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(D) The radius of the circular loop is $r = 7 \ cm = 0.07 \ m$. The area of the circular loop is $A_1 = \pi r^2 = \pi (0.07)^2 = 0.0049 \pi \ m^2$.The

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$1.32$

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(D) The radius of the circular loop is $r = 7 \ cm = 0.07 \ m$. The area of the circular loop is $A_1 = \pi r^2 = \pi (0.07)^2 = 0.0049 \pi \ m^2$.The circumference of the loop is $C = 2 \pi r = 2 \pi (0.07) = 0.14 \pi \ m$.When converted to a square loop, the perimeter remains the same. Let the side of the square be $a$. Then $4a = 0.14 \pi$, so $a = 0.035 \pi \ m$.The area of the square loop is $A_2 = a^2 = (0.035 \pi)^2 = 0.001225 \pi^2 \ m^2$.The change in magnetic flux is $\Delta \phi = B(A_1 - A_2) = 0.2 	imes (0.0049 \pi - 0.001225 \pi^2)$.Using $\pi \approx 3.14159$, $A_1 \approx 0.01539 \ m^2$ and $A_2 \approx 0.01208 \ m^2$.$\Delta \phi = 0.2 	imes (0.01539 - 0.01208) = 0.2 	imes 0.00331 = 0.000662 \ Wb$.The induced $EMF$ is $\epsilon = \frac{|\Delta \phi|}{\Delta t} = \frac{0.000662}{0.5} = 0.001324 \ V$.Converting to $mV$, $\epsilon = 1.324 \ mV \approx 1.32 \ mV$.

$A$ circular loop of radius $7 \ cm$ is placed in a uniform magnetic field of $0.2 \ T$ directed perpendicular to the plane of the loop. The loop is converted into a square loop in $0.5 \ s$. The $EMF$ induced in the loop is . . . . . . $mV$.

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