Consider two long co-axial solenoids of same length l. The inner and outer coils have radii r1 and r2 and number of turns per unit length n1 and n2, respectively. Find the ratio of mutual inductance to the self inductance of the inner-coil.

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Consider two long co-axial solenoids of same length l. The inner and outer coils have radii r₁ and r₂ and number of turns per unit length n₁ and n₂, respectively. Find the ratio of mutual inductance to the self inductance of the inner-coil.

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$\frac{n_{2}}{n_{1}} \cdot \frac{r_{1}}{r_{2}}$

$\frac{n_{2}}{n_{1}}$

$\frac{n_{1}}{n_{2}}$

$\frac{n_{2}}{n_{1}} \cdot \frac{r_{2}^{2}}{r_{1}^{2}}$

answer is B.

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Detailed Solution

Mutual inductance $= μ_{0} n_{1} n_{2} R_{2}^{2} ℓ$

Self inductance of inner solenoid

$\begin{array}{l} = μ_{o} n_{1}^{2} R_{2}^{2} ℓ \\ Ratio = \frac{n_{2}}{n_{1}} \end{array}$

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