Three charges, each $+\mathrm{q}$, are placed at the comers of an isosceles triagle $A B C$ of sides $B C$ and $A C$, 2a. D and E are the mid-points of BC and CA. The work done in taking a charge $Q$ from $D$ to $E$ is

• A

  $\frac{\mathrm{eq} \mathrm{Q}}{8 \pi \varepsilon_{0} \mathrm{a}}$
• B

  $\frac{\mathrm{qQ}}{4 \pi \varepsilon_{0} \mathrm{a}}$
• Correct answer
  C

  Zero
• D

  $\frac{3 \mathrm{q} \mathrm{Q}}{4 \pi \varepsilon_{0} \mathrm{a}}$

Solution

Here, $\mathrm{AC}=\mathrm{BC}$
$$ \mathrm{V}_{\mathrm{D}}=\mathrm{V}_{\mathrm{E}}=\mathrm{V} $$ $$ \begin{array}{l} \mathrm{W}=\mathrm{Q}\left[\mathrm{V}_{\mathrm{E}}-\mathrm{V}_{\mathrm{D}}\right] \\ \mathrm{W}=\mathrm{Q}[\mathrm{V}-\mathrm{V}] \\ \mathrm{W}=0 \end{array} $$

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