What is an Electric Field?

What is an Electric Field

An electric field is an electric property of each point in space when a charged particle is present in any form.

An electric field is also known as an electric field strength or electric field intensity. The magnitude and direction of the electric field are represented by vector E.

The charged particle can be positive or negative charged. When charged particles come in contact with each other, it will experience a force. This force is represented by the line of force.

The direction of the force is depending on the polarity of charges. If charges have similar polarity, charges experience repulsive force. And if charges have different polarities, charges experience an attractive force.

Definition of Electric Field

The vector field can be associated with each point in space. And the electric field is mathematically defined in vector filed as the force per unit charge exerted on positive charge at rest of that point.

The formula of an electric field is,

    \[ \vec{E} = \frac{\vec{F}}{Q} \]


F = Force and Q = Charge

Coulomb’s Law

Coulomb’s law is an experimental law of physics that computes the amount of force between two stationary charged particles.

In 1784, a French physicist, Charles-Augustin de Coulomb found that the force is inversely proportional to the square of the distance between charges. And it is directly proportional to the products of charges.

For example, let’s take two point charges Q1 and Q2. And the distance between point charges is d. The force of repulsion or attraction between them is F. So,

    \[ F \propto Q_1 Q_2 \]

    \[ F \propto \frac{1}{d} \]


    \[ F \propto \frac{Q_1 Q_2}{d} \]

    \[ F = k \frac{Q_1 Q_2}{d} \]

Where, k is a proportionality constant. And the value of k is,

    \[ k = \frac{1}{4 \pi \varepsilon_0} \]

ε0= permittivity of vacuum = 8.854 X 10-12  C2 N-1 m-2

Therefore, the value of k is 9 X 109 Nm2/C2

What is the direction of the electric field?

The electric field is a vector quantity. Therefore, it has direction as well as magnitude. The effect and direction of an electric field are different for a point charge, distributed charge, and multiple point charge.

First, we consider a single isolated point charge Qi is present in space. The below equation is for a field for a single isolated point charge.

    \[ \vec{E} = \frac{1}{4 \pi \varepsilon_0} \frac{Q_i}{r^2} \hat{r_i} \]

The electric field direction points straight away from the positive charge and straight towards the negative charge.


If space has more than one charge, in this condition, the field is calculated by summing the field from the individual charge. And the equation of the total field is given as,

    \[ \vec{E} = \frac{1}{4 \pi \varepsilon_0} \sum_{i} \frac{Q_i}{r^2} \hat{r_i} \]

If the charges are distributed on a surface, the total charge can be calculated by the integral summation of the small part of the surface. And the equation of the total field is given as,

    \[ \vec{E} = \frac{1}{4 \pi \varepsilon_0} \int \frac{dQ}{r^2} \hat{r_i} \]

Where r represents the distance between small part of charge and the location where we measure the field. And vector ri gives the direction of force which is in line between the charge and the location.

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