Answer to Question #24663 in Electricity and Magnetism for adam hashem

Question

Two point charges -2Q and +3Q are on the x-axis, -2Q at the origin and +3Q at x = D. Choose the potential to equal zero at infinity. Find two points on the x-axis within the vicinity of the charges where the electric potential is zero. Find two points along the y-axis where the potential is zero within a finite distance from the charges.

Answer 1

The electric potential of point charge isV = kq/x where q is charge and x is distant to it. Hence, we must find points, where potentials from -2Q and 3Qare equal There two possibilities - you can add or subtractdistances between charges to x. So, there two point, where V=0.
The first
k*2Q/x = 3Q/(x+D)

2/x = 3/(x+D)
x=2D

The second
k*2Q/x = 3Q/(x-D)
2/x = 3/(x-D)
x=-2D