Question

With v = 0 at infinity, at what finite values of x is the net electric potential on the x-axis also zero? (a) positive value of x:

Answer 1

V = kq1/r1 + kq²/r² 
Factor out k since it appears in both terms
0 = 7e/x -14e/(0.3-x) where x is the point on the x axis between the two charges that are 0.3m apart.
7e/x = 14e/(0.3-x) => 7e*(0.3-x) = 14e*x => 2.1e -7ex = 14ex =>2.1e = 21ex => x = 0.1m
Now look for V = 0 on negative x axis. Let x be the distance to the left of the origin
0 = 7e/x -14e/(0.3+x) => 7e*(0.3+x) = 14e*x => 2.1e +7ex = 14ex =>2.1e = 7ex => x = 0.3m left from the origin.
V = 0 at x = 10cm and x = -30cm