MHT CET · Physics · Electromagnetic Induction
A coil of radius 'r' is placed on another coil (whose radius is 'R' and current flowing through it is changing) so that their centres coincide. \((\mathrm{R} \gg \mathrm{r})\) If both the coils are coplanar then the mutual inductance between them is proportional to
- A \(\frac{r}{R}\)
- B \(\frac{R}{r}\)
- C \(\frac{R}{r^{2}}\)
- D \(\frac{r^{2}}{R}\)
Answer & Solution
Correct Answer
(D) \(\frac{r^{2}}{R}\)
Step-by-step Solution
Detailed explanation
Magnetic field at the centre \(\mathrm{B}=\frac{\mu_{\mathrm{o}} \mathrm{I}}{\mathrm{R}}\)
\(\phi=\) Magnetic flux passing through the smaller coil \(=\pi r^{2} B\)
\(\therefore \phi=\pi r^{2} \times \frac{\mu_{0} I}{R}\)
\(\therefore M=\frac{\phi}{I}=\frac{\mu \pi r^{2}}{R} \quad \therefore M \propto \frac{r^{2}}{R}\)
\(\phi=\) Magnetic flux passing through the smaller coil \(=\pi r^{2} B\)
\(\therefore \phi=\pi r^{2} \times \frac{\mu_{0} I}{R}\)
\(\therefore M=\frac{\phi}{I}=\frac{\mu \pi r^{2}}{R} \quad \therefore M \propto \frac{r^{2}}{R}\)
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