Question

Two charges e and 3e are placed at a distance r. The distance of the point where the electric field will be zero is

Answer 1

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Given :

Two point charges of value e and 3e are placed at distance r.

To Find :

A point where electric field due to both charges will be zero.

Formula :

Formula of electric field is given by...

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \dag \: \underline{ \boxed{ \bold{ \rm{ \pink{E = \frac{kq}{ {r}^{2} }}}}}} \: \dag$

Calculation :

Let distance of null point from e charge be x m and distance from 3e charge be (r-x) m.

$\implies \rm \: \red{E_1 = E_2} \\ \\ \implies \rm \: \frac{ke}{ {x}^{2} } = \frac{k(3e)}{ {(r - x)}^{2} } \\ \\ \therefore \rm \frac{r - x}{x} = \sqrt{3} \\ \\ \implies \rm \: r - x = \sqrt{3} x \\ \\ \therefore \rm \: \orange{ x = \frac{r}{1 + \sqrt{3}}\:m }$