Coulomb's Law & Electric Field | Definition, Expression, Facts

Coulomb's Law:

According to Coulomb's law, the force of interaction between two point charges is directly proportional ($\propto$) to the product of two charge and inversely proportional ($\propto$) to the square of distance between them.

Let, $q_1$ and $q_2$ be the two point charge separate by a distance $r$.

We have force of interaction

$F \propto q_1q_2.........(i)$

$F \propto \frac{1}{r^2}.........(ii)$

From $(i)$ and $(ii)$ we get,

$F \propto \frac{q_1q_2}{r^2}$

$F = k\frac{q_1q_2}{r^2}.........(iii)$

Where,

$k=$ Electrostatic force constant.

In S.I. unit

$K=\frac{1}{4\pi\epsilon_0}$

Where, $\epsilon_0\to$ absolute permittivity of force in space.

$(iii)\Rightarrow F=\frac{1}{4\pi\epsilon_0}.\frac{q_1q_2}{r^2}$

In C.G.S. unit

$k=1$

$(iii) \Rightarrow F=\frac{q_1q_2}{r^2}$

In material medium,

$(iii) \Rightarrow F=\frac{1}{4\pi\epsilon}.\frac{q_1q_2}{r^2}$

Where, $\epsilon\to$ absolute permittivity of material medium.

Note: Without using point charge or source charge we can also produced Coulomb's law with the help of electrical fish we can produce Coulomb's law.

Electrical Fish:

The fish which can produce electric field is known as electrical fish. Example: Ray, Cat Fish etc.

Similarity between Coulomb's Law and Newton's Law of Gravitation is "For both law we used inverse square distance law".

Two differences between Coulomb's Law and Newton's Law of Gravitation

Coulomb's Law

1. Coulomb's law is valid for charge.

2. The proportionality constant of this law is known as Electrostatic force constant.

Newton's Law of Gravitation

1. Newton's law of Gravitation is valid for mass.

2. The proportionality constant of this law is known as Universal Gravitational constant.

Coulomb's law is not a universal law because it depends on medium.

The force arises between two static charge is known as central force because this force arises along the line joining between the center of charge.

Electric Field

If we placed a charge in a stage then the property of the stage is modified and the modified space is known as electric field.

We have two types of Electric Field

1. Uniform Electric Field.

2. Non-uniform Electric Field.

1. Uniform Electric Field

If the strength of the field at all point remains same then the field is known as Uniform Electric Field.

2. Non-uniform Electric Field.

If the strength of the field is different at all point then the field is known as Non-uniform Electric Field.

Note: For a point charge the electric field is infinite.

Electric Field Intensity

The amount of force experienced by unit positive charge placed in an electric field is known as electric field intensity.

Mathematically,

$E\,or\,I=F$

$=\frac{F}{I}$

$=\frac{F}{q_0}$

Electric field intensity is a vector quantity. Direction of electric field intensity is along the direction of force.

We have,

$E=\frac{F}{q_0}$

For electron, $q_0=-e$

$\therefore E=\frac{F}{-e}$

$\Rightarrow F=-eE$

That is direction of electric field or force is opposite to the direction of flow of electron.