Alternating Current Question 6
Question 6 - 29 January - Shift 1
Find the mutual inductance in the arrangement, when a small circular loop of wire of radius ’ $R$ ’ is placed inside a large square loop of wire of side $L$ $(L»R)$. The loops are coplanar and their centres coincide :
(1) $M=\frac{\sqrt{2} \mu_0 R^{2}}{L}$
(2) $M=\frac{2 \sqrt{2} \mu_0 R}{L^{2}}$
(3) $M=\frac{2 \sqrt{2} \mu_0 R^{2}}{L}$
(4) $M=\frac{\sqrt{2} \mu_0 R}{L^{2}}$
Show Answer
Answer: (3)
Solution:
Formula: Magnetic Flux
$\phi=Mi$
$\phi=(\mathbf{B A})$
$\phi=\pi R^{2}\left(4 \frac{\mu _0}{4 \pi} \frac{i}{\left(\frac{L}{2}\right)} \sqrt{2}\right)$
$\Rightarrow M=\frac{2 \sqrt{2} \mu _0 R^{2}}{L}$
