QJEEM21Phd36a: JEE Main 2021 Physics - Class 12 JEEM21Phd36a Solution: The magnetic field in a region is given by . A square loop of…

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 $\overrightarrow B = {B_0}\left( {{x \over a}} \right)\widehat k$

At x = 0,

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

$= 0$

$\therefore$ For part AD, Emf = 0

In BC part,

x = d

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

And Emf for BC part,

$\varepsilon$ $= Bvd$

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

$\therefore$ $\varepsilon$ $= {B_0}\left( {{d \over a}} \right) \times {v_0} \times d$

$= {{{B_0}{v_0}{d^2}} \over a}$