Two parallel wires P and Q Placed at a separation d= 6 cm on x-axis carry electric current i₁=5A and i₂=2 A in opposite directions as shown in figure. Find the point on the line PQ where the resultant magnetic field is zero. 

) At the desired point, the magnetic fields due to the two wires must have equal magnitude but opposite directions. The point should be either to the left of P or to the right of Q. As the wire Q has smaller current, the point should be closer to Q. Let this point R be at a distance x from Q. The magnetic field at R due to the current i₁, will have magnitude

$B_1=\frac{{\mu }_{0}i}{2\pi (d+x)}$

and will be directed in the plane of the figure. The field at the same point due to the current  i₂will be

$$\begin{gathered} B_2=\frac{{\mu }_0{i}_2}{2\pi x} \\ \text{ directed upward in the plane of the figure. If the resultant field at }R\text{ is zero, we should have }{B}_1=B_2\text{, so that }\frac{i_1}{d+x}=\frac{i_2}{x} \\ \text{ Hence, }x=\frac{i_{2}d}{i_1-i_2}=\frac{(2 \mathrm{A})(6 \mathrm{cm})}{(3 \mathrm{A})}=4 \mathrm{cm} \end{gathered}$$