Electric Displacement

We all have seen a ceiling fan used in the summer season.

In the ceiling fan, a capacitor is used to start the rotation of the fan.

Because it has a property of storing electrical energy in the form of charge.

And in the capacitors, a dielectric material is used.

A dielectric material is an electrical insulator, that can be polarised, when an electric field is applied.

As it is an electric insulator, so, there will no flow of electric charges.

But, they displace from their equilibrium positions resulting in dielectric polarisation.

Hence, the charge per unit area that would be displaced across an electric field is called electric displacement.

Let's discuss electric displacement.

Electric displacement is defined as the charge per unit area that would be displaced across a layer of a conductor across the electric field.

It is also known as the electric flux density.

Now, the relation between the induced charge density and polarisation is,

And this equation is true for any shape of dielectric materials.

As the polarisation, is long the unit vector and is opposite to unit vector at the left surface.

Hence, the induced charge density is positive at the right surface and negative on the left surface.

Now, the equation of the electric field () in vector form is,

Hence, we get,

The term is called electric displacement and it is denoted by .

Hence, it can be written as,

Now, for a dielectric medium, and are directly related to the free charge density.

And as the direction of is in the direction of . So, all three vectors , , and are parallel.

Now, the ratio of the magnitude of and is

Hence, the magnitude of electric displacement,

And the magnitude of polarisation,

Hence, it gives the formula for electric susceptibility.

Because the electric susceptibility is,

Therefore, this is all about the electric displacement.

Revision

Electric displacement is defined as the charge per unit area that would be displaced across a layer of a conductor across the electric field.

The induced charge density is positive at the right surface and negative on the left surface.

We get electric displacement as,

And gives the formula for electric susceptibility.

The End