Question

Three long, straight and parallel wires carrying currents are arranged as shown in the figure. The wire C Wh carries a current of 5.4 is so placed that it experience no force. The distance of wire C from wire D is the

• A. 9 cm
• B. 7 cm
• C. 5 cm
• D. 3 cm

Answer 1

The correct option is A 9 cm

For no force on wire $C$,

force on wire $C$ due to wire $D=$ force on wire $C$ due to wire $B$

Force on one wire due to the other current carrying wire is given by:

$F=\frac{{\mu }_0}{4\pi }\frac{2i_1{i}_2}{x}\times l$

So, it can be simplified as:

$\Rightarrow \frac{{\mu }_0}{4\pi }\times \frac{2\times 15\times 5}{x}\times l=\frac{{\mu }_0}{4\pi }\times \frac{2\times 10\times 5}{(15-x)}\times l$

$\Rightarrow x=9cm$