Question

Two point charges + I q and -2 q are located at x = 0 and x = 1 respectively. The location of a point on the X-axis at which the net electric field due to these two point charges is zero is

Easy

Solution

Let the electric field be zero at a distance d from x = o as shown in fig.
The electric field E at O is given by
$E = \frac{1}{4 {πε}_{0}} \cdot \frac{8 q}{d^{2}} + \frac{1}{4 {πε}_{0}} \frac{(- 2 q)}{(L - d)^{2}} or \frac{8}{d^{2}} = \frac{2}{(L - d)^{2}}$
Solving, we get d = 2L

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