The Intensity of Electric Field Due to a Dipole

The intensity of an electric field E at a point due to a dipole can be determined by considering the dipole moment p and the distance r from the center of the dipole. The relationship between the intensity of the electric field and the distance r is given by E ∝ 1/r^3.

Explanation:

1. Definition of a Dipole:
A dipole is a pair of equal and opposite charges separated by a small distance. The dipole moment p is a vector quantity that represents the magnitude and direction of the dipole. It is defined as the product of the charge magnitude and the separation distance between the charges, p = qd.

2. Electric Field Due to a Dipole:
The electric field E at a point due to a dipole is the vector sum of the electric fields produced by the positive and negative charges of the dipole. The electric field lines originate from the positive charge and terminate on the negative charge.

3. Electric Field at a Point on the Axial Line:
Consider a point P on the axial line of the dipole, which is a line passing through the midpoint of the dipole and perpendicular to the dipole axis. The distance of point P from the center of the dipole is r. Due to the axial symmetry, the electric field components produced by the charges along the axial line cancel each other in the perpendicular direction, leaving only the axial component.

4. Calculation of Electric Field:
The electric field E at point P is given by the formula E = k(p/r^3), where k is the electrostatic constant. The formula shows that the electric field is inversely proportional to r^3.

5. Variation of Electric Field with Distance:
As the distance r increases, the electric field intensity decreases. This is because the electric field lines spread out over a larger area as the distance increases, resulting in a decrease in the electric field strength.

6. Inverse Cubic Relationship:
The inverse cubic relationship between the electric field intensity and the distance r is observed due to the dipole nature. The dipole moment p is a vector quantity, and the electric field decreases with the cube of the distance due to the combination of the inverse square law for the point charge and the dipole nature of the system.

In conclusion, the intensity of the electric field E due to a dipole at a point a distance r from the center of the dipole is inversely proportional to r^3. This relationship arises from the dipole nature of the system and the combination of the inverse square law for the point charge and the dipole separation distance.