Question

A straight conductor carrying current $i$ and a loop closed by a sliding connector of resistance $R$ lies in the same plane as shown in the figure. The connector slides towards right with a uniform velocity $v$. The induced current generated in the loop in terms of distance $r$ of the connector from the straight conductor will be

• A. $\frac{{\mu }_{0}ilv}{\pi rR}$
• B. $\frac{{\mu }_{0}ilv}{3\pi rR}$
• C. $\frac{{\mu }_{0}ilv}{2\pi rR}$
• D. $\frac{2{\mu }_{0}ilv}{\pi rR}$

Answer 1

The correct option is C $\frac{{\mu }_{0}ilv}{2\pi rR}$


The magnetic field due to an infinite straight conductor is given by,

$B=\frac{{\mu }_{0}i}{2\pi r}$

Induced $emf$,

$E=Bvl=\frac{{\mu }_{0}i}{2\pi r}\times v\times l$

$\therefore$ Induced current, $i=\frac{E}{R}$

$\Rightarrow i=\frac{{\mu }_{0}ilv}{2\pi rR}$

Hence, option $\left(C\right)$ is correct.