Electromagnetic Induction

JEE Main level, single correct, medium

136 of 153

Question 136 of 153

There are two long co-axial solenoids of same length ll. The inner and outer coils have radii r1r_{1} and r2r_{2} and number of turns per unit length n1\mathrm{n}_{1} and n2\mathrm{n}_{2}, respectively. The ratio of mutual inductance to the self-inductance of the inner-coil is :

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Answer: (D) n2n1\frac{n_{2}}{n_{1}}

The rate of mutual inductance is given by

M=μ0n,n2πr12…(i)\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

L=μ0n12πr12…(ii)\mathrm{L}=\mu_{0} \mathrm{n}_{1}^{2} \pi \mathrm{r}_{1}^{2} \quad \ldots(\mathrm{ii})

Dividing (i) by (ii) ⇒ML=n2n1\Rightarrow \frac{\mathrm{M}}{\mathrm{L}}=\frac{\mathrm{n}_{2}}{\mathrm{n}_{1}}

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