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  • A small square loop of wire of side l is place inside a large square loop of wire of side  L(L > > l). The loops are coplanar and their centers coincide. The mutual inductance of

A small square loop of wire of side l is place inside a large square loop of wire of side 
L(L > > l). The loops are coplanar and their centers coincide. The mutual inductance of the system is proportional to :

Option: 1

l/L


Option: 2

l^{2} /L


Option: 3

L/l


Option: 4

L^{2} /l


Answers (1)

best_answer

Magnetic field produced by a current I in a large square loop at its center,
\mathrm{\begin{aligned} & B \propto \frac{i}{L} \\ & \text { Say } \quad B=K \frac{i}{L} \\ & \end{aligned}}
 \mathrm{\therefore } Magnetic flux linked with smaller loop,
         \mathrm{ \begin{aligned} \phi & =B . S . \\ \phi & =\left(K \frac{i}{L}\right)(R) \end{aligned}}
Therefore, the mutual inductance
\mathrm{ \begin{aligned} & M=\frac{\phi}{i}=K \frac{l^2}{L} \\ & \text { or } \quad M \propto \frac{l^2}{L} \end{aligned}}

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