Energy Density for Capacitor
We all might have used radio in our life.
The selection of stations on the radio is done with the help of capacitors.
The capacitors are also used in the fans, coolers, water pumps, etc.
It is a passive electronic device used to store electrical energy in an electrical field.
And the energy stored per unit volume by the capacitor is called energy density of the capacitor.
Now, we are interested in finding the energy density for a capacitor.
Let's discuss the energy density for a capacitor.
As the energy density is the energy per unit volume.
Hence, the energy density of a capacitor will be the energy stored by the capacitor per unit volume.
And it is denoted by
$u$
.
Now, suppose we have a parallel plate capacitor.
And one of the plates is positively charged, whereas, another plate is negatively charged.
There is free space between the plates.
So, the energy stored in the capacitor will be,
Now, the capacitance in the two parallel plates capacitor is calculated by,
We assume the electric field between these two plates is uniform throughout.
So, the potential difference
$V$
will be calculated as,
Now, we put the value of potential difference and capacitance in the equation of energy stored.
After putting the values, we get
On simplification, it will be,
Hence, we can say that the energy stored in the capacitor is directly proportional to the square of the electrical energy.
As the energy density of the capacitor is,
Hence, after putting the values,
Hence, this is the equation for energy density for the capacitor.
Now, suppose there is a dielectric material is present between the two plates instead of free space.
So, the permittivity for dielectric material will be,
Hence, we have to multiply by the dielectric constant in the equation of energy density.
Hence, this is the equation for energy density in a parallel plate capacitor when a dielectric material is present.
Therefore, we can easily calculate energy density for the capacitor on behalf of this equation.
Revision
The energy density of a capacitor is the energy stored by the capacitor per unit volume.
This is the two parallel plates capacitor.
So, the energy stored in the capacitor is,
Hence, the energy density of the capacitor is,
And this is the equation for energy density in a parallel plate capacitor when a dielectric material is present.
The end