JEE Main 2025 Jan 28 Shift 2, Physics Q21: Motional EMF

JEE Main2025Jan 28, Shift 2Physics

A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field $B$ exists into the page. The bar starts to move from the vertex at time $t = 0$ with a constant velocity. If the induced EMF is $E \propto t^{n}$ , then value of $n$ is _____ .

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Solution

Let $x = v t$ be the distance from the vertex along the bisector at time $t$ . From the geometry of the V-rails with half-angle $θ$ , the length of the bar between the rails is $ℓ = 2 x tan θ$ , so $ℓ$ grows linearly with $t$ .

Induced EMF: $ε = B ℓ v = B (2 v t tan θ) v = 2 B v^{2} tan θ \cdot t$ .

So $ε \propto t^{1}$ , giving $n = 1$ .

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JEE Main 2025 Jan 28 Shift 2, Physics Q21: Motional EMF

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