Question

Three charges $-q,Qand-q$ 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 $Q:q$ is :

• A. $1:2$
• B. $2:1$
• C. $1:1$
• D. $1:4$

Answer 1

Answer: (D)

$\text{Step 1 : Figure of arrangement}$ $\text{[Ref.Fig.]}$

$\text{Step 2 : Expression of potential Energy of system of charged particles.}$

As potential energy is scalar quantity, so it will be added for all the combinations:

$U=\frac{K{Q}_1{Q}_2}{d}+\frac{K{Q}_2{Q}_3}{d}+\frac{K{Q}_1{Q}_3}{2d}$

$\Rightarrow U=\frac{-KQq}{d}-\frac{KQq}{d}+\frac{K{q}^2}{2d}=0$ (Given that, the Total Potential Energy of system is equal to zero)

$\Rightarrow q^2=4qQ$

$\Rightarrow Q:q=1:4$

Hence ratio od $Q:q$ is equal to $1:4$

Option $D$ correct.