Three charges $-\mathrm{q}, \mathrm{Q}$ and $-\mathrm{q}$ are placed at equal distances on a straight line. If the total potential energy of the system of three charges is zero, then the ratio $\frac{\mathrm{Q}}{\mathrm{q}}$ is

• A

  1 : 2
• B

  1 : 1
• Correct answer
  C

  1 : 4
• D

  1 : 3

Solution

Potential energy of the system is zero. $$ \begin{aligned} & \therefore \frac{1}{4 \pi \varepsilon_0}\left(\frac{-\mathrm{q} \cdot \mathrm{Q}}{\mathrm{x}}+\frac{-\mathrm{q} \cdot \mathrm{Q}}{\mathrm{x}}+\frac{(-\mathrm{q})(-\mathrm{q})}{2 \mathrm{x}}\right)=0 \\ & \therefore-2 \mathrm{qQ}+\frac{\mathrm{q}^2}{2}=0 \\ & \therefore 2 \mathrm{Q}=\frac{\mathrm{q}}{2} \text { or } \frac{\mathrm{Q}}{\mathrm{q}}=\frac{1}{4} \end{aligned} $$

Hence, the correct answer is option: 'C'.