ELECTRIC FLUX

Electric Flux:

Electric Flux (𝜓) is a greek letter psi is the total number of lines of force emanating from a charge.

In the case of an isolated charge of strength q coulombs, 𝜓 = q , as charge of one coulomb is supposed to emanate a single line of force, and is independent of the nature of the medium.

In M.K.S. units, therefore, 𝜓 is also in coulombs.

ELECTRIC FIELD AND LINES OF FORCE

Electric field:-

The electric field is a region or space surrounding a charge in which electrostatic force can exist.

The electrostatic force is of repulsion for similarly charged bodies and of attraction for dis-similarly charged bodies which are placed in that region.

Just like magnetic lines of force to represent the influence of a magnet upon its surroundings, similarly in electrostatics, we imagine electrostatic lines of force to exist around an electric charge.

These lines are taken as beginning from a positive charge and terminating at a negative charge. 

They differ from the magnetic lines of force, in the sense that electric field lines do not form a closed circuit.

In M.K.S. system one line of force is assumed to be emanating from a unit charge or q lines of force from from a charge of q units, whatever be the surrounding insulating media.

These lines of force radiate from the charge uniformly in all directions.

Lines of force also indicate the path which a positive charge would take if it were placed near a charge of +q units and were free to move.

The arrows indicate the direction of movement of such a charge.

MATHEMATICAL TREATMENT OF COULOMB'S LAW

Consider two charges of magnitude 𝑞₁ and 𝑞₂ , assumed to be concentrated as point sources at a distance d from each other.

According to the second law of electrostatics, the force F between them may be expressed mathematically as:

F∝q1×qkmfafaie2

F∝1d2

or        F∝q1q2d2

F=k⋅q1q2d2N

                                                      ..................................(1)

where, N is Newton and k is a Constant depending on the nature of the medium between the charges. 

The value of k has been found experimentally, 

k=14πϵ0ϵr

                                                     ....................................(2)

where ,

ϵr

ϵ0

ϵ0

ϵ0

ϵ0

𝜖ᵣ is the relative permittivity of the medium intervening the charges

𝜖₀ is the permittivity of the evacuated free space

The value of 𝜖₀ in rationalised  M.K.S. unit is 8.854×10⁻¹² farads per meter.

When d is measured in meters, the constant 4𝜋 , the proportionality factor for the rationalised M.K.S. units.

Substituting the value of k from Eq. (2) in Eq. (1) we get,

F=q1q24πϵ0ϵrd2N

where,

𝑞₁ and 𝑞₂ are measured in coulombs

d in meters

𝜖 in farad / meter

F in newtons

For air         𝜖ᵣ = 1

∴    F=q1q24πϵ0d2N

when     

𝑞₁ = 𝑞₂ = 1 coulomb

d = 1 meter

𝜖₀ =  8.854×10⁻¹² farad / meter

F=1×14π×8.854×10−12×12

F=8.997×109