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What are Dielectrics?

  • Dielectrics are basically insulating and non-conducting substances. They are bad conductors of electric current. Dielectrics are capable of holding electrostatic charges while emitting minimal energy. This energy is usually in the form of heat.
    Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced
  • The common examples of dielectrics include mica, plastics, porcelain, metal oxides and glass etc. It is important for you to note that dry air is also a dielectric.

What is the Dielectric Constant?

When we put a dielectric slab in between two plates of a parallel plate capacitor, the ratio of the applied electric field strength to the strength of the reduced value of electric field capacitor is called the dielectric constant. It is given as

K = Eo/E

Eo is greater than or equal to E, where Eo is the field with the slab and E is the field without it. The larger the dielectric constant, the more charge can be stored. Completely filling the space between capacitor plates with a dielectric, increases the capacitance by a factor of the dielectric constant:

C = KCo,

where Co is the capacitance with no slab between the plates. This is all about a quick recap. Now let us move ahead and see what effect dielectrics have on the capacitance.

Force Between the Plates of a Capacitor

In a capacitor as plates carry equal and opposite charges, there is a force of attraction between the plates. To calculate this force, we use the fact that the electric field is conservative and in a conservative field Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced.
In the case of parallel plate capacitor:

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced [as Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced]

So, Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

The negative sign implies that the force is attractive.

Effect of Dielectric on Capacitance

We usually place dielectrics between the two plates of parallel plate capacitors. They can fully or partially occupy the region between the plates. When we place the dielectric between the two plates of a parallel plate capacitor, the electric field polarises it.
The surface charge densities are σp and – σp. When we place the dielectric fully between the two plates of a capacitor, then it’s dielectric constant increases from its vacuum value.

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

The electric field inside a capacitor is as follows:

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Hence we have:

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Therefore:
Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Ɛ is the permittivity of the substance. The potential difference between the plates is given by
Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced
For linear dielectrics:
Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced
Where k is a dielectric constant of the substance, K = 1.
Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

How does the dielectric increase the capacitance of a capacitor?

The electric field between the plates of parallel plate capacitor is directly proportional to capacitance C of the capacitor. The strength of the electric field is reduced due to the presence of dielectric. If the total charge on the plates is kept constant, then the potential difference is reduced across the capacitor plates. In this way, dielectric increases the capacitance of the capacitor.
Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced


Capacitors with Dielectric

(i) In absence of dielectric

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

(ii) When a dielectric fills the space between the plates then molecules having dipole moment align themselves in the direction of electric field.

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

sb = induced charge density (called bound charge because it is not due to free electrons).

* For polar molecules dipole moment ¹ 0

* For non-polar molecules dipole moment = 0

(iii) Capacitance in the presence of dielectric

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced                 Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Here capacitance is increased by a factor K.

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

(iv) Polarisation of material :

When a non-polar substance is placed in an electric field then dipole moment is induced in the molecule. This induction of dipole moment is called polarisation of material. The induced charge also produces electric field.

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

σb = induced (bound) charge density.

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

It is seen the ratio of electric field between the plates in absence of dielectric and in presence of dielectric is constant for a material of dielectric. This ratio is called 'Dielectric constant' of that material. It is represented by er or k.

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

(v) If the medium is not filled between the plates completely then electric filed will be as shown in figure.

Case : (1)

The total electric field produced by bound induced charge on the dielectric outside the slab is zero because they cancel each other. 

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Case : (2)

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

so potential difference between plates

v = Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

so equivalent capacitance

C = Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

 

10.1 Introduction of a Dielectric slab of dielectric constant K between the plates

(a) When the battery is disconnected

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced                   Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Let q0, C0, V0, E0 and U0 represents the charge, capacity, potential difference, electric field and energy associated with charged air capacitor respectively. With the introduction of a dielectric slab of dielectric constant K between the plates and the battery disconnected.

(i) Charge remains constant, i.e., q = q0, as in an isolated system charge is conserved.

(ii) Capacity increases, i.e., C = KC0, as by the presence of a dielectric capacity becomes K times.

(iii) Potential difference between the plates decreases, i.e.,Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced, as

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced [Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced q = q0 and C = KC0]

(iv) Field between the plates decreases, i.e., Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced, as

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced                [as Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced]

and Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

(v) Energy stored in the capacitor decreases i.e.

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced, as

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced (as q = q0 and C = KC0]

(b) When the battery remains connected (potential is held constant)

(i) Potential difference remains constant, i.e., V = V0, as battery is a source of constant potential difference.

(ii) Capacity increases, i.e., C = KC0, as by presence of a dielectric capacity becomes K times.

(iii) Charge on capacitor increases, i.e., q = Kq0, as

q = CV = (KC0)V = Kq0 [Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced q0 = C0V]

(iv) Electric field remains unchanged, i.e., E = E0, as

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced [as V = V0 and Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced]

(v) Energy stored in the capacitor increases, i.e., U = KU0, as

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced [as C = KC0 and Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced]


Solved Examples

Example.1 Assertion: In a circuit where two capacitors with capacitance C1 and C2 are connected in series with C1 followed by C2. A slab is inserted in C2. The potential difference across C2 will decrease.
Reason: The current flows in the clockwise direction, after the introduction of the slab.
Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

(a) Both the statements are correct and the reason is the correct explanation of the assertion.
(b) They both are correct but the reason is not the correct explanation of the assertion.
(c) The assertion is correct but the reason is not.
(d) The reason is correct but the assertion is not.
Solution: B) Upon inserting the slab, the value of C2 will increase to KC2. In series, V distributes in the inverse ratio of capacitance. As C2 increases, its potential will decrease. As C2 increases, the positive charge on both the capacitors will have to increase. Thus the current will flow in the clockwise direction.

Example.2 A parallel plate air capacitor is made using two square plates each of side 0.2 m, spaced 1 cm apart. It is connected to a 50V battery.

(a) What is the capacitance?

(b) What is the charge on each plate?

(c) What is the energy stored in the capacitor?

(d) What is the electric field between the plates?

(e) If the battery is disconnected and then the plates are pulled apart to a separation of 2 cm, what are the answers to the above parts?

Sol. (a) Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

(b) Q0 = C0V0 = 3.54 × 10-5 × 50 = 1.77 × 10-3 mC

(c) Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

(d) Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

(e) If the battery is disconnected the charge on the capacitor plates remains constant while the potential difference between the plates can change.

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Q = Q0 = 1.77 × 10-3 mC

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Example.3 In the last illustration, suppose that the battery is kept connected while the plates are pulled apart. What are the answers to the parts (a), (b), (c) and (d) in that case?

Sol. If the battery is kept connected, the potential difference across the capacitor plates always remains equal to the emf of battery and hence is constant.

V = V0 = 50V

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Example.4 A parallel plate capacitor has plates of area 4 m2 separated by distance of 0.5 mm. The capacitor is connected across a cell of emf 100 V.

(a) Find the capacitance, charge and energy stored in the capacitor.

(b) A dielectric slab of thickness 0.5 mm is inserted inside this capacitor after it has been disconnected from the cell. Find the answers to part (a) if K = 3.

Sol. (a) Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Q0 = C0V0 = (7.08 × 10-2 × 100)mC = 7.08 mC

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

(b) As the cell has been disconnected

Q = Q0

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced = 118 × 10-6 J

Example.5 If a dielectric slab of thickness t and area A is inserted in between the plates of a parallel plate capacitor of plate area A and distance between the plates d (d > t) then find out capacitance of system. What do you predict about the dependence of capacitance on location of slab ?

Sol. Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced (Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced t1  t2 = d - t)

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

* Capacitance does not depend upon the position of dielectric (it can be shifted up or down & still capacitance does not change).

* If the slab is of metal then

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Example.6 Find out capacitance between A and B if two dielectric slabs of dielectric constant K1 and K2 of thickness d1 and d2 and each of area A are inserted between the plates of parallel plate capacitor of plate area A as shown in figure.

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Sol. Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced ; Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced Effect of Dielectric on Capacitance | Physics for JEE Main & AdvancedEffect of Dielectric on Capacitance | Physics for JEE Main & Advanced

This formula suggests that the system between A and B can be considered as series combination of two capacitors.

Example.7 Find out capacitance between A and B if two dielectric slabs of dielectric constant K1 and K2 of area A1 and A2 and each of thickness d are inserted between the plates of parallel plate capacitor of plate area A as shown in figure.

Sol. Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced      Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced, Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced ; Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced  Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced    

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

The combination is equivalent to :

Therefore, C = C1  C2

Example.8 Find out capacitance between A and B if three dielectric slabs of dielectric constant K1 of area A1 and thickness d1 K2 of area A2 and thickness d2 and K3 of area A2 and thickness d3 are inserted between the plates of parallel plate capacitor of plate area A as shown in figure. (Given distance between the two plates d = d1  d2)

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Sol. It is equivalent to

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced             

 Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

Example.9 A dielectric of constant K is slipπεd 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

Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

(A) Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced         
 (B) Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced           
 (C) Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced           
 (D) Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced

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

The document Effect of Dielectric on Capacitance | Physics for JEE Main & Advanced is a part of the JEE Course Physics for JEE Main & Advanced.
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FAQs on Effect of Dielectric on Capacitance - Physics for JEE Main & Advanced

1. What are dielectrics and how do they affect capacitance?
Ans. Dielectrics are insulating materials that are placed between the plates of a capacitor. They are used to increase the capacitance of the capacitor by reducing the electric field between the plates. When a dielectric material is introduced, it polarizes and creates an opposing electric field, which reduces the overall electric field and increases the capacitance.
2. What are some examples of dielectric materials?
Ans. Some common examples of dielectric materials include air, paper, plastic, ceramic, glass, and oil. These materials are chosen based on their ability to insulate and their dielectric constant, which determines their effectiveness in increasing capacitance.
3. How does the dielectric constant affect the capacitance?
Ans. The dielectric constant, also known as relative permittivity, is a measure of how well a material can store electrical energy in an electric field. It determines the extent to which the electric field is reduced by the dielectric material. The higher the dielectric constant, the greater the increase in capacitance.
4. Can a dielectric material decrease the capacitance of a capacitor?
Ans. No, a dielectric material cannot decrease the capacitance of a capacitor. Its purpose is to increase the capacitance by reducing the electric field between the plates. The dielectric material acts as an insulator and enhances the storage of electric charge, resulting in a higher capacitance value.
5. How does the thickness of the dielectric material affect capacitance?
Ans. The thickness of the dielectric material affects the capacitance by influencing the distance between the plates of the capacitor. As the thickness increases, the distance between the plates also increases, leading to a larger capacitor. Thus, a thicker dielectric material generally results in a higher capacitance value.
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