Question

Three charges are located in the x-y plane (see plot below), with Q1 = -4.00 μC, Q2 = -3.00 μC and Q3 = 3.00 μC. Note that the charges are located at grid intersection points. 

a) Calculate the total electrostatic potential energy.

b) Calculate the work required (by external forces) to transport Q3 from its location on the figure to infinity.

Answer 1

Q1 = -4 *10^-6 C

Q2 = -3 *10^-6 C

Q3 = 3 * 10^-6 C

separation between Q1 and Q2 is r = 5 m

separation between Q1 andQ3 is r ' = 6m

separation between Q2 andQ3 is r " = √[ r^ 2+ r'^ 2]

                                                        = 7.81 m

(a). Total electrostatic potential energy U = [-KQ1Q2 / r ]+[-KQ2Q3 / r" ] +[-KQ3Q1/ r']

where K = coulomb's constant = 8.99*10^9 Nm^ 2/ C^ 2

plug the values we get U = (-0.021576 J ) + (0.010359759 J ) + (0.01798)

                                       = 6.763*10^-3 J

(b).potential at Q3 due to other charges V = [KQ1 / r' ]+[ KQ2 / r"]

plug the values we get V = 5993.333 volt + 3453.26

                                      = 9446.59 volt

∴ required work W = VQ3

                                = 0.02833 J