Question

Two charges $1\mu \text{C}$ and $3\mu \text{C}$ are placed at separation of $1\text{m}$. Where should a third charge be placed such that it experiences no net force due to these charges?

• A. $\frac{\sqrt{3}+1}{2}\text{m}$ from $1\mu \text{C}$ charge
• B. $\frac{\sqrt{3}-1}{2}\text{m}$ from $1\mu \text{C}$ charge
• C. $\frac{\sqrt{3}-1}{2}\text{m}$ from $3\mu \text{C}$ charge
• D. $\frac{\sqrt{3}+1}{4}\text{m}$ from $1\mu \text{C}$ charge

Answer 1

The correct option is B $\frac{\sqrt{3}-1}{2}\text{m}$ from $1\mu \text{C}$ charge

Let the third charge $Q$ be placed at point $B$ at a distance $x$ from the charge $q_1$, such that it experiences no net force due to the other two charges $q_1$ and $q_2$ as shown in the figure.

As the net force on charge $Q$ is zero, according to Coulomb’s law:
$\frac{k{q}_{1}Q}{x^2}=\frac{k{q}_{2}Q}{(1-x{)}^2}$
$\Rightarrow \frac{1\times {10}^{-6}}{x^2}=\frac{3\times {10}^{-6}}{(1-x{)}^2}$
$\Rightarrow x=\frac{\sqrt{3}-1}{2}\text{m}$
Hence, the correct answer is option (b).