(a) Depict the equipotential surfaces for a system of two identical positive point charges placed a distance 'd' apart.

(b) Deduce the expression for the potential energy of a system of two point charges q1 and q2 brought from infinity to the points begin mathsize 11px style stack straight r subscript 1 with rightwards arrow on top space and space stack straight r subscript 2 with rightwards arrow on top end style respectively in the presence of external electric field begin mathsize 11px style straight E with rightwards arrow on top end style.

Asked by Topperlearning User | 24th Apr, 2015, 09:10: AM

Expert Answer:

(a) An equipotential surface is a surface with a constant value of potential at all points on the surface.

Equipotential surfaces for two identical positive charges.

(b) First, we calculate the work done in bringing the charge q1 from infinity to r1.

Work done in this step is q1 V (r1).

Next, we consider the work done in bringing qto r2. In this step, work is done not only against the external field E but also against the field due to q1.

Work done on qagainst the external field = q2V (r2)

Work done on qagainst the field due to q1,  begin mathsize 11px style straight W space equals space fraction numerator straight q subscript 1 straight q subscript 2 over denominator 4 πε subscript 0 straight r subscript 12 end fraction end style

where r12is the distance between q1and q2. By the superposition principle for fields, we add up the work done on q2 against the two fields (E and that due to q1):

Work done in bringing q2 to r2= q2 V(r2) + begin mathsize 11px style fraction numerator straight q subscript 1 straight q subscript 2 over denominator 4 πε subscript 0 straight r subscript 12 end fraction end style  

Thus,

Potential energy of the system

= the total work done in assembling the configuration

Answered by  | 24th Apr, 2015, 11:10: AM