Question

A -3.0 nC charge is on the x-axis at x = -9 cm and a +4.0 nC charge is on the x-axis at x = 15 cm. At what point or points on the y-axis is the electric potentialzero.
y = _____ cm

Answer 1

The electric potential is a scalar and is given by:

V = k * q / r

Assuming that the net potential on the y axis at y = d cm is zero, then at this point (assuming P)

V_net = V1 + V2 = 0

k * q1 / r1 + k * q2 / r2 = 0

k * q2 / r2 = -k * q1 / r1

q2 / r2 = -q1 / r1

Assumption: q1 = -3.0 nC&q2 = 4.0 nC

r1 = distance between q1 and P = sqrt((-9.0-0)^2 +(0-d)^2) = sqrt(81 + d^2)

r2 = distance between q2 and P = sqrt((19-0)^2 +(0-d)^2) = sqrt(361 + d ^ 2)

and so,

4.0 / square foot (361 + d ^ 2) = 3.0 / square foot (81 + d ^ 2)

Square sides

16.0 / (361 + d ^ 2) = 9.0 / (81 + d ^ 2)

16 * 81 + 16 * d ^ 2 = 9.0 * 361 + 9.0 * d ^ 2

d ^ 2 = [9.0 * 361-16 * 81] /7.0 = 279

d = square feet [279] = \ pm 16.7 cm

So the potential will be zero at the point

y = 16.7 cm & y = -16.7 cm