Gauss Law vs Coulomb Law
Gauss’s law and Coulomb’s law are two very important laws used in electromagnetic field theory. These are two of the most fundamental laws, which lead to the development of the electromagnetic field. These laws, along with Ampere’s law, lead to Maxwell’s equations. Maxwell’s equations are a set of four equations that can describe any phenomenon in electromagnetic theory. A thorough understanding in these two laws is required, to understand the theories of electromagnetism fully. In this article, we are going to discuss what Gauss’s law and Coulomb’s law are, their applications, the definitions, the similarities between these two, and finally the differences between Gauss’s law and Coulomb’s law.
Gauss’s Law
Gauss’s law is a very important law that describes the properties of electric fields, magnetic fields and gravitational fields. The Gauss’s law for electric fields states that the electric flux through any closed surface is proportional to the electric charge enclosed by the surface. It can be expressed as ∅=Q/ε_{0} where φ is the total electric flux over the surface, Q is the charge enclosed by the surface, and ε_{0} is the dielectric constant. To understand this concept, one must first understand the concept of electric flux. The electric flux over a surface is a measurement of the number of electric field line passing through a surface. This is directly proportional to the number of electric field lines across the surface. The Gauss’s law for the magnetic fields is a very important law. The Gauss’s law for magnetic fields states that the total magnetic flux over any closed surface is zero. This is because magnetic monopoles do not exist. Magnetic poles only exist as dipoles. In any given closed surface, the net magnetic polarity is zero. Therefore, the magnetic flux over any closed surface is zero.
Coulomb’s Law
Coulomb’s law is a law describing the interactions between electrically charged particles. This states that the force between two electrically charged particles is proportional to the charges and inversely proportional to the square of the distance between the two particles. This can be expressed using the equation F = Q_{1}Q_{2}/ 4πr^{2}ε_{0} where Q_{1} and Q2are the charges of the particles, r is the distance between the two charges, and ε_{0} is the dielectric constant of free space. If this equation is defined for a medium other than free space, ε_{0} should be replaced with ε, where ε is the dielectric constant of the medium. If these charges were of the same sign, F would be a positive value. This means the two charges are repelling each other. If these two charges are of different signs, F becomes a negative value; thus, describing an attraction between the two charges.
What is the difference between Coulomb’s law and Gauss’s law? • Coulomb’s law describes the interactions between two charges while Gauss’s law describes the flux over a closed surface from the property enclosed inside the surface. • Coulomb’s law is applicable only to electric fields while Gauss’s law is applicable to electric fields, magnetic fields and gravitational fields.

Waseem Akram says
Gauss’s law can be used in case of rapidly moving charges but coulombs law is for charges at rest(that move very slowly)