# Force on a charged particle due to an uncharged infinite conducting plate

How can I calculate the force on a charged particle due to an uncharged infinite conducting plate?

If there is a small object with positive charge placed above a metal plate, the object induces a negative charge on the surface of the plate facing the object. Let's call this surface as $S_1$.

Since the conductor was uncharged initially, and charges always reside on the surface of a conductor, $S_2$ gets a positive charge.

From the picture above, the particle would experience an upward force due to $S_2$ and downward force due to $S_1$. So is the force zero?

The physical interpretation is that the electrons in the neutral conductor will rearrange themselves because of the field from $q$. Since the conductor is infinite the charges will not go from one side to the other. They will rather be brought in from infinity.