Maxwell's Equations

Maxwell was the first person to calculate the speed of propagation of electromagnetic waves which was same as the speed of light and came to the conclusion that EM waves and visible light are similar.

These are the set of partial differential equations that form the foundation of classical electrodynamics, electric circuits and classical optics along with Lorentz force law. These fields highlight modern communication and electrical technologies.

Maxwell’s equations integral form explain how the electric charges and electric currents produce magnetic and electric fields. The equations describe how the electric field can create a magnetic field and vice versa.

Maxwell equations

  1. Gauss Law

Gauss law describes the nature of electric field around electric charges. The law is expressed in terms of electric charge density and electric charge density.Gauss LawThe inverted triangle is called as the divergence operator.

The equations hold good at any point in space. When the electric charge exists any somewhere, the divergence of D at that particular point is nonzero, else it is zero.

  1. Gauss’ Magnetism Law

You need to be familiar with Gauss Law for the electric field to understand this equation.Gauss' Magnetism LawYou can see that both the equations indicate the divergence of the field. The top equation states that the divergence of the Electric flux density D equals the volume of electric charge density.

The second equation states the divergence of the Magnetic Flux Density (B) is null.

  1. Faraday’s Law

Faraday’s LawFaraday was a scientist whose experiment setup led to Faraday’s Law which is shown in the figure below.Faraday’s Law SetupThe experiment is not very complex. When a battery is disconnected, no electricity flows through the wire. Hence, no magnetic flux is induced in the iron (Magnetic Core). The iron acts like a magnetic field that flows easily in a magnetic material. The purpose of the core is to form a path for the flow of magnetic flux.

  1. Ampere’s Law

Ampere’s LawThe law shows the relationship between the flow of electric current and the magnetic field around it. Suppose the wire carries a current I, the current produces a magnetic field that surrounds the wire.

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Practise This Question

A car move goes from A to B in 4 hours at an average speed of 40 miles per hour. At t=1 hour, its speed would be: