Question

A +13.4 nC charge is located at (0,9.4) cm and a -4.23 nC charge is located (4.99, 0) cm. Where would a -14.23 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

In order to solve this problem, we will first need to find the electric field at the origin without the 3rd charge

E1 = (9x10^9)(13.4x10^-9)/(9.4x10^-2)^2 = 13648.7 V/m towards the negative y-axis

E2 = (9x10^9)(4.23x10^-9)/(4.99x10^-2)^2 = 15289.1 V/m towards the positive x-axis

The red arrow shows the direction of which the electric field points.

To make the electric field at the origin 0, we must find a location where q3 = the magnitude of q1 and q2

Etotal = sqrt(E1+E2) = 20494.97 V/m

E3 = 20494.97 = (9x10^9)(14.23x10^-9)/(d)^2

d = 0.079 m = 7.9 cm