Question

A square loop of edge length $a$ is placed in the same plane as long straight wire carrying current $i$. The center of the loop is at distance $r$ from wire where $r$>>$a$. If loop is moved away from the wire at a constant velocity of $v$ induced emf in the loop is

• A. $\frac{{\mu }_{0}iv}{2\pi }$
• B. $\frac{{\mu }_{0}iav}{2\pi r}$
• C. $\frac{{\mu }_{0}i{a}^{2}v}{2\pi r^2}$
• D. $\frac{{\mu }_{0}i{a}^{3}v}{2\pi r^3}$

Answer 1

The correct option is C $\frac{{\mu }_{0}i{a}^{2}v}{2\pi r^2}$


$\Phi =B.A=\frac{{\mu }_0}{2\pi }\frac{i}{r}{a}^2$

$\epsilon =\frac{d\Phi }{dt}=\frac{{\mu }_0}{2\pi }i{a}^2$.$\frac{d}{dt}{r}^{-1}=\frac{{\mu }_0}{2\pi }\frac{i{a}^2}{r^2}v$