Question

Two point charges Q1 = 10µc and Q2 = -2µc are arranged along the x-axis at x
= 0 and x =4m respectively. Find the positions along the x-axis where v = 0

Answer 1

Potential is kQ/r
testing three cases: to the left of Q1, to the right of Q2, and inbetween.
: to the left (x<0)
V=k*10/x-k2/(4+x)
or 2x=10(4+x)
x=-40/8=-5m
: in between
V=k10/x-2k/(4-x) or
0=40-x-2x or x=40/3 which is not in between the points.
: to the right
V=10k/(x)-2k/((x-4) or
10x-40=2x
8x=40 or x=5m

Answer 2

check my work.