Question

Two charges $q$ and $3q$ are separated by a distance $r$ in air. At a distance $x$ from charge $q$, the resultant electric field is zero. The value of $x$ is:

• A. $\frac{1 + \sqrt{3}}{r}$
• B. $\frac{r}{3(1 + \sqrt{3})}$
• C. $\frac{r}{1 + \sqrt{3}}$
• D. $r (1 + \sqrt{3})$

Answer 1

Answer: (C)

$\frac{r}{1 + \sqrt{3}}$

Answer 2

Given two charges $q$ and $3q$ separated by a distance $r$. The electric field at a point $x$ from charge $q$ where the net electric field is zero is:

$\vec{E}_{\text{net}} = 0$

Equating the electric fields due to both charges:

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

Simplifying:

$(r - x)^2 = 3x^2$ $r - x = \sqrt{3}x$

Rearranging gives:

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