Effect Of Dielectric On Capacitance, Polarisation, Important Topics For JEE 2024

Effect Of Dielectric On Capacitance : We know that a capacitor is a device that stores electrical energy. In this article, we will discuss what changes a dielectric can bring when we introduce it into the space between the conductors of a capacitor.  Also, we will discuss the force on a dielectric slab in a capacitor.

Dielectrics And Polarisation

Dielectrics And Polarisation : Insulating or non-conducting materials which transmits electric effect without conducting. If a very high electric field is created, the dielectric then behaves like a conductor. This phenomenon is called as dielectric breakdown. The maximum value of electric field that a dielectric material can tolerate without breakdown is called dielectric strength.

A molecule which has permanent dipole moment even in the absence of electric field is called polar molecule. But in the absence of electric field, the net dipole moment will be zero as the molecules are randomly sounded. In non-polar molecules, each molecule has zero dipole moment. When electric field is applied molecules become induced electric dipole. The process of inducing equal and opposite charges on two faces of the dielectric on applying electric field is called polarization of a dielectric slab.

If E is the main field and E _i is the induced field, the electric field between the plates in the presence of dielectric medium is

Dielectric constant of the material, is also known as relative permittivity of the material.

(i) Partially filled with dielectric slab

Let the thickness of the slab is t ( t < d ).

The potential V is given by

Where E ₀ is the field between the plates and E is the field inside the slab.

We know,

(ii) Completely filled with dielectric slab

Here t = d

(iii) Partially filled with conducting slab

For conductors,

(i) Distance division  : In this case, the distance between the plates d is divided into d ₁ and d ₂ filled dielectric constants and respectively. Here the capacitors are in series.

where and

If

(ii) Area division : I n this case, area of the plates A is divided into A ₁ and A ₂ filled with dielectric of dielectric constant and respectively. Here capacitors are in parallel.

where and

If

Force On Dielectric Slab In A Capacitor

Let F is the external force applied to take out a dielectric from a capacitor. Let dx is the differential displacement of the dielectric. Net force on the dielectric is kept zero so that the dielectric moves slowly without acceleration.

Dielectric On Capacitance Example

Example 1 : A dielectric of constant k is filled between the plates of parallel plate condenser in half of the space as shown in the figure. If the capacity of air condenser is C , then new capacitance between A and B will be.

A. B.

C. D.

Sol. This system is equivalent to two capacitors in parallel with area of each plate

Example 2 : Find out capacitance between A and B if three dielectric slabs of dielectric constant k ₁ of area A ₁ and thickness d , k ₂ of area A ₂ and thickness d ₁ and k ₃ of area A ₂ and thickness d ₂ are inserted between the plates of parallel plate capacitor of plate area A as shown in figure. (Given distance between the two plates d = d ₁ + d ₂ )

Sol. It is equivalent to