Question

Two identical electric charges +Q are located at two corners A and B of an isosceles triangle as shown above.

a. How much work does the electric field do on a small test charge +q as the charge moves from point C to infinity,

b. In terms of the given quantities, determine where a third charge +2Q should be placed so that the electric field at point C is zero. Indicate the location of this charge on the diagram above.

Answer 1

a. V_C = kQ/a + kQ/a = 2kQ/a; W = –qΔV = – (+q)(V_∞ – V_C) = –q(0 – 2kQ/a) = 2kQq/a

b. Looking at the diagram below, the fields due to the two point charges cancel their x components and add their y components, each of which has a value (kQq/a²) sin 30º = ½ kQ/a² making the net E field (shown by the arrow pointing upward) 2 × ½ kQ/a² = kQ/a². For this field to be cancelled, we need a field of the same magnitude pointing downward. This means the positive charge +2Q must be placed directly above point C at a distance calculated by k(2Q)/d² = kQ/a² giving d = √2a.