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Electrostatics Coulomb’s Law to Gauss Law

This blog covers complete electrostatics Coulomb's Law, electric field, electric potential, Gauss Law, equipotential surface.

6 minutes long
Posted by Mahak Jain, 20/10/2020
Electrostatics Coulomb’s Law to Gauss Law

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As the name suggest, electrostatics means the study of charges (electron, proton) at rest (static) . We can see the electrostatic phenomena in our everyday life. For instance, if we comb our hair (dry hair) then both hair and comb become charged. The brush attracts dust or small bits of paper and our hair stand on their roots . This phenomenon results from the forces between charges at rest. Coulomb’s law gives the force between point charges and hence forms the basics of electrostatics.


Matter produces and experiences electrical and magnetic effects because of a property of matter called charge . Although, every atom contains charges, it is electrically neutral. This is because number of electrons and number of protons in neutrons is same. One can create charged particles by disturbing the neutrality of an atom. Loss of electrons gives positive charge and gain of electrons gives negative charge to a particle.

Properties of Charge :

1. Conservation of charge: We cannot either destroy or create charge.

2 .Charge produces Electric field and magnetic field :  Charged particle at rest produces only Electric field . If charged particle is in unaccelerated motion , it produces Electric and Magnetic field. And if charged particle accelerates, then it not only produces electric and magnetic fields but also radiates energy in the form of electromagnetic waves .

3. Quantization of charge: The smallest charge that exists in nature is the charge of an electron. Charge on any body will be integral multiple of e. It can never be +1/3e or -1/3e.


Coulomb’s Law forms the basics of electrostatics.

As per the Coulomb’s experiment, electric force has following properties –

  1.  Electric force is inversely proportional to the square of the distance between the particles and directed along the line joining them;
  2. Electric force is proportional to the product of the charges on the two particles;
  3. Force is attractive in nature if charges are of opposite sign and repulsive if the charges have the same sign.
Coulomb's law  formula

Properties of Coulomb’s Law :

  1. Coulomb Force between two charges is an action – reaction pair which is conservative in nature and is a central force .It act’s along the line joining two point charges .
  2. Coulomb’s Law is valid only for point charges. We consider charged objects to be point charges if separation between them is very large as compared to their dimensions.
  3. The force between two point charges is independent of the presence or absence of any other charges.
  4. Electrostatic force is a conservative force.
  5. Coulomb’s Law obeys Newton’s third law ,the forces exerted by two charges on each other are equal and opposite.
coulomb's law - direction of forces


By Coulomb’s law we can calculate magnitudes and directions of electrostatic forces. But its use is limited to the point charges only. Then what about distributed and continuous charges and their interactions ?…..

We describe distributed and continuous charges and their interactions with the help of Electric Field.

We define electric field as the space around a charge in which its influence can be felt by any other charged particle.

In electrostatics, mathematically electric field is force (given by Coulomb’s Law) divided by charge.

Direction of Electric field-

  1. For a positive source charge , the electric field points radially outward.
  2. For a negative source charge ,the electric field points radially inward.
  3. Positive charge placed in an electric field ; force on the charge is in the same direction as Electric field .
  4. Negative charge placed in an electric field ; force on the charge is in opposite direction as Electric field.
Electric field due to point charges

Electric Field Lines

Graphical representation of electric field by drawing certain curves known as lines of electric force or electric field lines. The lines of force provide an idea to visualize the pattern of electric field in a given space.

These lines of force are drawn in space in such a way that the tangent to the line at any point gives the direction of the electric field at that point.

electric field lines


Gauss’s law is an alternative to Coulomb’s law. It provides a different way to express the relationship between electric charge and electric field.

Gauss’s Law states that the total electric flux through a closed surface is proportional to the total electric charge enclosed within the surface.

Electric field given by the Gauss’s law  is the resultant of electric fields due to all the charges present inside, as well as, outside the given closed surface. Charges that appears in the law (formulae) are only the charges contained within the closed surface. Flux due to charges outside the closed (Gaussian) surface is zero as the flux entering the surface leaves it. The net flux through the surface is proportional to the net number of lines leaving the surface. Net number of lines means the number of lines leaving the surface minus the number of lines entering the surface. Thus, net flux is positive if more lines are leaving than entering and net flux is negative if more lines are entering than leaving.

One point regarding Gauss Law to be kept in mind is that if Coulomb’s Law (fundamental of electrostatics) fails the Gauss Law will also fail.

Gaussian Surface

A surface on which Gauss’s law is applied is called Gaussian surface. We choose different Gaussian surface for different charge distributions. Moreover, we usually consider spherical gaussian surface around point charge and spherical charge distribution and cylindrical Gaussian surface around linear charge distribution.

gauss law


The potential at any observation point in static electric field is the work done by the external agent(or negative of work done by the electrostatic field) in slowly moving a unit positive point charge from infinity to observation point

electric potential formulae derivation

Potential difference –

Potential difference between any two points 1 and 2 is equal to the work done by an external agent in slowly moving the unit test charge from 1 to 2.

  1. In the direction of the electric field , potential always decreases.
  2. Potential difference is the difference of potential between two points. It is also called voltage.
  3. Potential difference between two points is independent of the reference point.
  4. In fact, the potential at a point is the potential difference between that point and infinity.


As the name suggests, equipotential surface is a surface with same potential at its every point. So, for a given charge distribution, locus of all points having same electric potential, are equipotential regions.

Properties of Equipotential Surface-

  1. Two equipotential surfaces can not intersect each other.
  2. Electric force lines always intersect an equipotential surface perpendicularly.
  3. If a charge moves between two points on an equipotential surface, then it requires zero work.
  4. One has to do some work to move a charge from one equipotential surface to another as potential of two different equipotential surfaces are different.

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