Three charges, each +q, are placed at the corners of an isosceles triangle ABC of sides BC, AC and AB, D and E are the mid points of BC and CA. The work done in taking a charge Q from D to E is ?

Three charges, each +q, are placed at the corners of an isosceles triangle ABC of sides BC, AC and AB, D and E are the mid points of BC and CA. The work done in taking a charge Q from D to E is ?

\( \text{(a)} \ \frac{3qQ}{8\pi \varepsilon_0 a} \)

\( \text{(b)} \ \frac{qQ}{4\pi \varepsilon_0 a} \)

\( \text{(c)} \ \text{zero} \)

\( \text{(d)} \ \frac{3qQ}{4\pi \varepsilon_0 a} \)

Answer :  \( \text{(c)} \ \text{zero} \)

\( \text{By symmetry we can see:} \quad U_E = U_D \)

\( \text{Work} = \text{change in P.E.} \)

\( W = \Delta U \)

\( = U_f - U_i \)

\( = U_E - U_D \)

\( = 0 \)