Question

A square frame with side $a$ and a long straight wire carrying a current $i$ are located in the same plane as shown in figure. The frame translates to the right with constant velocity $v$. Find the emf induced in the frame as a function of distance $x$.

• A. $\frac{{\mu }_0}{7\pi }\frac{2i{a}^{3}v}{x(x+a)}$
• B. $\frac{{\mu }_0}{4\pi }\frac{2i{a}^{2}v}{x(x+a)}$
• C. $\frac{{\mu }_0}{2\pi }\frac{2i{a}^{4}v}{x(x+a)}$
• D. $\frac{{\mu }_0}{3\pi }\frac{7i{a}^{2}v}{x(x+a)}$

Answer 1

The correct option is B $\frac{{\mu }_0}{4\pi }\frac{2i{a}^{2}v}{x(x+a)}$

$e_{net}=e_1-e_2$
$=B_{1}va-B_{1}va$
$=[\frac{{\mu }_0}{2\pi }\frac{i}{x}-\frac{{\mu }_0}{2\pi }\frac{i}{x+a}]va$

$=\frac{{\mu }_0}{4\pi }\frac{2i{a}^{2}v}{x(x+a)}$