MHT CET · Physics · Magnetic Effects of Current
A thin ring of radius ' \(R\) ' meter has charge ' \(q\) ' coulomb uniformly spread on it. The ring rotates about its axis with a constant frequency of \(f\) revolution/s. The value of magnetic induction in \(\mathrm{Wb} \mathrm{m}{ }^{-2}\) at the center of the ring is ( \(\mu_0=\) Permeability of free space)
- A \(\frac{\mu_0 q \mathrm{f}}{2 \pi R}\)
- B \(\frac{\mu_0 q}{2 \pi R}\)
- C \(\frac{\mu_0 \mathrm{qf}}{2 \mathrm{R}}\)
- D \(\frac{\mu_0 \mathrm{q}}{2 \pi \mathrm{fR}}\)
Answer & Solution
Correct Answer
(C) \(\frac{\mu_0 \mathrm{qf}}{2 \mathrm{R}}\)
Step-by-step Solution
Detailed explanation
For circular coil of radius \(\mathrm{R}\) carrying a current \(\mathrm{I}\), the magnetic field at the center is given by
\(
B=\frac{\mu_0 I}{2 R}
\)
Here \(\mathrm{I}=\mathrm{qf}\)
\(
\therefore \mathrm{B}=\frac{\mu_0 \mathrm{qf}}{2 \mathrm{R}}
\)
\(
B=\frac{\mu_0 I}{2 R}
\)
Here \(\mathrm{I}=\mathrm{qf}\)
\(
\therefore \mathrm{B}=\frac{\mu_0 \mathrm{qf}}{2 \mathrm{R}}
\)
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