Electromagnetic Induction Part 2

Concept:The induced EMF is given by the rate of change of magnetic flux through the loop, as per Faraday's law.Explanation:The loop is reshaped from a circle to a square, keeping the wire length constant.This changes the area and thus the magnetic flux.Initial radius: $r = 7 \text{ cm} = 0.07 \text{ m}$.Initial area: $A_1 = \pi r^2 = \pi (0.07)^2 = 0.0154 \text{ m}^2$.Circumference of circle = $2\pi r = 2\pi \times 0.07$ m.Perimeter of square = same as circumference, so side $a = \frac{2\pi r}{4} = \frac{\pi \times 0.07}{2} = 0.11$ m.Final area: $A_2 = a^2 = (0.11)^2 = 0.0121$ m$^2$.Change in area: $\Delta A = A_2 - A_1 = -0.0033 \text{ m}^2$.Magnetic field $B = 0.2$ T is constant and perpendicular to the plane.Change in flux: $\Delta \phi = B \cdot \Delta A = 0.2 \times (-0.0033) = -0.00066$ Wb.Time taken: $\Delta t = 0.5$ s.Induced EMF magnitude: $|E| = \left|\frac{\Delta \phi}{\Delta t}\right| = \frac{0.00066}{0.5} = 0.00132$ V.Convert to mV: $0.00132 \times 1000 = 1.32$ mV.Answer:The induced EMF is $1.32$ mV, so option C is correct.