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

$\phi=\mathrm{Mi}$

$\phi=(\mathbf{B A})$

$\phi=\pi \mathrm{R}^{2}\left(4 \frac{\mu_{0}}{4 \pi} \frac{\mathrm{i}}{\left(\frac{\mathrm{L}}{2}\right)} \sqrt{2}\right)$

$\Rightarrow \mathrm{M}=\frac{2 \sqrt{2} \mu_{0} \mathrm{R}^{2}}{\mathrm{~L}}$