Two charges e and 3 e are placed at a distance r . distance of point where electric field intensity

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1. Electric Charges and Fields

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

A

$\frac{r}{(1+\sqrt{3})}$ from $3 e$ charge

B

$\frac{r}{(1+\sqrt{3})}$ from $e$ charge

C

$\frac{r}{(1-\sqrt{3})}$ from $3 e$ charge

D

$\frac{r}{1+\sqrt{\frac{1}{3}}}$ from $e$ charge

Solution

(b)

Net electric field at $P$ is zero then

$O=E_1-E_2$

$E_1=E_2$

$\frac{k e}{x^2}=\frac{k 3 e}{(r-x)^2}$

so, $\frac{1}{x}=\frac{\sqrt{3}}{r-x}$

$r-x=\sqrt{3} x$

$r=x[1+\sqrt{3}]$

$x=\frac{r}{(1+\sqrt{3})}$

Standard 12

Physics

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