A 20 m long uniform copper wire held horizontally is allowed to fall under the gravity (g = 10 m/s²) through a uniform horizontal magnetic field of 0.5 Gauss perpendicular to the length of the wire. The induced EMF across the wire it travells a vertical distance of 200 m i $s _____$ mV.
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Question

A 20 m long uniform copper wire held horizontally is allowed to fall under the gravity (g = 10 m/s²) through a uniform horizontal magnetic field of 0.5 Gauss perpendicular to the length of the wire. The induced EMF across the wire it travells a vertical distance of 200 m i $s _____$ mV.

Options

G1 Physics · Accepted Answer

The wire falls freely through height h = 200 m. Starting from rest, v = √(2gh) = √(2×10×200) = √4000 = 20√10 m/s. The magnetic field is B = 0.5 Gauss = 0.5 × 10⁻⁴ T. The wire length is ℓ = 20 m. Since the wire moves perpendicular to its length and to the magnetic field, the motional emf is ε = Bℓv. Therefore, ε = (0.5 × 10⁻⁴)(20)(20√10) = 20√10 × 10⁻³ V. Since 1 V = 10³ mV, ε = 20√10 mV. Correct option: B.

A 20 m long uniform copper wire held horizontally is allowed to fall under the gravity (g = 10 m/s²) through a uniform horizontal magnetic field of 0.5 Gauss perpendicular to the length of the wire. The induced EMF across the wire it travells a vertical distance of 200 m i s _____ mV.