Question

A +10.8 nC charge is located at (0,8.66) cm and a -2.81 nC charge is located (5.44, 0) cm. Where would a -14.31 nC charge need to be located in order that the electric field at the origin be zero? Express your answer, in cm, as the magnitude of the distance of q3 from the origin.

Answer 1

To make the origin have a electric field of 0, we first need to find the electric field at the point right now.

E1 = (10.8x10^-9)(9x10^9)/(8.66x10^-2)^2 = 12960 V/m

E2 = (2.81x10^-9)(9x10^9)/(5.44x10^-2)^2 = 8548 V/m

Now to find E total

E1+2 = sqrt(E1^2 + E2^2) = 15524.5 V/m

So if we want to make the origin have an E-field of 0 V/m, we will need to make an E-field equal and opposite to the current one

E3 = 15524.5 = (14.31x10^-9)(9x10^9)/(d)^2

d = 0.00829 meters = .8 cm