Particles A and B, each carrying a charge of \(2.0 \mathrm{nC}\), are at the base corners of an equilateral triangle \(2.0 \mathrm{~m}\) on a side.

(a) What is the potential (relative to zero at infinity) at the apex of the triangle?

(b) How much work is required to bring a positively charged particle carrying a charge of \(5.0 \mathrm{nC}\) from infinity to the apex if \(\mathrm{A}\) and \(\mathrm{B}\) are held fixed?

(c) Answer parts \(a\) and \(b\) for the case where particle \(B\) is replaced by a particle carrying a charge of \(-3.0 \mathrm{nC}\).

(d) Calculate the electric potential energy for each of the two triangular charge distributions.