Electric Field Intensity

In electrostatics, when there are two charges in space, an electric force acts between them which is directly proportional to the two charges’ magnitude and inversely proportional to the square of their distance. This is called Coulomb’s law of electrostatics.

Force is a vector quantity and its formula is presented:

F = (kq₁q₂/r²) r̂

Where 

• q₁ and q₂ are the charges

• r = distance between charges

• k = 1/4πε₀ ( a constant)

• ε₀ = permittivity of free space and it is equal to  8.85 × 10⁻¹² m⁻³kg⁻¹s⁴A².

There are two types of charges: positive and negative. All charges have their own electric field intensity, and their magnitude can be determined by the amount of electric force experienced by a test charge q₀ in presence of that electric field.

The formula for electric field is:

E=F/qo

Since the electric field is a vector quantity whose direction is the same as the direction of the force.

Properties of Charges

• Charges are scalar quantities; they do not depend upon the direction

• Like charges repel each other and opposite charges attract each other

• Charges can neither be created nor destroyed, so they follow the conservation of charge

• Electric charges do not depend upon the frame of reference.

• Free charges are always found in the integral multiple of the basic electronic charge. They are quantized in nature as q = ne, where 

  • q = total charge 

  • n = integer

  • e = charge of an electron which is equal to 1.6 × 10⁻¹⁹ C.

Electric Field Intensity

Electric field intensity is the strength of the electric field at a particular point in space.

The units for electric field intensity are: 

• Newton per coulomb

• Volt per metre

The magnitude of electric field intensity can be determined by the amount of electric force experienced by a test charge q₀ in presence of the electric field.

E=F/qo= kqq₀/r²q₀ = (kq/r²)r̂

In electrostatics, the electric field is conservative. This indicates that when work is done by a force in moving a charge from one place to another, it depends only on its initial and final position, not on the path followed. And according to Maxwell’s equation, curl E = 0, where E is the conservative field.

Electric field intensity for continuous charge distribution is given as:

E= (k∫dq/ r²)r̂

1. For linear charge distribution:

• dq = λdl

• λ = linear charge density

• E = k∫λdl/r²

2. For surface charge distribution:

• dq = σds

• σ = surface charge density

• E = k∫σds/r²

3. For surface charge distribution:

• dq = ρdv

• ρ = volume charge density

• E = k∫ρdv/r²

Formulae Related to Electric Field Intensity

• Electric field intensity at a point along the axis of a uniformly charged ring:

E = kqx/ ( x²+R²)3/2

• Electric field intensity at a point due to an infinitely long charged wire:

E = λ/2πε₀r

• Electric field intensity at a point due to an infinite charged thin sheet:

E = σ/2ε₀

And due to infinite thick sheet: 

E = σ/ε₀ 

• Electric field intensity at the centre of charged semicircular wire:

E = 2kλ/r

• Electric field intensity at a point due to a charged disc:

E = σ/2ε₀ [1- x/{√(R² + x²)}]

• Electric field intensity at a point due to a hollow charged sphere:

E = 0 (r<R)

E = kQ/r² (r>R)

• Electric field intensity at a point due to a charged solid sphere:

E = ρr/3ε₀ (r<R)

E = kQ/r² (r>R)

• Electric field intensity at a point due to uniformly charged infinite cylinder:

E = ρr/2ε₀ (r<R)

E = ρR² /2ε₀r (r>R)

• Electric field intensity at equatorial point of a dipole:

E = kp/ ( r² + a² )3/2

E = kp/ r³ ( a <<< r )

• Electric field intensity at the axial point of a dipole:

E = k 2p/ r³

Properties of Electric Field Lines

• Electric fields originate from positive charges and terminate in negative charges.

• Electric field lines never intersect each other.

• The lines are perpendicular to the surface of the charge.

• Field lines are always continuous.

• They do not form closed loops.

• The tangent drawn at any point in the electric field gives the direction of the field at that point.

• The greater the magnitude of electric field intensity, the more the field lines.

• Electric fields depend on the frame of reference.

Electric Flux

Electric flux is the measure of the amount of electric field passing through a given surface. The formula for electric flux is:

Φₑ = EA= E.A cosθ

Gauss Law of Electrostatics

According to Gauss Law, electric flux through a closed surface is directly proportional to the charge enclosed by that closed surface.

• φ = ∮ E.ds = qen/ε₀ (Integral form of Maxwell’s equation)

• ▽E= ρ/ ε₀ (Differential form of Maxwell’s equation)

Conclusion

According to Coulomb’s law, the force acting between two charges is inversely proportional to the square of their distance. In the case of point charges, the electric field intensity is directly proportional to 1/r². And in the case of a dipole, the intensity is directly proportional to 1/r³.

Same charges like electron and electron repel each other, and opposite charges like electron and proton attract each other. In electrostatics, electric fields are conservative in nature.

According to Gauss Law, electric flux through a closed surface is directly proportional to the charge enclosed by that closed surface.