Consider three point charges located at the points shown in

Consider three point charges located at the points shown in the figure below. Note that q_3 is located at the point (-0.3m, 0.4m). Find the potential VA at the point A - (0, 0.4m) and V_0 at the origin 0 - (0, 0). Find the work (in mJ) needed to transfer a charge q = -3.5 mu C from point A to the origin. 0.840 mJ

Solution

1a)

Potential at A due to q1 = 9*10^9*(-10*10^-9)/.3=-300V

Potential at A due to q2 = 9*10^9*(30*10^-9)/(root((.3^2)+root(.4^2)))=385.71V

Potential at A due to q3 = 9*10^9*(-60*10^-9)/(root((.3^2)+root(.4^2)))=-771.42V

total = -685.71V

1b)potential at origin

Potential at origin due to q1 = 9*10^9*(-10*10^-9)/(root((.3^2)+root(.4^2)))=-128.57V

Potential at origin due to q2 = 9*10^9*(30*10^-9)/0.3=900V

Potential at origin due to q3 = 9*10^9*(-60*10^-9)/0.3=-1800V

total = -1028.57V

work = - change in potential energy = -q\'(change in potential)=-3.5*10^-6*(-1028.57-(-687.71))=0.001193J