A 20 m long uniform copper wire held horizontally is allowed to fall under the gravity $\left(g=10 \

Question

A 20 m long uniform copper wire held horizontally is allowed to fall under the gravity $\left(g=10 \mathrm{~m} / \mathrm{s}^2\right)$ through a uniform horizontal magnetic field of 0.5 Gauss perpendicular to the length of the wire. The induced EMF across the wire when it travells a vertical distance of 200 m is $\_\_\_\_$ mV .

Professor PC Thomas Classes · Answer

The velocity of the wire after falling $200 	ext{ m}$ is $v = \sqrt{2gh} = \sqrt{2 	imes 10 	imes 200} = \sqrt{4000} = 20\sqrt{10} 	ext{ m/s}$. The motional EMF induced in the wire is $E = Bvl$. Given $B = 0.5 	ext{ Gauss} = 0.5 	imes 10^{-4} 	ext{ T}$ and length $l = 20 	ext{ m}$. Substituting these values: $E = (0.5 	imes 10^{-4}) 	imes (20\sqrt{10}) 	imes 20 = 200 	imes 10^{-4} 	imes \sqrt{10} = 0.02\sqrt{10} 	ext{ V}$. Converting to millivolts (mV) gives $0.02\sqrt{10} 	imes 1000 = 20\sqrt{10} 	ext{ mV}$.