Question

As shown in the figure, a rectangular loop of a conducting wire is moving away with a constant velocity 'v' in a perpendicular direction from a very long straight conductor a steady conductor carrying a steady current 'I'. When the breadth of the rectangular loop is very small compared to its distance from the straight conductor.

• A. $E\propto \frac{1}{t^2}$
• B. $E\propto \frac{1}{t}$
• C. $E\propto ln\left(t\right)$
• D. $E\propto \frac{1}{t^3}$

Answer 1

The correct option is A $E\propto \frac{1}{t^2}$

$\epsilon =-\frac{d\varphi }{dt}$
$\epsilon =-\frac{d(B.A)}{dt}$
$\epsilon =-A\frac{dB}{dt}$
$=-A\frac{d}{dt}\frac{{\mu }_{o}i}{2\pi \left(vt\right)}$
$\Rightarrow -Ai\frac{{\mu }_o}{2\pi v}\frac{d}{dt}\left(t^{-1}\right)$
$\Rightarrow Ai\frac{{\mu }_o}{2\pi v}{t}^{-2}$
$\epsilon \propto \frac{1}{T^2}$.