Concept of charge and energy density

Population difference in different parts of India

Population of Himachal Pradesh is 68.6 Lakhs

And that of Mumbai is 1.84 Crore, which is almost 3 times of Himachal !!

Area of Mumbai is 603.4 Sq.KM. whereas that of Himachal is 55,673 Sq.KM.

Which means that Mumbai has very high population accommodated in a very small area

Hence population to area ratio in Mumbai is much higher as compared to Himachal

This ratio is known as the population density. Population per unit area is population density

The term density of anything shows that how densely is it concentrated in certain length or area or volume

Similarly the term density is used for mass. Mass per unit volume is known as mass density

In case of population we found the density per unit area whereas in case of mass we found it per unit volume

Hence, in case of density of anything, we have three types: Volume density Area density Linear density

Similarly in case of charge we calculate density

Charge densities

In case of charges we have three types of densities, i.e. Liner, Surface (area) and Volume charge density

Linear charge density is used for linear charge distribution. It is charge per unit length

Similarly surface charge density is used for areal charge distribution. It is charge per unit area

Volume charge density is the amount of charge concentrated per unit volume

Whenever we have charge distributions, electric fields are generated

Just like mass creates gravitational field, a gravitational potential energy is observed due to the field

Similarly due to electric field, electrostatic potential energy is observed

The concentration of this potential energy per unit volume is electrostatic energy density

Electrostatic energy density

Electrostatic potential energy per unit volume is the electrostatic energy density

The magnitude of electrostatic energy density can be calculated as above

To calculate energy, we multiply energy density by volume

And by this we obtain the total energy in certain volume

To verify the same, let us calculate energy of capacitor

Energy of capacitor

We have a capacitor. And due to charge on plates, we have electric field inside the capacitor

Correspondingly, we have energy due to this electric field, which can be calculated as above

And here we have the final energy stored in a capacitor

Revision

We have three types of densities for charges i.e. linear, surface and volume charge density

We can calculate the electrostatic potential energy density by the above formula

Electrostatic potential energy for capacitor can be calculated by the above formula

The End