Question

A point charge $4\mu C$ is placed at x = 0 and another point charge $-6\mu C$ is placed at x = 40 cm. If a third point charge is placed so that it experiences zero net force, its distance from the origin is nearly equal to

• A. 2 m on the negative x-axis
• B. 2m on the positive x-axis
• C. 20 cm on the positive x-axis
• D. 20 cm on the negative x-axis

Answer 1

The correct option is A 2 m on the negative x-axis

Since the charge at x is in equilibrium,
$\frac{1}{4\pi {ϵ}_0}\frac{\left(4\mu C\right)Q}{x^2}=\frac{1}{4\pi {ϵ}_0}\frac{\left(6\mu C\right)Q}{(0.4+x{)}^2}$
$\frac{4}{x^2}=\frac{6}{(0.4+x{)}^2}\Rightarrow x\approx 2m$