Question
Find the mutual inductance between the circular coil and the loop shown in figure.
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Answer
emf induced $=\frac{\pi\mu_0\text{Na}^2\text{a}'^2\text{ERV}}{2\text{L}(\text{a}^2+\text{x}^2)^{\frac{3}{2}}\Big(\frac{\text{R}}{\text{L}\text{x}}+\text{r}\Big)^2}$
$\frac{\text{dl}}{\text{dt}}=\frac{\text{ERV}}{\text{L}\Big(\frac{\text{Rx}}{\text{L}}+\text{r}\Big)^2}$
$\mu=\frac{\text{E}}{\frac{\text{di}}{\text{dt}}}=\frac{\text{N}\mu_0\pi\text{a}^2\text{a}'^2}{2(\text{a}^2+\text{x}^2)^{\frac{3}{2}}}$
$\frac{\text{dl}}{\text{dt}}=\frac{\text{ERV}}{\text{L}\Big(\frac{\text{Rx}}{\text{L}}+\text{r}\Big)^2}$
$\mu=\frac{\text{E}}{\frac{\text{di}}{\text{dt}}}=\frac{\text{N}\mu_0\pi\text{a}^2\text{a}'^2}{2(\text{a}^2+\text{x}^2)^{\frac{3}{2}}}$
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