First slide
Inductance
Question

A long solenoid of length L, cross section A having N1 turns has wound about its center a small coil of N2 turns as shown in figure. The mutual inductance of two circuits is

Moderate
Solution

ϕ2=N2B1A  or  ϕ2=N2μ0N1I1LA or  ϕ2=μ0N1N2ALI1 Comparing with ϕ2=MI1, we get M2=μ0N1N2AL

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