=\frac{2 R B}{\mu_0 N}
\end{array}\)
...[From(i)]

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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