Two concentric circular coils, one of small radius $${r_1}$$ and the other of large radius $${r_2},$$ such that $${r_1<<r_2},$$  are placed co-axially with centres coinciding. The mutual inductance of the arrangement is:
1. $$\dfrac{\mu_0\pi r_1^2}{3r_2}$$

2. $$\dfrac{2\mu_0\pi r_1^2}{r_2}$$
3. $$\dfrac{\mu_0\pi r_1^2}{r_2}$$
4. $$\dfrac{\mu_0\pi r_1^2}{2r_2}$$

Subtopic: Â Mutual Inductance |
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The dimensions of mutual inductance $$(M)$$ are:
1. $$\left[M^2LT^{-2}A^{-2}\right]$$
2. $$\left[MLT^{-2}A^{2}\right]$$
3. $$\left[M^{2}L^{2}T^{-2}A^{2}\right]$$
4. $$\left[ML^{2}T^{-2}A^{-2}\right]$$

Subtopic: Â Mutual Inductance |
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A small solenoid is kept inside a much larger solenoid, with their axes parallel to each other. The small solenoid has a cross-sectional radius $$r_1,$$ length $$l_1$$ and the total number of turns $$N_1.$$ The corresponding quantities for the larger solenoid are: $$r_2,~ l_2,~ N_2$$ respectively.
Their mutual inductance is (nearly) given by:
1. $$\frac{\mu_0\pi r^2_1N_1N_2}{l_2}$$
2. $$\frac{\mu_0\pi r^2_1N_1N_2}{\sqrt{l_1l_2}}$$
3. $$\frac{\mu_0\pi r^2_1N_1N_2}{l_1}$$
4. $$\frac{\mu_0~\pi r_1r_2N_1N_2}{\sqrt{l_1}}$$
Subtopic: Â Mutual Inductance |
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