A 20 m long uniform copper wire held horizontally is allowed to fall under the gravity ( g=10 ~m / s^ 2 ) through a uniform horizontal magnetic field of 0.5 Gauss perpendicular to the length of the wire. The induced EMF

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Correct answer: A. 20 10

For a conducting wire falling in a magnetic field, induced EMF is:

\mathcal{E} = BLv

After falling through height

h = 200

m, velocity:

v = \sqrt{2gh} = \sqrt{2 \times 10 \times 200} = \sqrt{4000} = 20\sqrt{10}

m/s
Converting magnetic field:

B = 0.5

Gauss

= 0.5 \times 10^{-4}

T
Induced EMF:

\mathcal{E} = (0.5 \times 10^{-4}) \times 20 \times 20\sqrt{10} = 200 \times 10^{-4}\sqrt{10} = 0.02\sqrt{10}

V

= 20\sqrt{10}

mV

A 20 m long uniform copper wire held horizontally is allowed to...

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