Electrostatics

“The branch of engineering which deals with charges at rest is called electrostatics”

The word “electrostatics” means electricity at rest.

Electric Charge

When a body has deficiency or excess of electrons from the normal due share, it is said to be charged or electrified. The study of atomic structure reveals that matter is electrical in nature. Under ordinary conditions, the body is electrically neutral because it contains equal amounts of positive and negative charges. When this equality or balance is disturbed by removing or supplying electrons, the body acquires a net charge. The body will acquire a positive or negative charge depending upon whether electrons are removed from it or added to it.

Unit Of Charge

The charge on an electron is so small that it is not convenient to select it as the unit of charge. In practice, coulomb is used as the unit of charge. One coulomb of charge is equal to the charge on 625×10²⁵ electrons.

Properties Of Electric Charge

The following are the properties of electric charge:

• Electric charge is quantized i.e. only certain values of charge are allowed.

Charge on a body, Q = ± n e

where n = 1,2,3….. and e = 1.6×10^-19 C

• Electric charge is a conserved quantity.
• The magnitude of electric charge on a body is independent of the speed of the body.
• Electric charge is a scalar quantity.

Coulomb’s Law Of Electrical Force

According to this law ” the electrostatic force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of distance between their centers.”

This force will be repulsive or attractive depending upon whether the charges are like or unlike. Further, the force always acts along the line joining the centers of the two charges.

Consider two point charges Q₁ and Q₂ held d distance apart in vacuum. According to Coulomb’s law, the magnitude of electrostatic force between the charges is given by :

F ∝ Q₁Q₂/d²

F = k Q₁Q₂/d²

Where k is a constant whose value depends upon the medium in which the charges are placed and the system of units employed. In SI units, force is measured in newtons, charge in coulombs, distance in meters and the value of k is given by:

k = 1/4πε_oε_r

where ε_o = Absolute permittivity of vacuum or air.

ε_r = Relative permittivity of the medium in which the charges are placed. For vacuum or air, its value is 1.

The value of ε_o = 8.854×10-¹² F/m and the value of ε_r is different for different media.

F = Q₁Q₂/4πε_oε_rd²

Now,

1/4πε_o = 1/4π×8.854×10-¹² = 9×10⁹

Absolute And Relative Permittivity

Permittivity is the property of a medium and effects the magnitude of force between two point charges. The greater the permittivity of a medium, the lesser the force between the charged bodies placed in it. Air or vacuum has a minimum value of permittivity. The absolute permittivity ε_o of air or vacuum is 8.854×10-¹² F/m. The absolute permittivity ε of all other insulating materials is greater than ε_o. The ratio ε/ε_o is called the relative permittivity of the material and is denoted by ε_r.

ε_r = ε/ε_o

where,

ε = Absolute permittivity of the material.

ε_o = Absolute permittivity of air or vacuum 

ε_r = Relative permittivity of the material.

Obviously, ε_r for air would be ε_o/ε_o = 1.

Permittivity of a medium plays an important role in electronics. For instance, the relative permittivity of insulating oil is 3. It means that for the same charges (Q₁ and Q₂) and distance (d), the force between the two charges in insulating oil will be one-third of that in air.

Superposition Principle

If we are given two charges, the electronic force between them can be found by using Coulomb’s law. However, if a number of charges are present, then force on any charge due to the other charges can be found by superposition principle stated below:

“When a number of charges are present, the total force on a given charge is equal to the vector sum of the forces due to the remaining other charges on the given charges.”

This simply means that we first find the force on the given charge ( by Coulomb’s law) due to each of the other charges in turn. We then determine the total or net force on the given charge by finding the vector sum of all the forces.

Electric Field

“The electric field due to a charge is the space around the charge in which any other charge experiences a force of attraction or repulsion.”

Electric Lines Of Force (Field Lines)

Electric field to a charge or group of charges is represented by electric lines of force. This is a very useful representation of electric field. An electric lines of force is the path along which a small positive test charge would move it free to do so. Following this convention, it is clear that electric lines of force would always originate from a positive charge and end on a negative charge. The following relation exists between field lines and electric field. 

• The number of field lines emerging from a positive charge ( or terminating on a negative charge ) is proportional to the magnitude of the charge.
• The field lines point in the direction of the electric field.
• The field lines may be straight. The direction of electric field at any point is given by the direction of tangent of the field line at that point.
• The separation of neighboring field lines indicates the electric field strength in that region. If the field lines are close, together, the electric field in that region is relatively strong, if the field lines are far apart, the field is weak.

Thus representation of electric field by field lines allows us to infer relative field strength as well as direction of the electric field.

Properties Of Electric Lines Of Force

• The electric field lines are directed away from a positive charge and towards a negative charge so that at any point, the tangent to a field line gives the direction of electric field at that point.
• Electric lines of force start from a positive charge and end on a negative charge.
• Electric lines of force leave or enter the charged surface normally.
• Electric lines of force cannot pass through a conductor. This means that electric field inside a conductor is zero.
• Electric lines of force never intersect each other. In case of two electric lines of force intersect each other at a point, then two tangents can be drawn at that point. This would mean two directions of electric field at that point which is impossible.
• Electric lines of force have tendency to contract in length. This explains attraction between oppositely charged bodies.
• Electric lines of force have a tendency to expand laterally, they tend to separate from each other in the direction perpendicular to their lengths. This explains repulsion between like charges.

Electric Field Intensity Or Field Strength

To describe an electric field, we must specify its intensity or strength. The intensity of electric field at any point is determined by the force acting on a unit positive charge placed at that point.

Electric Intensity at a point in an electric field is the force acting on a unit positive charge placed at that point. Its direction is the direction along which the force acts.

Electric intensity at a point, E = F/+Q  N/C(Unit)

The following points may be noted:

• Since electric intensity is a force, it is a vector quantity possessing both magnitude and direction.
• Electric intensity can also be described in term of lines of force. Where the lines of force are close together, the intensity is high and where the lines of force are widely separated, intensity will be low.
• Electric intensity can also be expressed in V/m.

1 V/m = 1 N/C

Electric Flux And Electric Density

To compare electric fields, we usually use the term electric flux, instead of electric lines of force. The electric flux is measured in coulombs. Thus a body charged to Q coulombs emits a total electric flux of Q coulombs

Electric flux = Q coulombs

The electric flux density is defined as the electric flux passing normally through a unit area. Thus if an electric flux of Q coulombs is passing normally through an area A m², then,

Electric flux density, D = ψ/A  = Q/A C/m²

The ratio D/E is equal to the absolute permittivity ()

D/E = ε or D = εE = ε_oε_rE

Electric Dipole

“A system of two equal and opposite point charges separated by a small distance is called an electric dipole.”

Electric Potential

Consider an isolated point charge +Q fixed in space. If a small test charge +q is placed at infinity, the force on it due to charge +Q is zero. If the test charge at infinity is moved towards +Q, a force of repulsion acts on it and hence work is required to be done to bring it to a point. This work done is stored in the charge as electric potential energy. We say that electric potential energy of the test charge at A is U_A. The electric potential at any point is defined as the potential energy per unit charge.

Electric potential at A,  V_A = U_A/q_o

The SI unit of electric potential is 1 J/C which has been given the name 1 volt. Thus, when we say that electric potential at a point A is 5 V, it means that 5 J of work has been done in moving a unit positive charge from infinity to that point against the electric field along any path. This is the same thing as the potential energy of 1 C charge placed at point A is 5 J.

Electric Potential Difference

In practice, we are more concerned with potential difference between two points rather than their absolute potentials.

Electric potential difference between two points in an electric field is the amount of work done/coulomb in bringing a small positive test charge from the point of lower potential to the point of higher potential along any path.

The SI unit of electric potential is volt, one can expect that the SI unit of potential difference will also be volt.

Potential Gradient: “The change of potential per unit distance is called potential gradient.”

Potential Gradient = (V₂ – V₁)/S

Where (V₂ – V₁) is the change in potential between two points S meter apart. Obviously, the unit of potential gradient will be volts/m.

Electron Volt (eV)

The conventional unit of energy is joule. But this unit is very large for computing atomic physics problems. Therefore, a smaller unit called electron-volt is used.

One electron-volt is the amount of energy gained by an electron when accelerated through a potential difference of 1 V. 

The energy gained by a charge q when accelerated through a potential difference of V volts = qV.

1 eV = 1.6×10^-19 × 1 = 1.6×10^-19 

1 eV = 1.6×10^-19  J