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Question
Obtain the expression for mutual inductance of a pair of long coaxial solenoids each of length l and radii r1 and r2 (r2 >> r1). Total number of turns in the two solenoids are N1 and N2, respectively.
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Solution
Suppose a current i is passed through the inner solenoid S1.
A magnetic field B=μ0n1i is produced inside S1 , whereas the field outside it is zero.
The flux through each turn S2 is Bπr12=μ0n1iπr12
The total flux through all the turns in a length l of S2 is
ϕ=(μ0n1iπr12)n2l=(μ0n1n2πr12l)i
⇒M=μ0n1n2πr12l
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