Dimension of Electric Field & its derivation

Dimension of Electric Field: The Electric Field is an invisible field surrounding electrically charged particles. Any charged particle that enters the field experiences a force which, depending upon the nature of the charge on it, repels or attracts it. The dimensional formula of electric field intensity is:

M¹L¹T ^-3 I ^-1

In this article, we tell you what is Dimension of Electric Field and its derivation.

See Also:

Dimension of Speed of Light	Dimension of Surface Tension
Dimension of Wavelength	Dimension of Tension

Derivation of Dimension of Electric Field | Derivation of Electric Field Dimensional Formula

As we know Electric Field is equal to 

Hence,

To calculate Dimensions of Charge q, we use the formula

Where i is current, and

t is time

Hence,

The Dimensions of Force is 

Thus, the Dimensional Formula of Electric Field Intensity is

 

 

Hence proved that the Dimension of Electric Field is M¹L¹T ^-3I^-1 

Electric Field

When a charged body is present in space, the charged bodies in the vicinity of the object experience a force. This area around a charged body is called an electric field, and the force experienced by the other charged bodies is called Electric Force. The Electric Field is defined as the Electrostatic Force per unit charge experienced by a charged body at rest at a point in space.

Ideally speaking, the Electric Field around a charged object stretches to infinity. But practically, the Electric Field is weak for farther objects. This is because the density of the electric field is inversely proportional to the square of the distance between the two charged bodies. Thus, when the distance between two charged bodies doubles, the force they experience decreases by a factor of four. These forces are governed by Coulomb’s law and also depend upon the amount of charge present on both bodies.

An Electric Field is an electromagnetic spatial perturbance. This means that like all electromagnetic things, the Electric Field also travels at the speed of light. In vacuum, it is nearly equal to 3 × 10 8 m/s. It also means that the removal of the Electric Field happens at the same speed. Thus, if a highly charged body is placed at a distance of 1 Astronomical Unit from the Earth and is somehow suddenly made to disappear, we wouldn’t experience the absence of its electric field for about eight minutes. 

Electrostatic Force

At the core of the Electric Field is the electrostatic force. As mentioned above, it is a force experienced by a charged body when placed in an electric field. This is not just true for large bodies, but also for subatomic particles. The force is experienced between a nucleus and the electrons of an atom. The force is also experienced between molecules of a substance and is responsible for Tension in them when an external force stretches it. It is also known as the Coulomb Force.

The Electrostatic Force can be attractive as well as repulsive. Coulomb, through experimentation, found out that bodies with like electric charges repel each other and those with opposite charges attract each other. Coulomb also discovered with experimentation that the magnitude of the force between two charged bodies is inversely proportional to the square of the distance between them. It is known as the inverse square law. 

Where k = 1/4πε₀

Where ε0 is vacuum permittivity, which signifies the density of the Electric Field permitted to form in space (vacuum) after a charged body is placed there. It is equal to  8.8541 × 10⁻¹² C² kg⁻¹m⁻³s²

Q and q are charges

R is the distance between Q and q

However, the Coulomb’s Law is based on a few assumptions. They are:

1. The charge on the bodies must be uniformly distributed. Thus, point charges are used to demonstrate the law.
2. The charged bodies must be at some distance from each other, i.e., they must not overlap.
3. The charged bodies must be at rest.