Suppose we have a grounded conducting sphere (potential of sphere = 0) and we bring a charged particle to its surface.
Since work done by us would be equal to the change in potential energy of the charge, it will be equal to zero, As potential at infinity = potential on sphere = 0 therefore change in potential energy = 0.
But this is not possible as when we move the charge, it will induce a negative charge on the sphere, thus for charge to move without acceleration, a negative force (with respect to our displacement) would be required. Thus we would do negative work all over the path and work done can never be zero.
Am I wrong in assuming that the work done = change in potential in this case? Because only that would make sense. Any help would be appreciated.