Question

Two parallel-plate capacitors, identical except that one has twice the plate separation of the other, are charged by the same voltage source. Which capacitor has a stronger electric field between the plates? Which capacitor has a greater charge? Which has greater energy density? Explain your reasoning.

Answer 1

Field E = V * d. For a given V, E, the field is proportional to the distance.

So plates having wider separation would have greater field.

part 2) Q = C V

For a given V, Q is proportional to capacitance.

But C is inversely related to d the distance between the plates.

Because $C = \frac{ \epsilon_o A}{ d}$ where Eo is the permittivity of air.

So the one closer would have more charges.

part 3) we have the energy density formula for parallel capacitor

$U = ½ \epsilon_0* E^2$

it does not depends on the plate seperation of the capacitors.