Q79 / 100 · BITSAT 2024 (Memory Based Paper 2) · Physics
There are two long co-axial solenoids of same length $l$. The inner and outer coils have radii $r_1$ and $r_2$ and number of turns per unit length $n_1$ and $n_2$, respectively. The ratio of mutual inductance to the self-inductance of the inner-coil is:
- A$\frac{n_1}{n_2}$
- B$\frac{n_2}{n_1} \cdot \frac{n_1}{r_2}$
- C$\frac{n_2}{n_1} \cdot \frac{r_2^2}{r_1^2}$
- Correct answerD$\frac{n_2}{n_1}$
Solution
The rate of mutual inductance is given by
$\mathrm{M}=\mu_0 \mathrm{n}_1 \mathrm{n}_2 \pi \mathrm{~m}_1^2$ ....(i)
The rate of self inductance is given by
$\mathrm{L}=\mu_0 \mathrm{n}_1^2 \pi \mathrm{r}_1^2$ .....(ii)
Dividing (i) by (ii)
$\Rightarrow \frac{\mathrm{M}}{\mathrm{L}}=\frac{\mathrm{n}_2}{\mathrm{n}_1}$
Hence, the correct answer is option: 'D'.