Question
A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of 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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Solution
induced EMF $= \frac{d\phi}{dt}$
circumference $\simeq 14\pi$
side length of square loop $= \frac{14\pi}{4} = \frac{7\pi}{2}$
$${\Delta\phi = B\left( A_{1} - A_{2} \right) }{= (.2)\left( \left( \frac{7\pi}{2} \right) \times \frac{7\pi}{2} - 49\pi \right) \times 10^{- 4} }{= .2\left( \frac{49\pi^{2}}{4} - 49\pi \right) \times 10^{- 4} }{\Delta\phi = .2 \times 33.07 \times 10^{- 4} }{\Delta\phi = 6.614 \times 10^{- 4} }{EMF = \frac{6.614 \times 10^{- 4}}{\frac{1}{2}}\text{ }V = 13.23 \times 10^{- 4}\text{ }V }{EMF = 1.32mV}$$
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