This problem has been solved!
see the answer
two charges of equal magnitude q are held a distance d apart. consider only points on the line passing through both charges.
for parts a through d answer with "midway between charges", "at the points, where the charges are", aor "there are no such points"
a) if the two charges have the same sign, find the location of all points (if there are any) at which the potential (relative to infinity) is zero.
b) if the two charges have the same sign, find the location of all points (if there are any) at which the electric field is zero.
c) if the two charges have opposite signs, find the location of all points (if there are any) at which the potential (relative to infinity) is zero.
d) if the two charges have opposite signs, find the location of all points (if there are any) at which the electric field is zero.