Question

15. Three point charges, which initially are infinitely far apart, are place at the corners of an
equilateral with sides d. Two of the point charges are identical and have a charge q. If zero
net work is required to place the three charges on the corners of the triangle, what must the
value of the third charge be?

Answer 1

Concept:

Concept 1:
Work Done on a point charge(q) to bring it from infinity to point A is,
W = q(V)

Where V is the electric potential at the potential at point A.

Concept 2:
Potential due to a point charge (q) at a distance (d) is,

k is coulomb's constant

Now,
Let's assume the third charge to be x.
work done to bring 1st charge at one of the triangle's corner will be zero. Because there is no charge initially and potential is zero at that point.

Work done to bring second charge at one of the other corners,

Work done on third charge,
W₂ = x(potential due to 1st charge) + x(potential due to 2nd charge)

Given,

Solving which we get,