# Two charges +Q and -Q are kept at $(-x_2, 0)$ and $(x_1, 0)$ respectively in the X-Y plane. Find the magnitude and direction of the net electric field at the origin (0, 0).

Electric field intensity at O due to +Q charge
$E_1 =\large\frac{1}{4 \pi \in _0 }\frac{Q}{(x_2)^2}$------(i)
Electric field intensity at O due to Q charge
$E_2 =\large\frac{1}{4 \pi \in _0 }\frac{Q}{(x_1)^2}$------(ii)
$E_1$ and $E_2$ act along the same direction.
Net electric field intensity
$E=E_1 +E_2$
$\qquad =\large\frac{1}{4 \pi \in _0 }\frac{Q}{(x_2)^2}+\large\frac{1}{4 \pi \in _0 }\frac{Q}{(x_1)^2}$
$\qquad=\large\frac{Q}{4 \pi \in _0 } \bigg[\frac{1}{(x_2)^2}+ \frac{1}{x_1^2}\bigg]$