A small square loop of side 'a' and one turn is placed inside a l… - Vidyadip

MCQ

A small square loop of side $'a'$ and one turn is placed inside a larger square loop of side ${b}$ and one turn $(b \gg a)$. The two loops are coplanar with thei centres coinciding. If a current $I$ is passed in the square loop of side $'b',$ then the coefficient of mutual inductance between the two loops is

✓
$\frac{\mu_{0}}{4 \pi} 8 \sqrt{2} \frac{{a}^{2}}{{b}}$
B
$\frac{\mu_{0}}{4 \pi} \frac{8 \sqrt{2}}{{a}}$
C
$\frac{\mu_{0}}{4 \pi} 8 \sqrt{2} \frac{{b}^{2}}{{a}}$
D
$\frac{\mu_{0}}{4 \pi} \frac{8 \sqrt{2}}{{b}}$

✓

Answer

Correct option: A.

$\frac{\mu_{0}}{4 \pi} 8 \sqrt{2} \frac{{a}^{2}}{{b}}$

a
${B}=\left[\frac{\mu_{0}}{4 \pi} \frac{{I}}{{b} / 2} \times 2 \sin 45\right] \times 4$

$\phi=2 \sqrt{2} \frac{\mu_{0}}{\pi} \frac{{I}}{{b}} \times {a}^{2}$

$\therefore {M}=\frac{\phi}{{I}}=\frac{2 \sqrt{2} \mu_{0} {a}^{2}}{\pi {b}}=\frac{\mu_{0}}{4 \pi} 8 \sqrt{2} \frac{{a}^{2}}{{b}}$

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