JEE Main 2026 — Jan 23, Shift 1 — Physics solution

JEE Main2026Jan 23, Shift 1Physics

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 across the wire as it travels a vertical distance of $200 m$ is ______ mV.

A
$0.2 10$
B
$2010$
C
$210$
D
$20010$

Solution

EMF for a wire moving through a perpendicular magnetic field: $ε = v B ℓ$ .

Speed after falling $h = 200 m$ : $v = 2 g h = 2 \times 10 \times 200 = 4000 = 2010 m/s$ .

Magnetic field: $B = 0.5 Gauss = 0.5 \times 1 0^{- 4} T$ . Length $ℓ = 20 m$ .

$ε = (2010) (0.5 \times 1 0^{- 4}) (20) = 2010 \times 1 0^{- 3} V = 2010 mV$ .

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