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.
Best Answer
The potential at a point is the work done in order to bring a unit positive charge from infinity to that point, without any acceleration. Electric potential is a location-dependent quantity that expresses the amount of potential energy per unit of charge at a specified location.
For a conservative field, we have by definition
$$\vec{E}=-\nabla V$$
which means the electric field at a point is equal to the negative gradient of the absolute potential at that point. This assumes the fact that the work done by the external agency in moving a charged particle through a uniform static electric field is the same for all paths, otherwise dependent only on the initial and final positions.
So, the electric field is due to some charge, say $q$ and the potential is observed on some other charge $Q$, a unit test charge, which by definition, should not alter or distort the electric field of the charge $q$.
This means, simply you cannot take into account the negative charge formed on the sphere. To solve such problems, you need to use the method of images