There are two long co-axial solenoids of same length $l$. The inner and outer coils have radii $r_{1}$ and…

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 $\mathrm{n}_{1}$ and $\mathrm{n}_{2}$, respectively. The ratio of mutual inductance to the self-inductance of the inner-coil is :
  1. $\frac{n_{1}}{n_{2}}$
  2. $\frac{n_{2}}{n_{1}} \cdot \frac{r_{1}}{r_{2}}$
  3. $\frac{n_{2}}{n_{1}} \cdot \frac{r_{2}^{2}}{r_{1}^{2}}$
  4. $\frac{n_{2}}{n_{1}}$

Solution

The rate of mutual inductance is given by $ \mathrm{M}=\mu_{0} \mathrm{n}, \mathrm{n}_{2} \pi \mathrm{r}_{1}^{2} \quad \ldots(\mathrm{i}) $ The rate of self inductance is given by $\mathrm{L}=\mu_{0} \mathrm{n}_{1}^{2} \pi \mathrm{r}_{1}^{2} \quad \ldots(\mathrm{ii})$ Dividing (i) by (ii) $\Rightarrow \frac{\mathrm{M}}{\mathrm{L}}=\frac{\mathrm{n}_{2}}{\mathrm{n}_{1}}$

Asked in: JEE Main 2019 (11 Jan Shift 1)

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