Question

Two point charges q1 and q2 are located at r1 and r2, respectively in an external electric field E. Obtain the expression for the total work done is assembling this configuration.​

Answer 1

Given: Two point charges q1 and q2 are located at r1 and r2, respectively in an external electric field E.

To find:  The total work done in assembling this configuration.

Solution:

• Now we have provided with two charges with the particular distance r1 and r2.

• According to the question an electric field is applied externally.

• Work-done in bringing a charge q1 in the electric field at a distance r1 will be:

                  W1 = q1 x V(r1)

• Work-done in bringing a charge q2 in the electric field at a distance r2 will be:

                  W2 = q2 x V(r2)

• Now the work-done on q2 to move it against the force of charge q1 will be:

                  1 / 4π∈0 x q1q2/r(12)

• So the total work done will be:

                  W = W1 + W2

                  W = q1 x V(r1) + q2 x V(r2) + 1 / 4π∈0 x q1q2/r(12)

Answer:

                 The total work done in assembling this configuration is

q1 x V(r1) + q2 x V(r2) + 1 / 4π∈0 x q1q2/r(12)