Point charge above conducting plate · CAP 2006 #20
Physics · electromagnetism
Problem
A point particle carries a positive charge +q and is maintained at a distance h above a large conductive uncharged plate. The electric force of interaction between the charge and the plate is best described as: (a) zero force; (b) an attractive force proportional to q/h²; (c) an attractive force proportional to q²/h²; (d) an attractive force proportional to q²/ 4h²; (e) a repulsive force proportional to q²/ h².Intuitive explanation
When a charge sits above a conductor, the conductor's free electrons rearrange to cancel the field inside the metal—this is the key to solving the problem. You can find the resulting force by imagining a "mirror image" of your charge (with opposite sign) located the same distance below the surface; this image charge creates the same boundary condition as the real conductor. The force between your charge and its image then tells you both the magnitude and nature of the interaction.
Intuitive explanation
When a charge sits above a conductor, the conductor's free electrons rearrange to cancel the field inside the metal—this is the key to solving the problem. You can find the resulting force by imagining a "mirror image" of your charge (with opposite sign) located the same distance below the surface; this image charge creates the same boundary condition as the real conductor. The force between your charge and its image then tells you both the magnitude and nature of the interaction.