Electrostatics Complete Theory Simple Way

ELECTROSTATICS

Electrical charge – It is the quantity of electricity contained in or on a body .

Coulomb – It is the unit of electric charge in the S.I. system .

The charge on one electron = 1.602 x 10–19 Coulomb

Coulomb’s Law – The force of attraction or repulsion between two charged bodies whose charges behave as through concentrated at a point is directly proportional to the magnitude of the charges and inversely proportional to the square of the distance between them i.e.,

F = (in S.I. System)

Where,  = 9×109 Newton – metre2 coulomb2, ε0 = permittivity of free space and

K = relative permittivity of dielectric constant of the medium.

Here K is a dimensionless constant whose value is 1.005 for air, which is taken as unity for all practical purpose, thus for air the equation for F reduces to

F = 

Electric Field Intensity (E) – At any point it is defined as a vector whose magnitude and direction are equal to the force per unit charge on a very small charged body at that point.

Electric Potential (V) – It is defined as the amount of work done in taking a unit positive charge from infinity to the point of consideration.

Potential deference – The difference of potential between two points in an electric field is defined as the work done in taking a unit positive charge from one point to other against the electric force.

Electric field intensity (E) and potential (V) due to a point charge (q) at a distance ‘r’

E = Newton coulomb

V = Volt

Relation between E and V:

E = N/C

Where represents the potential gradient.

Electric field intensity (E ) and potential (V) due to an electric dipole – Two equal and opposite charges (+q& – q) separated by the distance 2/ form a dipole and its dipole moment (P) is directed from – q to + q along the line joining them

P = 2/ x q = 2q/

The electric field intensity (E) at a distance on it perpendicular bisector (r >> 2/) is

E = Newton / Coulomb

The electric field at a distance r on its axis (r >> 2/) is.

E = Newton / Coulomb

The electric potential at a distance ‘r’ on it’s perpendicular bisector is,

V = 0

The electric potential as at distance ‘r’ on it’s axis (r >> 2/) is,

V =  Volt

Capacitor – It is a device in which electric charge may temporarily be stored.

Capacity of a Capacitor (C) – If q is the charge given to a capacitor and V is the potential difference to which it has been raised, then,

C =  farad

Capacity of a sphere of radius ‘a’ metre –

C = 4πε0a farad

Capacity of a parallel plate Capacitor

C = farad in air

And C = farad in medium of dielectric constant K.

When ε0 = permittivity of free space (8.86 x 10–12 farad / metre)

A = area of one of the two plates

d = distance between the two plates

Electric Field between the plates of a parallel plate capacitor – A uniform electric filed is produced between the plates and its intensity is given by

E = 

Capacitor in series – For capacitors in series –

V = V1 + V2 + V3 + …….

Q = Q1 + Q2 = Q3 = ……..

Capacitors in parallel – For capacitors in parallel

V = V1 = V2 = V3 = ………………

Q = Q1 + Q2 + Q3 + ……………..

C = C1 + C2 + C3 + ………………

Energy of a charged capacitor –

E = 

Loss of energy in connecting two capacitors C1 and C2 charged to V1 and V2 –

Loss of energy = 

Capacitance of parallel plate capacitor when the space between the plates is partly filled with dielectric –

C =  farad

Where d = distance between the two plates of the capacitor

T = thickness of the dielectric

K = dielectric constant for the dielectric

Gauss’s Theorem – States that the total electric flux through a closed surface is equal to the ratio of the total electric charge Σq enclosed by the surface to the permittivity (s = ε0K) of the medium in which the charges are situated

Φ0 = 

Energy Density of Electric Field – equal ε0KE2

Remember:

1. Electric filed inside a charged conductor is zero.
2. Electric filed on and near a charged conductor is always normal to surface.

1. Surface of a conductor is an equipotential surface.
2. Charge density on a charged conductor is more at pointed surfaces than at flatter surface.
3. Density of electric lines of field force is a measure of E.
4. In charging a capacitor C to a voltage V through a resistor R the amount of energy spent by a source of emf is CV2 which is twice the energy stored in the capacitor.
5. A capacitor cannot by charged discharged instantly.
6. A capacitor hates a change in voltage across it and therefore REACTs.
7. A displacement current proportional to the rate of change of electric flux flows through a capacitor.
8. Coulomb force between two charges is extremely large compared to gravitational force of attraction between their masses.
9. A separation r between two charges kept in a dielectric medium of dielectric constant K is equivalent to a separation r  in vacuum / air.
10. A separation d between the plates of a parallel capacitor of area A filled with a dielectric is equivalent to a separation d/k if the space between plates were completely filled with vacuum /air.