When electric potential is zero at a point in system of opposite charges does it mean that work done to bring point charge from infinity to that point is zero how can it be zero?

Answer 1

Yes, that's what it means. No force would be required to keep a test point-charge

moving along a line of zero potential in the direction toward that point, and there

would be no force attracting it toward that point in the combined field. Of course

that's physically impossible in the real world, probably because there's no such

thing as a point charge. The smallest possible test-charge would still have some

non-zero physical dimensions, and be made of atoms whose charge distribution

inside it is non-uniform. So it could never stay exactly on the line, and any slight

perturbation would require force to execute a mid-course correction and put it

back on the zero-potential.

Even if there is no continuous contour of zero potential available for the trip, if the

test charge starts out and arrives at points of zero potential, then the work done

along the way to push it against an occasional repelling force is exactly equal to the

work done by an occasional attracting force, and they add up to zero for the trip.

Answer 2

When the electric potential is zero at a point in a system of opposite charges, it means that the work done to bring a point charge from infinity to that point is indeed zero. This is because the potential energy difference between infinity and that point is zero due to the cancellation of the charges. In this scenario, the external work required to move the charge is zero because the charges interact and essentially negate the need for external work.