JEE Main 2021 — Electromagnetic Induction Question with Solution

We know, Emf = Blv

where B, l and v are mutually perpendicular to each other. If any two are not perpendicular to each other then Emf = 0.

Here for part AB and DC, length l and velocity v is parallel to each other so, Emf by AB and DC is zero.

Given $$\overrightarrow{B}=B_0\left(\frac{x}{a}\right)\hat{k}$$

At x = 0,

$$B=B_0\left(\frac{0}{a}\right)$$

$$=0$$

$$\therefore$$ For part AD, Emf = 0

In BC part,

x = d

$$\therefore$$ $$B=B_0\left(\frac{d}{a}\right)$$

And Emf for BC part,

$$\epsilon$$ $$=Bvd$$

Here B, v, d are mutually perpendicular to each other.

$$\therefore$$ $$\epsilon$$ $$=B_0\left(\frac{d}{a}\right)\times v_0\times d$$

$$=\frac{B_0{v}_0{d}^2}{a}$$