Answer to Question #234236 in Electricity and Magnetism for Fizza

Question

Where is zero field occur between two opposite charges of sme magnitude

Answer 1

$E_1+E_2=E=0,$

$E_1=-E_2,$

$q_1>0,~q_2<0,$

$\frac{kq_1}{x^2}=-\frac{kq_2}{(r-x)^2},$

$\sqrt{-\frac{q_1}{q_2}}=\frac x{r-x},$ $\implies$

$x=\frac{r\sqrt{-\frac{q_1}{q_2}}}{1+\sqrt{-\frac{q_1}{q_2}}}=\frac{r\sqrt{q_1}}{\sqrt{q_1}+\sqrt{-q_2}}.$