First slide

Inductance

Question

The mutual inductance between two planar concentric rings of radii $r_{1}$ and $r_{2}$ (with $r_{1} > r_{2}$ ) placed in air is given by

Moderate

A

$\frac{μ_{0} π r_{2}^{2}}{2 r_{1}}$
B

$\frac{μ_{0} π r_{1}^{2}}{2 r_{2}}$
C

$\frac{μ_{0} π {(r_{1} + r_{2})}^{2}}{2 r_{1}}$
D

$\frac{μ_{0} π {(r_{1} + r_{2})}^{2}}{2 r_{2}}$

Solution

$\frac{μ_{0} i}{2 r_{1}} x π r_{2}^{2} = ϕ = M i M = \frac{μ_{0}}{2 r_{1}} x π r_{2}^{2}$

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