Maxwell's Equations And Their Meaning

Today, the flagship equation of physics is the mass energy equivalence, the E = mc^2. This equation is so famous that even a layman has come across it or has seen it somewhere at least once in his life. The mass energy equivalence belongs to the theory of special relativity, devised by Albert Einstein in 1905. But, what is the origin of special relativity? The answer is Electricity and Magnetism. Yes! You read it correct. The roots of theory of relativity are embedded in the four famous equations of electricity and magnetism, the Maxwell's Equations.

The Four Maxwell's Equations

James Maxwell was a theoretical physicist who proved Faraday right. Faraday hypothesised that the light is an electromagnetic wave. Faraday wasn't a rigorous theoretical scientist, but Maxwell was. These 4 equations are not formulated by Maxwell. The first two equations are Gauss's laws in electricity and magnetism respectively, the third equation is the Faraday's law and the fourth one is the Ampere's circuital law with a correction term that was introduced by Maxwell. So why are they named after him? The reason is that Maxwell brought these independent equations of electricity and magnetism together and showed that the two are deeply connected.

Maxwell's equations were the turning point in the history of mankind. As Carl Sagan said," They have had a greater impact on human history than any ten presidents." Let us now look at these game changing equations and what do they really mean.

1. Gauss' Law of Electrostatics Gauss' law in electrostatics. Remember, if the electric field did not follow the inverse square law, Gauss' law would not have been possible.

Meaning of equation

Gauss' law in electrostatics tells us three important things. First: There can exist an independent electric charge in space. This means a single positive charge or a single negative charge can have its own existence. They do not have to exist in pairs. Second: The number of electric field lines that comes out of a volume is directly proportional to the charge that is contained in it. Third: The electric field, like the gravitational field, follows the inverse square law. Thus the Gauss' law is just another version of Coulomb's law in electrostatics. To read about Gauss' law in detail, click here.

2. Gauss' Law In Magnetostatics

Meaning of Equation

This is the easiest of the four Maxwell's equations. The one line meaning of this equation is: Magnetic monopoles do not exist in nature. So if you cut a bar magnet into two pieces, you won't have a separate north and south poles. Instead, you'll have two new bar magnets, each having its own pair of north and south poles. If magnetic monopoles are discovered, the right hand side of the equation will change. To read this law in detail, click here.

Meaning of Equation

If you are using anything that runs on electricity, thank this equation. Nothing would have been possible without this third equation, known as the Faraday's law. This equation is the architect of the modern world. It says, A changing magnetic flux through a closed circuit will produce an electromotive force in that circuit. A remarkable statement in itself. Thus you can produce an electric field from the magnet itself. No other equation captures the beautiful link between the two diverse fields than this one. The Faraday's equation made it possible to construct solenoids, electric motors, generators and transformers. To read about this law in detail, click here.