First slide

Inductance

Question

Two loops with sides L and l (L>>l) are placed concentrically and coplanar as shown in fig. (9). The
mutual inductance of the system is proportional to

Moderate

A

l²/L²
B

L²/l²
C

l/L²
D

l²/L

Solution

The value of B is given by
$B = \frac{2 \sqrt{2} μ_{0} i}{πL}$
The flux linked with the smaller loop
$\begin{array}{l} Φ = Mi = BA = {Bl}^{2} \\ ∴ Mi = \frac{2 \sqrt{2} μ_{0} {il}^{2}}{- I} or m \propto l^{2} / L \end{array}$

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