Question

Three long straight and parallel wires carrying currents are arranged as shown in figure. The wire $\text{B}$ which carries a current of $5\text{A}$ is placed such that it experiences no force. The distance of wire $\text{B}$ from wire $\text{A}$ is ____ $\text{cm}$ (Give integer value)

Answer 1

$\frac{F_{AB}}{l}=\frac{{\mu }_0{i}_a{i}_b}{2\pi x}$ towards $C\dots .\left(1\right)$

$\frac{F_{CB}}{l}=\frac{{\mu }_0{i}_b{i}_c}{2\pi (15-x)}$ towards $A....\left(2\right)$

Since, wire $\text{B}$ experiences no force, $\frac{F_{AB}}{l}=\frac{F_{CB}}{l}$

$\Rightarrow \frac{{\mu }_0{i}_a{i}_b}{2\pi x}=\frac{{\mu }_0{i}_b{i}_c}{2\pi (15-x)}$

Substituting the data given in the question we get,

$\Rightarrow \frac{i_a}{x}=\frac{i_c}{(15-x)}$

$\frac{15}{x}=\frac{10}{(15-x)}\Rightarrow 45-3x=2x$

$\Rightarrow x=9\text{cm}$

Accepted answer : $9$