Question

Two parallel wires separated by a distance of $10cm$ carry currents of $10A$ and $40A$ along the same direction. Where should a third current be placed so that it experiences no magnetic force ?

Answer 1

Force acting on the third wire by other two wires must be equal in magnitude.

$\frac{{\mu }_{0}10i}{2\pi x}=\frac{{\mu }_{0}i40}{2\pi (10-x)}$

$\Rightarrow \frac{10}{x}=\frac{40}{10-x}\Rightarrow \frac{1}{x}=\frac{4}{10-x}$

$\Rightarrow 10-x=4x\Rightarrow 5x=10\Rightarrow x=2cm$

The third wire should be placed $2cm$ from the $10A$ wire and $8cm$ from $40A$ wire.