Question

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 midpoints of BC and CA. The work done in taking a charge Q from D to E is:
(Given BC = AC )

• A. $\frac{eqQ}{8{ϵ}_{0}a}$
• B. $\frac{qQ}{4{ϵ}_{0}a}$
• C. zero
• D. $\frac{3qQ}{4{ϵ}_{0}a}$

Answer 1

The correct option is C zero

$\text{Step 1: Potential diffrence between point D and E}$

As the triangle is Isosceles with $AC=BC$ and $D$ & $E$ are midpoints of $BC$ and $AC$ respectively.

Therefore, Using geometry it can be proved that $BE=DA$

As all charges at A, B and C are equal and points D and E are equidistant from all three charges.

Therefore, it can be concluded from symmetry that the potentials at D and E are equal.

i.e., $V_D=V_E$

$\text{Step 2: Work done}$

Work done in moving charge $Q$ from D to E will be

$W=q\Delta V$ $=Q(V_E-V_D)=0$

Hence, Workdone in moving charge from D to E will be zero.

Option C is correct.