Question

Derive an expression for the potential energy due to two-point charges separated by distance
r12 in an electric field.

Answer 1

Explanation:

Let, V(r1) and V(r2) be the electric potentials of the field E at the points having position vectors r1 and r2.

Work done in bringing q1 from infinity to r1 against the external field = q1V(r1)

Work done in bringing q2 from infinity to r2 against the external field= q2V(r2)

Work done on q2 against the force exterted by q1 = 1/4πεo.(q1q2/r12)

Here, r12 is the distance between q1 and q2.

So, the total potential energy of the system= The work done in assembling the two charges

U= q1V(r1)+q2V(r2)+1/4πεo.(q1q2/r12)