Light, a mysterious thing; people said that it is a ray; physicist said that it is a photon beam, and Faraday said it is an electromagnetic wave. No one believed him, some physicist laughed at him, until Maxwell came with mathematical solution. A different idea, different thought and perception built on the basis of four equations. It was not only the problem solving in advanced mathematics, but changing the concept of people, changing the vision of scientists and physicists; to understand universe, to understand the hidden mystery and to know how god created this world.
The understanding of light and wave in terms of Maxwell’s equations is easy and efficient. But if asked, most people outside physics would not be able to identify Maxwell’s equations, nor would they be able to state that they dealt with electricity and magnetism. However, Maxwell’s equations have many very important implications in the life of a modern person, so much so that people use devices that function on the principles in Maxwell’s equations every day without even knowing it.
I, being an engineering student can see its use in day to day life. Even in the lectures of Optical fibers, Antennas & wave Propagation, we use them to find Electric and Magnetic fields of radiation pattern of antennas in different coordinate systems. Many of us used to get bored solving the equations because of calculation complexity and problem in interchanging coordinate system. Obviously, they are challenging but I respect these four equations and never forget as long as I live.
1. Gauss’ Law for electric fields: ∇.D=ρ
The electric field tends to point away from positive charges and towards negative charges. More technically, it relates the electric flux through any hypothetical closed "Gaussian surface" to the electric charge within the surface.
The divergence of the outgoing electric field over an area enclosing a volume equals the total charge inside, in appropriate units.
2. The corresponding formula for magnetic fields: ∇.B=0
There are no "magnetic charges" (also called magnetic monopoles), analogous to electric charges. Instead the magnetic field is generated by a configuration called a dipole, which has no magnetic charge but resembles a positive and negative charge inseparably bound together. The total magnetic flux through any Gaussian surface is zero, or that the magnetic field is a solenoidal vector field.
No magnetic charge exists: no “monopoles”.
3. Faraday’s Law of Electro-Magnetic Induction: ∇×E= - ∂B/∂t
How a changing magnetic field can create ("induce") an electric field. This aspect of electromagnetic induction is the operating principle behind many electric generators: A bar magnet is rotated to create a changing magnetic field, which in turn generates an electric field in a nearby wire.
The first term is curl of Electric field, usually a wire, and gives the total voltage change around the circuit, which is generated by a time varying magnetic field threading through the circuit.
4. Ampere’s Law plus Maxwell’s displacement current: ∇×H=J+ ∂D/∂t
Magnetic fields can be generated in two ways: by electrical current (this was the original "Ampere's law") and by changing electric fields (this was "Maxwell's correction"). Maxwell's correction to Ampere's law is particularly important: It means that a changing magnetic field creates an electric field, and a changing electric field creates a magnetic field. Therefore, these equations allow self-sustaining "electromagnetic waves" to travel through empty space.
Total magnetic force around a circuit in terms of the current through the circuit, plus any varying electric field through the circuit (that’s the “displacement current”).
Maxwell’s above equations describe the electric and magnetic fields arising from varying distributions of electric charges and currents, and how those fields change in time. The equations were the mathematical distillation of decades of experimental observations of the electric and magnetic effects of charges and currents. Maxwell’s own contribution is just the last term of the last equation but realizing the necessity of that term had dramatic consequences. It made evident for the first time that varying electric and magnetic fields could feed off each other; these fields could propagate indefinitely through space, far from the varying charges and currents where they originated. Previously the fields had been envisioned as tethered to the charges and currents giving rise to them. Maxwell’s new term (he called it the displacement current) freed them to move through space in a self-sustaining fashion, and even predicted their velocity it was the velocity of light!
Maxwell solved these equations and the important two equations came, this gave the idea about light being a wave. Physicists started talking about wave nature of light and in the history of physics; it climbed one more step in a long endless journey.These were space and time dependence of electric and magnetic field. It was clear from these equations that the free space propagation of wave, which was variation of electric(E) and magnetic(B) field can only occurs at a particular speed c=2.99×108 (m/s), which was the speed of light(c). In free space, wave propagates at the speed of light. Faraday was true! Maxwell had proven Faraday! Light is an electromagnetic wave.
The concept for the understanding of light helped Einstein for the discovery of his world famous equation: E=mc2. This equation is simply says mass is convertible to energy and the energy is mass times the square of velocity of light. The speed of light is 3×108 m/s, its square is 9×1016, which is very large. If a small amount of mass is converted into energy than large energy can be created. One thing we have to know is how to disintegrate mass? Scientists of today know it and they have made Hydrogen and Atom bombs using these principles.
We human have come so far from the beginning and we have achieved so much. The application of Maxwell’s equations is in various areas. But there are also lots to explore. I suggest readers to use them, try to solve in your own way and luckily you may get different results, may be that would be helpful for understanding our universe more clearly, that may change the perception of people and you may get Nobel Prize.
(This article was published in Annual magazine of department of Electrical and Electronics, encipher-2010)
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