Question

An ideal air-filled parallel-plate capacitor has round plates and carries a fixed amount of equal but opposite charge on its plates. All the geometric parameters of the capacitor (plate diameter and plate separation) are now DOUBLED. If the original energy density between the plates was u0 , what is the new energy density?

Answer 1

Answer:

The new energy density is same as initial energy density u0 as it is independent of plate dimensions

Explanation:

As we know that energy density is total energy per unit volume

so we know that isolated plates of capacitor is placed here

$C = \frac{\epsilon_0 A}{d}$

here we have energy density given as

$u = \frac{Q^2}{2(\epsilon_0 A/d)} Ad$

so we have

$u = \frac{Q^2d^2}{2\epsilon_0}$

so it is independent of the dimensions of the plate while total charge on the plates is constant always

so energy density will not change and remains the same