MHT CET · Physics · Electromagnetic Induction
A coil of radius ' \(r\) ' is placed on another coil (whose radius is ' \(\mathrm{R}\) ' and current through it is changing) so that their centers coincide. \((R \gg r)\). If both are coplanar, then the mutual inductance between them is proportional to
- A \(\frac{R}{r^2}\)
- B \(\frac{r}{R}\)
- C \(\frac{\mathrm{R}}{\mathrm{r}}\)
- D \(\frac{r^2}{\mathrm{R}}\)
Answer & Solution
Correct Answer
(D) \(\frac{r^2}{\mathrm{R}}\)
Step-by-step Solution
Detailed explanation
Magnetic field at the center, \(B=\frac{\mu_0 I}{R}\)
\(\phi=\) Magnetic flux passing through the smaller coil \(=\pi \mathrm{r}^2 \mathrm{~B}\)
\(
\begin{aligned}
& \phi=\pi r^2 \times \frac{\mu_0 I}{R} \\
& M=\frac{\phi}{I}=\frac{\mu_0 \pi r^2}{R} \\
& M \propto \frac{r^2}{R}
\end{aligned}
\)
\(\phi=\) Magnetic flux passing through the smaller coil \(=\pi \mathrm{r}^2 \mathrm{~B}\)
\(
\begin{aligned}
& \phi=\pi r^2 \times \frac{\mu_0 I}{R} \\
& M=\frac{\phi}{I}=\frac{\mu_0 \pi r^2}{R} \\
& M \propto \frac{r^2}{R}
\end{aligned}
\)
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