A 20 m long uniform copper wire held horizontally is allowed to fall under gravity through a uniform horizontal magnetic field of 0.5 Gauss perpendicular to the length of the wire. [2026]

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Solution

Q.
A 20 m long uniform copper wire held horizontally is allowed to fall under 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 across the wire when it travels a vertical distance of 200 m is ________ mV. [2026]

1 $20 \sqrt{10}$

2 $0.2 \sqrt{10}$

3 $200 \sqrt{10}$

4 $2 \sqrt{10}$

Ans.
(1)

$ε = v B ℓ$

$v = \sqrt{2 g h} = \sqrt{2 \times 10 \times 200} = 20 \sqrt{10}$

$ε = (20 \sqrt{10}) (0.5 \times 10^{- 4}) 20$

$= 20 \sqrt{10} \times 10^{- 3} = 20 \sqrt{10} mV$

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