Two concentric co-planar circular loops of radius R and r(

Question

Two concentric co-planar circular loops of radius R and r( < < R) are placed as shown in the figure. The mutual inductance of the system will be <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-cxvrw5ida4h70qhw.jpg" /> (A) (π μ 0 r2/2 R) (B) (π μ 0 r2/4 R) (C) (π μ 0 R2/4 r) (D) (π μ 0 R2/2 r)

Tardigrade Admin · Accepted Answer

The magnetic flux through the smaller loop due to the bigger loop is

(ϕ)_{21} = (\frac{( μ ) _{0} i}{2 R}) \times π r^{2}

\Rightarrow M = \frac{( ϕ ) _{21}}{i} = (\frac{π ( μ ) _{0} r ^{2}}{2 R})

Q. Two concentric co-planar circular loops of radius $R$ and $r (<< R)$ are placed as shown in the figure. The mutual inductance of the system will be

$\frac{π μ _{0} r ^{2}}{2 R}$

$\frac{π μ _{0} r ^{2}}{4 R}$

$\frac{π μ _{0} R ^{2}}{4 r}$

$\frac{π μ _{0} R ^{2}}{2 r}$

The magnetic flux through the smaller loop due to the bigger loop is
$(ϕ)_{21} = (\frac{( μ ) _{0} i}{2 R}) \times π r^{2}$
$\Rightarrow M = \frac{( ϕ ) _{21}}{i} = (\frac{π ( μ ) _{0} r ^{2}}{2 R})$

Q. Two concentric co-planar circular loops of radius R and r(<<R) are placed as shown in the figure. The mutual inductance of the system will be

2Rπμ0​r2​

4Rπμ0​r2​

4rπμ0​R2​

2rπμ0​R2​