Permittivity of Free Space

We can say that a dipole is a pair of opposite charges with equal magnitudes and they are separated by a distance d. We can assume two charges with equal magnitude Q and they both are separated by a distance D. At this point, we can assume that the first charge is negative, and the second charge is positive. This particular combination can be called an electric dipole. Therefore, it can be said that the formation of an electric dipole is because the equal and opposite charges are grouped together and separated by a distance.

What is the Electric Dipole Moment?

Generally, the electric dipole moment is the measurement of the intensity of the electric dipole. The magnitude of the dipole moment is the product of any of the charges and the distance between them. We must remember that the dipole moment is a vector that moves from a negative to a positive direction. The formula to calculate the electric dipole moment of equal and opposite charges is:

P = q × d

Where the magnitude of charges is denoted by q, d denotes the distance between them, and p denotes the electric dipole moment.

Most of the materials are electrically neutral, as they are made up of atoms and molecules. On the behaviour of charges, we can classify the molecules into two categories, i.e., polar and nonpolar molecules.

Electric Potential Due to a Dipole

We can assume that two charges, i.e., -q and +q are placed at a small distance l and this combination is called as electric dipole.  The electric potential at distance r from the dipole is given by:

V = (1 ⁄ 4 π ε0) (p cosθ / r2)

Where V denotes the electric potential, the electric potential is denoted by p, r denotes the distance of a point of potential, and the angle subtended by the dipole to the point is denoted by θ.

Dipole Placed in an Electric Field

Regardless of the fact that two forces act on a dipole end and cancel out each other as free vectors, they still function as separate points. Therefore, torque is formed on the dipole. Moreover, the dipole would have a spinning action because of the torque. We can assume an electric dipole in the existence of an electric field. A force would be subjected to the electric dipole, which is denoted as the torque. The force that is exerted on the dipoles in an external field is termed torque. We can calculate it by:

τ = p × E

or

τ = p E sinθ

where the torque on the dipole is τ, p is the dipole moment, E denotes the electric field, and the angle between the electric field and dipole is θ.

The Permittivity of Free Space

The ability of a vacuum to let an electric field pass through it is known as the permittivity of free space. Permittivity is the measurement of how tough or easy it is to form an electric field inside a medium. The ability to pass an electric field in a vacuum is known as free space. The permittivity of free space is a physical quantity and is denoted by ε0. Farad per metre is the Si unit of permittivity of free space. Generally, it is equivalent to 8.85×10-12 F/m. 

Calculation of Permittivity of Free Space

We can define the value of ε0 by using the formula:

ε0 = 1/ μ0c2

In the above formula, c denotes the speed of light, and the permittivity of free space is denoted by μ0.

The value of μ0 is around 4π×10-7 H/m, and the value of c is 299792458 m/s. Hence, we can calculate the value of ε0 by using the formula:

ε0 = 1/ 4π×10-7 × 2997924582 = 625000 / 22468879468420441π

The value approximates 8.85418781×10-12 F/m.

Conclusion

We know that a dipole is a pair of opposite charges with equal magnitudes that are separated by a distance between them. The electric dipole moment is the measure of the magnitude of the electric dipole. The concept of the dipole moment is very useful when we can observe the effects of microscopic separation of charge. However, the actual distance between the charges is so small that it cannot be measured. Molecules may have a permanent dipole moment. The atoms and molecules that do not have a permanent dipole moment can obtain one when they are placed in an external electric field.