Two point charges of $q_1=2\times 10^{-6}\text{ C}$ and $q_2=8\times 10^{-6}\text{ C}$ are placed $12\text{ cm}$ apart. The location of the neutral point where the electric field is zero is at a distance of:

Solution

1. Let $x$ be the distance from the $q_1=2\times 10^{-6}\text{ C}$ charge to the neutral point, where the total distance $d=12\text{ cm}$.
2. At the neutral point, the electric field magnitudes are equal: $k\frac{|q_1|}{x^2}=k\frac{|q_2|}{(d-x{)}^2}$.
3. Taking the square root of both sides gives $\frac{\sqrt{q_1}}{x}=\frac{\sqrt{q_2}}{d-x}$, which simplifies to $x=\frac{d}{1+\sqrt{q_2/q_1}}$.
4. Substituting the given values, $$\begin{array}{rl}x& =\frac{12}{1+\sqrt{8/2}}\\ & =\frac{12}{1+2}\\ & =4\text{ cm}\end{array}$$.
5. Hence the answer is (A).