Question

A charge q1 = –1 μC is located at (-1 m, 1 m). A second charge q2 = +2 μC is located at (2 m, -1 m). How much work is done by the electrical field of these two charges when a third charge q3 = +3 μC is moved from the origin to the point (1 m, 1 m)?

Answer 1

work done on teh charge q3 is stored in the form of potential energy at that point

that is the electrostatic potential energy of the three charge system is  

U = U12+ U13+U23

U = kq1*q2/r

here r12 = sqrt(3^2+(-2)^2) m = 3.6056 m

r13 = sqrt(2^2+0^2) = 2 m

r23 = sqrt((-1)^2 + (2^2)) m = 2.236068 m

now the potential energies are

u12 = kq1q2/r12 = 9*10^9*(1*10^-6)(2*10^-6)/(3.6056^2)J = 0.001385 J

u13 = kq1q3/r13 = 9*10^9*(1*10^-6)(3*10^-6)/(2^2)J = 0.00675 J

u23 = kq3q2/r12 = 9*10^9*(3*10^-6)(2*10^-6)/(2.236068^2)J = 0.0108 J

the total potential energy = work done  

U = U12+ U13+U23

U = 0.001385 +0.00675 +0.0108 J = 0.018935 J