Three charges q, -q, q_o are placed as shown in figure. The magnitude of the net force on the charge q_o at point O is $\left\{\mathrm{k}=\frac{1}{4{\mathrm{\pi \epsilon }}_0}\right\}$

Let repulsive force on q₀ due to q be $\overrightarrow{\mathrm{F}}$ and attractive force on q₀ due to -q be $\overrightarrow{{\mathrm{F}}_2}$
Now,


${\mathrm{F}}_1=\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{{\mathrm{q}}_0\cdot \mathrm{q}}{{\mathrm{a}}^2}\text{ and }{\mathrm{F}}_2=\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{{\mathrm{q}}_0\mathrm{q}}{{\mathrm{a}}^2}$
So magnitude of resultant force ${\mathrm{F}}_{\mathrm{R}}=\sqrt{{\mathrm{F}}_1^2+{\mathrm{F}}_2^2}$
$=\sqrt{{\left(\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{{\mathrm{q}}_0\cdot \mathrm{q}}{{\mathrm{a}}^2}\right)}^2+{\left(\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{{\mathrm{q}}_0\cdot \mathrm{q}}{{\mathrm{a}}^2}\right)}^2}=\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{{\mathrm{q}}_0\cdot \mathrm{q}}{{\mathrm{a}}^2}\sqrt{2}$