# Homework Help: Where is the electric field zero

1. Feb 20, 2015

1. The problem statement, all variables and given/known data
A -10.0 nC point charge and a +20.0 nC point charge are 15.0 cm apart on the x-axis.

a. What is the electric potential at the point on the x-axis where the electric field is zero?
b. What is the magnitude of the electric field at the point on the x-axis, between the charges, where the electric potential is zero?

2. Relevant equations
E = kQ/r^2
V = Ed
U = kQq/r

3. The attempt at a solution
Let x be the distance from the -10nC point where the field is zero in cm
r = .15m
k = Coulomb's constant (8.99*10^9)
q1 = -10nC
q2 = 20nC
I tried solving for where the electric field would be zero by first doing:
$$0 = \frac{k*q_1}{(x)^2} + \frac{k*q_2}{(r-x)^2}$$
Solving for x, I got x = -0.36m and 0.062m

I'm not really sure how to proceed from here since I have two points where it seems that the field is zero.

2. Feb 20, 2015

You have a positive charge say at (a,0) and a negetive charge at (b,0). Obviously the electric field is non zero in between the charges. Your equation is incorrect because you assumed the required point to be in between a and b.(you took r to be the distance between the charges and x to be the distance from q1 to the required point, and the other is r-x).
So change it to:
$$0=\frac{kq_1}{x^2} + \frac{kq_2}{(r+x)^2}$$
Same method is used for electric potential as well. Try to derive the expression for the point where the potential is zero. Then again find x.