Magnitude of Electric Field Intensity on Equatorial Line of Electric Dipole

The magnitude of electric field intensity at a point on the equatorial line of an electric dipole is given by the formula:

E = k (p/d^3)

Where,
k = Coulomb’s constant
p = electric dipole moment
d = distance between the charges of the dipole

Vector Form of Electric Field Intensity on Equatorial Line of Electric Dipole

The vector form of electric field intensity on the equatorial line of an electric dipole can be obtained by considering the two charges of the dipole as point charges and using the principle of superposition. The electric field intensity due to each charge is given by:

E1 = k (q/d^2) (cosθ)
E2 = k (q/d^2) (cosθ)

Where,
q = magnitude of charge
d = distance between the charges
θ = angle between the line joining the charges and the line joining the point on the equatorial line and the midpoint of the dipole

The net electric field intensity at a point on the equatorial line is obtained by adding the electric field intensity due to both charges. Since the charges are of equal magnitude and opposite in sign, the net electric field intensity is zero along the axis perpendicular to the dipole.

Magnitude of Electric Field Intensity on Axial Line of Electric Dipole

The magnitude of electric field intensity at a given distance from the centre of a short electric dipole on the axial line can be obtained by using the formula:

E = k (2p/d^3)

Where,
p = electric dipole moment
d = distance between the charges of the dipole

Explanation

The electric field intensity on the axial line is twice that of the equatorial line because the distance between the charges of the dipole is equal to the distance between the point on the axial line and the midpoint of the dipole. Therefore, the electric field intensity due to each charge on the axial line is given by:

E1 = k (q/d^2)
E2 = k (q/d^2)

The net electric field intensity at a point on the axial line is obtained by adding the electric field intensity due to both charges. Since the charges are of equal magnitude and opposite in sign, the electric field intensity on the axial line is given by:

E = E1 + E2 = k (q/d^2) + k (q/d^2) = k (2q/d^2)

Using the relation between electric dipole moment and charge, we can write:

p = qd
Therefore,
E = k (2p/d^3)

Hence, the magnitude of electric field intensity on the axial line is twice that of the equatorial line.