Question

Two long conductors, separated by a distance d carry currents $I_1$ and $I_2$ in the same direction. They exert a force F on each other. Now the current in one of them is increased to two times and its direction is reversed. The distance is also increased to 3 d. 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 acting between two current carrying conductors $F=\frac{{\mu }_0}{2\pi }\frac{I_1{I}_2}{d}l$ ?(i) where $d=$ distance between the conductors, $l=$ length of each conductor. Again $F=\frac{{\mu }_0}{2\pi }\frac{(-2I_1)(I_2)}{(3d)}.l$ $=-\frac{{\mu }_0}{2\pi }\frac{2I_1{I}_2}{3d}.l$ ...(ii) Thus, from Eqs. (i) and (ii) $\frac{F}{F}=-\frac{2}{3}$ $\Rightarrow$ $F=-\frac{2}{3}F$