A 13.0nC charge is at x = 0cm and a -1.1nC charge is at 6cm. At what point or points on the x-axis is the electric potential zero?
Let X0 be a position on the x-axis
Let V1 be the electrical potential at a point due to the 13nC charge
Let V2 be the electrical potential at a point due to the -1.1nC charge
V=k(q)*(1/r); k = Coulomb's constant, q = source charge for which at distance 'r' away, the electrical potential is V volts.
The Attempt at a Solution
There are three possible positions for which the electrical potential is 0:
1) To the left of the 13nC charge
2) Between 13nC charge and -1.1nC charge
3) To the right of the -1.1nC charge
For 1), I took the net voltage: V1 + V2 = 0 which is:
K(13E-9)*(X0) + K(-1.1E-9)*(X0) = 0, respectively. Simplifying the sum of two fractional terms, I only needed to find the X0 that would make the numerator 0 and thus obtain the X0 for which net Voltage is 0.
I applied similar calculation procedures for 2) and 3). My results were that X0 = -.0655m, .05532m, .07109m, 1) to 3) respectively.
Attached is a diagram of the problem solving approach I took.