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