A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular t

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 .

Professor PC Thomas Classes · Answer

The initial area of the circular loop is $A_i = \pi r^2 = \frac{22}{7} 	imes (0.07)^2 = 0.0154 	ext{ m}^2$. The perimeter of the loop is $2\pi r = 2 	imes \frac{22}{7} 	imes 0.07 = 0.44 	ext{ m}$. When reshaped into a square, the side length is $a = \frac{0.44}{4} = 0.11 	ext{ m}$. The new area is $A_f = a^2 = (0.11)^2 = 0.0121 	ext{ m}^2$. The change in magnetic flux is $\Delta \Phi = B|A_f - A_i| = 0.2 	imes (0.0154 - 0.0121) = 0.2 	imes 0.0033 = 0.00066 	ext{ Wb}$. The induced EMF is $E = \frac{\Delta \Phi}{\Delta t} = \frac{0.00066}{0.5} = 0.00132 	ext{ V} = 1.32 	ext{ mV}$.