what is the capacitance and charge of the capacitor if the space between plates is fully filled by a conductor
Answers
Answer:
The misunderstanding comes from using the standard capacitance formula with the infinite DC permittivity of metals to arrive at an erroneous conclusion.
Although somewhat surprising, it can be shown that the DC relative permittivity (or the DC “dielectric constant”) of metals is infinite. This is because metals have gobs of free electrons that easily shift position in the presence of any applied external electrical field. When a piece of metal is placed within a static electrical field, electrons within the metal shift around until they completely cancel the externally-applied field, leaving a zero E-field inside the metal. Since metals behave as though they are perfectly polarizable, they’re considered to have an infinite DC dielectric constant.
However, a capacitor performs its desired component function by storing electrostatic energy within the E-field in the dielectric. However, a metal “dielectric” doesn’t support an internal electrical field (unless current is continually flowing through the metal, i.e., the metal acts like a resistor). So, once a “metal capacitor” is disconnected from an external power source, it lacks any capability of storing any electrostatic energy since the voltage between terminals will be always be zero volts. Instead, it behaves as a low-value resistor (or a short-circuit) as expected.