The magnetic field in a region is given by B = Bo(x/a)k. A square… | JEE Main 2021 (16 Mar, Shift 2)

Q41JEE Main 2021 · 16 MAR · SHIFT 2Medium

Motional EMF

The magnetic field in a region is given by $\vec{B} = B_o\left(\frac{x}{a}\right)\hat{k}$ . A square loop of side d is placed with its edges along the x and y axes. The loop is moved with a constant velocity $\vec{v}$ = v0 $\hat{i}$ . The emf induced in the loop is:

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Answer: (d)

Sides parallel to $x$ give no net emf; each side parallel to $y$ (length $d$ ) has emf $B d v_0$ .
Left side at $x$ : $B_1 = B_0\dfrac{x}{a}$ ; right side at $x + d$ : $B_2 = B_0\dfrac{x+d}{a}$ .
The two emfs oppose, so $e = (B_2 - B_1) d v_0 = \dfrac{B_0 d}{a} \cdot d v_0$
So the answer is (d) $\dfrac{B_0 v_0 d^2}{a}$ .

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