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

2. \(\frac{2\mu_0\pi r_1^2}{r_2}\)
3. \(\frac{\mu_0\pi r_1^2}{r_2}\)
4. \(\frac{\mu_0\pi r_1^2}{2r_2}\)

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

Subtopic:  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.  \(\frac{\mu_0~\pi rr_1r_2N_1N_2}{\sqrt{l_1}}\)
Subtopic:  Mutual Inductance |
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