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Mutual Induction

What is the m...

Question

What is the mutual inductance of a two-loop system as shown with centre separation l

A

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B

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C

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D

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Solution

The correct option is D
Magnetic field at the location of coil (2) produced due to coil (1)
$B_{1} = \frac{μ_{o}}{4 π} . \frac{2 M}{l^{3}}$
Flux linked with coil (2)
$ϕ_{2} = B_{1} A_{2} = \frac{μ_{o}}{4 π} \frac{2 i (π a^{2})}{l^{3}} \times (π a^{2})$

Also $ϕ_{2} = M_{i} \Rightarrow M = \frac{μ_{o} π a^{4}}{2 l^{3}}$

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