A charge +q is at the origin. A charge –2q is at x = 2.00 m on the x axis. For what finite value(s) of x is (a) the electric field zero? (b) the electric potential zero?

Answer 1

Let the point where E=0 be to the left from the charge q and separated by distance “x” from q and by distance (2+x) from -2q. Then
kq/x²=k2q/(2+x)²,
x²-4x-4 = 0
x= 2±√(4-4) =2.
The point where E=0 is x= - 2m.
Let the point where φ=0 be to the right from q and separated by distance x from it.
kq/x =k2q/(2-x),
x=2/3 m
The point where φ =0 is x=+ 2/3 m.