Question

In the given figure a straight long wire carrying a current i and a rod of length L coplanar with the wire and perpendicular to it moves with a constant velocity v in a direction parallel to the wire. The distance of the wire from the centre of the rod is L. Find the motional emf induced in the rod.

• A. $\frac{{\mu }_{0}iv}{2\pi }ln3$
• B. $\frac{{\mu }_{0}iv}{2\pi }ln3\frac{3}{2}$
• C. $\frac{{\mu }_{0}iv}{2\pi }ln3\frac{4}{3}$
• D. $\frac{{\mu }_{0}iv}{2\pi }ln3\frac{9}{4}$

Answer 1

The correct option is A $\frac{{\mu }_{0}iv}{2\pi }ln3$

$\epsilon ={\int }_{\frac{L}{2}}^{\frac{3L}{2}}Bvdx$
$={\int }_{\frac{L}{2}}^{\frac{3}{2}}\frac{{\mu }_0}{2\pi }\cdot \frac{i}{x}=\frac{{\mu }_0}{2\pi }vi[lnx{]}_{\frac{L}{2}}^{\frac{3L}{2}}=\frac{{\mu }_0}{2\pi }iv(ln3)$