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

The Correct Option is C

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:

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