Deduce an expression for the potential energy of a system of two point charges `q_1` and `q_2` located at positions `r_1` and `r_2` respectively in an external field `(vecE)`

Deduce the expression for potential energy of a system of charges?

Give the expression for potential energy of a system of two charges q_1 and q_2 in an external field.

(a) Depict the equipotential surfaces for a system of two identical positive point charges placed a distance 'd' apart. (ii) Deduce the expression for the potential energy of a system of two point charges q_1 and q_2 brought from infinity of the points vecr_1 and vecr_2 respectively in the presence of external electric field vecE .

Deduce the expression for the potential energy of a system of two point charges q_1 and q_2 brought from infinity to the points vecr_1 and vecr_2 respectively in the presence of electric field vecE .

Derive an expression for potential energy of a system of two charges in an external electric field.

Find out the expression for the potential energy of a system of three point charges q_1, q_2 and q_3 located at vecr_1, vecr_2 and vecr_n w.r.t the common origin O.

Derive an expression for the electric potential energy of a system of two point charges in the absence of an external electric field.