Question

Two long conductors, separated by a distance d carry current $I_1$ and $I_2$ in the same direction. They exert a force $F$ on each other. Now the current in one of them increased to two times and its direction reversed. The distance is also increased to $3d$. The new value of the force between them is

• A. −2F
• B. F/3
• C. −2F/3
• D. −F/3

Answer 1

Answer: (C)

Force between two long conductor carrying current
$F=\frac{{\mu }_0}{2\pi }\frac{I_1{I}_2}{d}\ell$
According to question
$F^{\prime }=\frac{{\mu }_0}{2\pi }\frac{\left(-2I_1\right)I_2}{d}\ell$
From equation $\left(i\right)$ and $\left(ii\right)$, $F^{\prime }=-\frac{3}{2}F.$