Why would you expect a plate to hold more excess charge on each of its conducting surfaces when the voltage difference between the two pieces of conductor increases?
When the voltage difference between two conductors (in this case, the two surfaces of a plate) increases, the excess charge on each of the surfaces also increases. This happens due to the principles of electrostatics.
To understand why, we need to consider the concept of capacitance. Capacitance is a measure of how much charge a conductor can hold for a given voltage difference across it. It depends on several factors, including the geometry and size of the conductor.
When the voltage difference across a capacitor (such as a plate) increases, the electric field between the two conductors also increases. This stronger electric field exerts a greater force on the electric charges within the conductor, causing more charge to accumulate on its surfaces.
To calculate the capacitance, we can use the following equation:
C = Q / V
Where C is the capacitance, Q is the total charge stored, and V is the voltage difference across the conductor. From this equation, we can see that as V increases, for a given capacitance value, Q must also increase. This means that more charge is held on each surface of the plate.
Additionally, the capacitors with larger surface areas tend to hold more charge than those with smaller areas, assuming all other factors are constant. The larger surface area provides more space for the excess charges to reside, increasing the overall capacitance and enabling the plate to hold more excess charge on each surface.
Therefore, when the voltage difference between the two surfaces of a plate increases, both the electric field strength and the capacitance increase, resulting in more excess charge being held on each conducting surface.