First slide

Inductance

Question

A small coil of radius r is placed at the center of a large coil of radius R, where R >> r. The two coils are coplanar. The mutual inductance between the coils is proportional to

Moderate

A

r/R
B

r²/R
C

r²/R²
D

r/R²

Solution

Magnetic field at the centre of a large coil $E \propto \frac{μ_{0} I}{2 R}$
Magnetic flux linked with smaller coil $= \frac{μ_{0} I}{2 R} \times π r^{2}$
$M = \frac{ϕ}{I} = \frac{μ_{0} π r^{2}}{2 R} ∴ M \propto \frac{r^{2}}{R}$

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