Physics Assignment 1

Definitions : –

1. Electric Field Intensity : – The electric field intensity at a point is the force per unit charge.

E = F/q 

2. Electric Flux : –Electric flux is the measure of electric field passing through a surface. Electric flux is proportional to the number of electric field lines going through a normally perpendicular surface. It is a vector quantity.ϕ=E×A=EAcosθ.

3. Coulomb’s Law : –The force between two electric charges is directly proportional to the product of the charges and inversely to the square of the distance between them.F = k[q₁q₂]/r²

4. Polarization : –Polarization is defined as induced surface charge per unit area.OR It is defined as dipole moment per unit volume of dielectric. P=N.µ

5. Dielectric Constant : –Dielectric constant (ϵ_r) is defined as the ratio of the electric permittivity of the material to the electric permittivity of free space (i.e., vacuum).Its value can be derived from a simplified capacitor model.ϵ_r=ϵ/ϵ₀.

6. Electric Susceptibility : –It is a measure of a materials ability to become polarized in electric field.χ_e = P/ϵ₀E.

7. Electric Dipole Moment : –An electric dipole moment is a measure of the separation between two opposite charges. It is the product of the charge separation and the distance between two charges. P=q(2a).

8. Magnetization : –Magnetization refers to the alignment of a magnetic dipole moments in a material when external magnetic field is applied.

9. Magnetic susceptibility : –It is a measure of a material’s ability to become magnetized in a magnetic field. It is the ratio of magnetization density to the magnetic field intensity.χ_m=M/H.

10. Permeability : -It is defined as the ratio of the magnetic induction ‘B’ to the applied field ‘H’. OR It is the ratio of magnetic field density to magnetic field intensity. Permeability is a measure of material’s ability to support the formation of magnetic field.µ=B/H

11. Magnetic Flux Density(B) : –It is a measure of the amount of magnetic field passing through a surface.B=μH.

12. Magnetic Flux : –Magnetic flux is defined as the number of magnetic field lines passing through a given closed surface.Φ=BAcosθ.

Questions and answers

Que 1: State and explain Coulomb’s law with suitable formula?

Ans: According to Coulomb’s law, the force of attraction or repulsion between two charged bodies is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

$$F = k\frac{[q_{1}q_{2}]}{r_{2}}$$

F = electrostatic force which exists between two-point charges 

K = Coulomb constant k = 1/4πϵ₀ ≅ 8. 988×10⁹ N.m²/c²

q₁ = charge of the first point charge(C)

q₂= charge of the second point charge(C)

r = refers to the distance between the charges (m)

Que 2: State and explain gauss law?

Ans: Gauss’s law is a fundamental law of physics that relates the electric flux through a closed surface to the charge enclosed within that surface. It is named after the German mathematician and physicist Carl Friedrich Gauss.

In mathematical terms, Gauss’s law can be written as:  $$∮S E⋅dA =\frac{Q}{ε_{0}}$$

Where, ∮S =surface integral over a closed surface S.

               E = electric field vector.

               dA = differential surface area element.

               Q = total electric charge enclosed by the surface S.

               ε₀ = electric constant, also known as the vacuum permittivity.

The law states that the electric flux through a closed surface is proportional to the charge enclosed within that surface. The flux is defined as the total number of electric field lines passing through the surface. If the enclosed charge is positive, the electric field lines emanate from the charge and pass through the surface, resulting in a positive flux. 

If the enclosed charge is negative, the electric field lines converge towards the charge and leave the surface, resulting in a negative flux.

Que 3: What is dielectrics? discuss the types of dielectric material.

Ans: A dielectric material is an insulating material that is able to store electrical energy in an electric field. When placed in an electric field, the atoms or molecules of the dielectric material become polarized, meaning that they align themselves with the electric field. This polarization leads to the creation of an induced electric dipole moment within the dielectric material, which produces an electric field that opposes the external electric field.

1. Non-polar Dielectrics: In non-polar dielectrics, the individual molecules or atoms have an even distribution of charge and do not possess a permanent electric dipole moment. These materials include:
   • Air: Air is a common non-polar dielectric used in various electrical and electronic systems.
   • Vacuum: Vacuum is another non-polar dielectric, and it is often used in high-voltage applications.
2. Polar Dielectrics: In polar dielectrics, the atoms or molecules have an uneven distribution of charge, resulting in a permanent electric dipole moment. When subjected to an electric field, these dipoles can align with the field. Common polar dielectric materials include:
   • Water (H2O): Water is a polar dielectric due to its polar covalent bonds. It is used in capacitors, especially in electrolytic capacitors.
   • Mica: Mica is a natural mineral with excellent dielectric properties, often used as an insulating material.

Que 4: What do you mean by dielectric material? How it behaves in the presence of electric field.

Ans: A dielectric material is an insulating material that is able to store electrical energy in an electric field. When placed in an electric field, the atoms or molecules of the dielectric material become polarized, meaning that they align themselves with the electric field. This polarization leads to the creation of an induced electric dipole moment within the dielectric material, which produces an electric field that opposes the external electric field.

The behavior of a dielectric material in the presence of an electric field can be described by its dielectric constant or relative permittivity. This constant is a measure of the ability of the material to store electric energy in an electric field relative to the ability of a vacuum to store electric energy in the same field. The dielectric constant of a material is typically greater than one, indicating that it can store more electric energy in an electric field than a vacuum.

 Dielectric materials are widely used in a range of electronic devices, such as capacitors, because of their ability to store electric energy. They are also used as insulators in electrical systems, to prevent electrical current from flowing between conductive materials.

Que 5: Derive the relation between polarization, dielectric constant and electric susceptibility?

Ans: Relation between Polarization (P), susceptibility (Xe) and dielectric Constant(𝜺_r).

Let us consider a parallel plate Capacitor between electric field E₀ exists.

If σ a surface change density them from Gauss’s law

$$E_{0}=\frac{σ}{𝜺_{0}}$$

If a dielectric slab as placed between the plates of the Capacitor them due to polarisation charges appear on the two phases of the slab and establish another field E₁ . within the dielectric.

A field E₁ will be an a direction opposite to that of E₀.

Resultant field, E= E₀ – E₁ ——-(i)

If σ_s is the induced surface change density on the slab then

$$E_{1} =\frac{σ_{s}}{𝜺_{0}}$$

$$E=\frac{σ}{𝜺_{0}}-\frac{σ_{s}}{𝜺_{0}}$$

$$𝜺_{0}E=σ-σ_{s}—-(ii)$$

But, σ_s = P (Polarization is change / unit area) by gauss’s law the electric flux density (D) is σ =D.

from eq(ii) 𝜺₀E = D – P

D = 𝜺₀E + P—–(iii)

Also, D = 𝜺E = 𝜺_r.𝜺₀E

Substituting eq-(iii)

𝜺_r.𝜺₀E = 𝜺₀E + P

P = 𝜺_r.𝜺₀E – 𝜺₀E

P = 𝜺₀E (𝜺_r – 1) —-(iv)

Equation (iv) gives relation between Polarisation P and Dielectric constant 𝜺_r.

We know that, $$X_{e}= \frac{P}{𝜺_{0}E}$$

$$X_{e}= \frac{𝜺_{0}E(𝜺_{r} – 1)}{𝜺_{0}E}$$

$$X_{e}= 𝜺_{r} – 1\,—-(v)$$

Equation (v) gives relation between susceptibility (Xe) and Dielectric constant 𝜺_r.

Que 6: Derive the Clausius-Mossett equation for the non-polar dielectric material?

Ans:

Que 7: What is Polarization in dielectric? Discuss the different types of polarization with necessary diagram?

Ans: Dielectric polarization is the polarization induced in a dielectric material by an external electric field. It is the displacement of electric charges within a dielectric material, which is caused by an external electric field.

Electronic Polarization:

Electronic polarization occurs due to the displacement of the electron cloud with respect to the nucleus of an atom. The direction of the induced dipole moment is opposite to that of the applied electric field. The net result is the polarization of the dielectric material in the direction of the applied electric field.

Ionic Polarization:

Ionic polarization occurs in ionic crystals, which have both positive and negative ions. When an electric field is applied to an ionic crystal, the positive ions are displaced in the direction of the field, while the negative ions are displaced in the opposite direction.

Orientation Polarization:

Orientation polarization occurs in non-polar molecules, which do not have a permanent dipole moment. When an electric field is applied to a non-polar molecule, the molecule becomes polarized due to the distortion of the electron cloud around the atoms. The induced dipole moment is aligned in the direction of the applied electric field.

Space Charge Polarization:

Space charge polarization is another type of polarization that can occur in a dielectric material. It occurs in a material that contains impurities or defects, which can result in the accumulation of charges at the interface between the dielectric material and the impurity or defect.

Que 8: Mention the major differences between diamagnetic, paramagnetic and ferromagnetic?

Ans: Diamagnetic, paramagnetic, and ferromagnetic materials are three types of magnetic materials that exhibit different responses to an external magnetic field. The major differences between these three types of magnetic materials are:

Que 9: What is ferromagnetic domain? What is the effect of external magnetic field on domain.

Ans: Ferromagnetic domain is a region within a ferromagnetic material where the atomic magnetic moments are aligned in the same direction, resulting in a net magnetic moment for that region. In a ferromagnetic material, there are many ferromagnetic domains, each of which has its own magnetic moment.

In the absence of an external magnetic field, the magnetic moments of the atoms in a ferromagnetic material are randomly oriented, resulting in no net magnetic moment for the material.

This alignment process starts with the smallest and weakest domains and gradually propagates through the material until all the domains are aligned with the external field.

The effect of an external magnetic field on a ferromagnetic domain is to cause the magnetic moments of the atoms within the domain to align with the external field. The process of aligning the domains continues until all the domains are aligned with the external field, at which point the material reaches saturation magnetization.

In summary, the effect of an external magnetic field on a ferromagnetic domain is to cause the magnetic moments of the atoms within the domain to align with the external field.

Que 10: What do you mean by Hysteresis loss? Define the retentivity and coercivity on the hysteresis loop diagram.

Ans: Distances is the lagging of magnetic induction ‘B’ in ferromagnetic material, which respect to applied magnetic field.

When magnetic field ‘H’ is increased from zero ‘0’ value in the positive direction shown along OH, the value of ‘B’ also increases, and the curve increases to OP.

After point P, ‘B’ remains constant inspite of the increase in ‘H’.

The value of ‘B’ at point P is known as Saturation Value.

Now when the value of ‘H’ decreases, ‘B’ starts from point P, facts to retrace the same path when it was increasing.

The new path is ‘PQ’

When H becomes zero, the value of B remains a value equal to OQ.

This residual value of magnetization is called laminae magnetization OR Retentivity.

When the value of applied magnetic field ‘H’ is reversed and increases gradually in point r, B becomes zero at point R.

Now, the material is completely demagnetized, this value of ‘H’=OR is called Coercivity.

Further increase in H causes the material to get magnetized in the opposite direction.

The curve traces to ST.

The variation of B with respect to ‘H’ along a close path gives one full cycle of magnetization and demagnetization and is called Hysterics loop OR curve.

Hysterics loss: – The energy loss in the form of heat that occurs during the full cycle of magnetization and demagnetization in a ferromagnetic material is called hysterics loss.

** Extra **

Derive relation between B, H and M? 

Ans: H is related to B through the equation

B = μ H     or    B = μ₀ μ_r H        ——–(1) & (2)

For air or vacuum,  μ_r = 1

B = μ₀H                   ————(3)

Equation (1) gives the value of magnetic induction or magnetic flux density set up by a magnetic Field H in a region where there is air or vacuum

Into this region, when a magnetic material of cross-sectional area A and relative permeability is brought, it develops a magnetic moment in the influence of the magnetic field. Due to this magnetic moment, extra flux lines will be set up inside the material medium. Thus, the additional flux density is the medium is given by

B = μ₀M ———-(4)

Where M is the intensity of magnetisation.

Hence over the region; there is a superposition of two types of magnetic fluxes. One due to the Magnetic field H and the other one setup due to the magnetic moment of the material (i.e.., due to the magnetization of the material by induction).

Thus, the resultant flux density B in the material can be given by

B = μ₀H + μ₀M

or

B = μ₀ (H+M) ———-(5)

Numericals

1. A magnetising field of 1000A/m produces a magnetic flux of 2×10 ^-5 Weber in a bar of iron of 0.2cm² cross-section. Calculate permeability and susceptibility of the bar.

2. Two parallel plates having equal and l opposite charges are separated by a 2cm thick slab that has dielectric constant 3. If the electric field inside is 10 ⁶ V/m, calculate the polarization and displacement vector.

3. A dielectric constant of diamon is 1.43. Calculate permittivity and electric susceptibility of diamond.

4. A solid dielectric is placed in an electric field of 750 Vm -1 and polarization is given by 3.8 x10 ^-8 C/m2 . Evaluate relative permittivity of material.

5. The dielectric permittivity of a solid material is 2.25 x 10 ^-10 F/m. Find out dielectric constant and electric susceptibility of material.

6. Calculate flux density and magnetization of nickel if its magnetic field strength is 10⁵A/m and magnetic susceptibility is 0.654 x 10 ^-5 .

7. Magnetic field intensity of a paramagnetic material is 10⁴ A/m. At room temperature, its susceptibility is 2.35 x 10 ^-3 .Calculate magnetization of material.

8. The magnetic field intensity in a piece of ferrite is 10 ⁶ A/m. If susceptibility of the material at room temperature is 2.90 x 10 ^-3 . Calculate magnetization and flux density of material.