Revision: Class 12 >> Electrostatic Potential and Capacitance NEET (UG) Electrostatic Potential and Capacitance

The phenomenon in which the electric field inside a cavity of a conductor is zero, irrespective of external charges or fields, is called electrostatic shielding.

The ratio of the permittivity of a medium to the permittivity of vacuum.

K = ε / ε₀

OR

Dielectric constant is the factor by which the capacitance of a capacitor increases when a dielectric is completely inserted between its plates.

The product of vacuum permittivity and dielectric constant of the medium.

ε = ε₀K

A capacitor is connected across the terminals of a d.c. battery.

The energy stored on a capacitor is equal to the work done by the battery.

The work required to transport a small amount of charge (dQ) from the negative to positive plates of a capacitor is equal to V dQ, where V represents the voltage across the capacitor.

dU = V dQ

= `Q/C dQ`

∴ Energy stored (U) = ∫V dQ

= `1/C int Q dQ`

= `1/2 Q^2/C`

= `1/2 CV^2`    ...(i)

Energy density is defined as the total energy per unit volume of the capacitor.

For a parallel plate capacitor,

C = `(A epsilon_0)/d`

Putting in eqn. (i),

U = `1/2 (A epsilon_0)/d V^2`

= `epsilon_0/2 Ad(V/d)^2`

= `epsilon_0/2 Ad E^2`    ...[Putting `V/d` = E]

A × d = Volume of space between plates

So, energy is stored per unit volume.

\[\vec{E}=\frac{\sigma}{\varepsilon_0}\hat{n}\]

where
σ = surface charge density
\[\hat n\] = outward normal unit vector

Magnitude form:

E = \[\frac{\sigma}{\varepsilon_0}\]