A parallel plate capacitor has square plates of side L, separated by a distance

Question

A parallel plate capacitor has square plates of side L, separated by a distance d, as shown in the figure. Capacitor is charged with a battery with a potential difference V0, the battery is then disconnected.

a. Determine the capacitance, C0, and the electric potential energy, U0, and energy density u0.stored in the capacitor at this point.

b. A slab made of a dielectric, with relative permittivity of K ( K >1) is then inserted so that it fills a ratio r of the volume between the plates (r=2/3), as shown in the figure. Determine the new capacitance C1, the new potential difference between the plates V1 and the new electric potential energy U1, stored in the capacitor.

c. Neglecting gravity, did the inserter of the dielectric slab have to do work or not?

Explanation / Answer

a.

Capacitance C0 = epsilon0*A/d

Potential Energy, E = 1/2 * C0*V0^2

Energy Density, U0 =( epsilon0/2 ) * E^2

b.

Capacitance C0 = K*epsilon0*A/d

Potential Energy, E = 1/2 * C0*V0^2

Energy Density, U0 =2/3 *( epsilon0/2 ) * E^2

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