Physics explains: The maxwell's equations

josselin84 (34)in #steemstem • 8 years ago

Once upon a time, there was a world where sparks, sticky papers, and magnets were fascinating to scientists.

These phenomena were used to build great things, but it wasn't until the 19th century that people began to understand how they were related, thanks to the work of lots of physicists determined to put the pieces together, a task to which Maxwell gave the blow, synthesizing all these electrical and magnetic phenomena into the equations we write today.

These are the Maxwell Equations.

Let's start with the basics:

Space is filled with a thing called The electromagnetic field. Only our protagonists can "feel it": The charges and the magnets.

The field is the medium through which charges and magnets can be influenced; by attracting, repelling, turning, etc. This intermediation has some rules; how charges and magnets disturb the field and how the field disturbs itself is condensed in the Maxwell Equations.

Now, how this field affects loads is given by another equation, the Lorentz Force equation.

So Maxwell's equations are not about how the charges move, but about how the field is how it changes.

The way we wrote them has changed a lot over time: at first, there were eight, but then it became clear that they could be reduced to four.

Thanks to our current knowledge, we know that the most natural way is to express them in two, but today I will not go into detail and speak in the traditional way that we all learn.

In this format, we separate the electromagnetic field into two different fields, the electric field, which tells you where and how strong a positive charge is going to be pushed into it, and the magnetic field, which tells you where and how strong a magnet is going to be directed.

First equation: Gauss' law.

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This describes how charges affect the electric field.

Specifically, it tells you that electric charges are sources of the electric field, if they are positive or sinks of electric field if they are negative, that it is nothing more than to say in terms of a fancy field that charges of the same sign repel and attract differently.

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Gauss' law also captures that the electric field decays with distance and does so in a very precise way: with the square of the distance.

This gives the electric field some very funny and useful geometric properties.

Second Equation: Gauss' law for magnetism

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The reality is that this law does not have an exact name, possibly because what it says is simple: The sources and sinks of the magnetic field do not exist.

That is not to say that there are no objects that can create magnetic fields; that is what magnets do; that is what magnets do since there are neither sources nor sinks, the magnetic field must always "close" on itself.

For example, if you try to split a magnet in two by wanting to split it into two monopoles, the field closes in the area you have cut, returning two magnets with two poles each.

In short: In our world, monopoles are not possible.

Even though, it is not unimaginable that in the crazy primitive universe these monopoles might have existed.

In this hypothetical case, the Gauss law of magnetism would be very similar to the Gauss law of the electric field and, using the appropriate mathematics, we could synthesize all Maxwell's equations not to two but to just one equation.

Third Equation: Faraday's law

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Behind this law is the basic principle behind almost every power plant on the planet, it tells us that if a magnetic field changes over time it activates the electric field in a precise way: by closing.

Specifically, if the magnetic field increases, the electric field is oriented clockwise, if it decreases it is oriented the other way round.

In short, we are told that not only can loads and magnets influence the fields, they can also influence each other. Yeah, in both directions.

Fourth equation: Ampere's law

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Ampere's Law: This one talks about an electric field changing in time or moving charges, that is to say, an electric current, activating the magnetic field (closing, as it should be).

This new element, the electric current element, is very useful in applications, as it allows the generation of artificial magnets.

It is enough to pass an electric current through a coil with the appropriate shape and you have a magnetic field, the more intense the current, the more intense the magnetic field.

This is an electromagnet and most of the world's magnetic fields are generated by it, including the one that protects us from the solar wind.