Two point charges of equal magnitude Q are held a distance d apart. Consider only points on the line passing through both charges; take V = 0 at infinity. (a) If the two charges have the same sign, find the location of all points (if there are any) at which (i) the potential is zero (is the electric field zero at these points?), and (ii) the electric field is zero (is the potential zero at these points?). (b) Repeat part (a) for two point charges having opposite signs.

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Two point charges of equal magnitude Q are held a distance
d apart. Consider only points on the line passing through both charges;
take V = 0 at infinity. (a) If the two charges have the same sign, find the
location of all points (if there are any) at which (i) the potential is zero
(is the electric field zero at these points?), and (ii) the electric field is
zero (is the potential zero at these points?). (b) Repeat part (a) for two
point charges having opposite signs.

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