Two point charges of equal magnitude q are held a distance d apart. consider only points on the line passing through both charges. (a) if the two charges have the same sign, find the locationof all points (if there are any) at which (i) the potential (relative to infinity) is zero (is the electric field zero at these points

let us consider that the two charges are of opposite nature .hence they will constitute a dipole .the separation distance is given as d and magnitude of each charges is q.

the mathematical formula for potential is

for positive charges the potential is positive and is negative for negative charges.

the formula for electric field is given as-

for positive charges,the line filed is away from it and for negative charges the filed is towards it.

we know that on equitorial line the potential is zero.hence all the points situated on the line passing through centre of the dipole and perpendicular to the dipole length is zero.

here the net electric field due to the dipole can not be zero  between the two charges,but we can find the points situated on the axial  line but  outside of charges where the electric field is zero.

now let the two charges of same nature.let these are positively charged.

here we can not find a point between two charges and on the line joining  two charges  where the potential is zero.

but at the mid point of the line joining two charges the filed is zero.

the bal will not change its velocity.