Three charges, each $+q$, are placed at the corners of an isosceles triangle $A B C$ of sides $B C$ and $A C, 2 a . D$ and $E$ are the mid points of $B C$ and $C A$. The work done in taking a charge $Q$ from $D$ to $E$ is

• A

  $\frac{e q Q}{8 \pi \varepsilon_0 a}$
• B

  $\frac{q Q}{4 \pi \varepsilon_0 a}$
• Correct answer
  C

  zero
• D

  $\frac{3 q Q}{4 \pi \varepsilon_0 a}$

Solution

$$ \text { Here, } A C=B C $$
$$ \begin{aligned} & V_D=V_E=V \\ & W=Q\left[V_E-V_D\right] \\ & W=Q[V-V] \\ & W=0 \end{aligned} $$

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