Two parallel wires P  and Q  placed at a separation $\mathrm{d}=6\mathrm{cm}$  carry electric currents  ${\mathrm{i}}_1=5\mathrm{A}$ and ${\mathrm{i}}_2=2\mathrm{A}$  in opposite directions as shown in figure. Find the point on the line PQ  (in cm) 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 ${\mathrm{B}}_1=\frac{{\mathrm{\mu }}_0{\mathrm{i}}_1}{2\mathrm{\pi }(\mathrm{d}+\mathrm{x})}$  

and will be directed downward in the plane of the figure. 

The field at the same point due to the current i₂   will be ${\mathrm{B}}_2=\frac{{\mathrm{\mu }}_0{\mathrm{i}}_2}{2\mathrm{\pi x}}$
directed upward in the plane of the figure. 

If the resultant field at R is zero, we should have

${\mathrm{B}}_1={\mathrm{B}}_2,\text{ so that }\frac{{\mathrm{i}}_1}{\mathrm{d}+\mathrm{x}}=\frac{{\mathrm{i}}_2}{\mathrm{x}}$
giving,    

$\Rightarrow \mathrm{x}=\frac{{\mathrm{i}}_2\mathrm{d}}{{\mathrm{i}}_1-{\mathrm{i}}_2}=\frac{\begin{array}{cc}\left(2\mathrm{A}\right)\left(6\mathrm{cm}\right)& \end{array}}{\left(3\mathrm{A}\right)}=4\mathrm{cm}$