Electromagnetism.
"The study of the physical interaction among electric charges, magnetic moments, and electromagnetic fields."
Table of contents:
1. Fields and their Properties.
2. Maxwell's Equations.
3. Consequences of Electric and Magnetic fields.
4. The Elusive Aether.
5. What is light?
6. The Fourth State.
1. Fields.
Introduction to Electromagnetism.
Electromagnetism is the study of electric and magnetic fields and whilst writing this, I was asked why it deserves an entire chapter of the Grail Diary whereas the other three fundamental forces have to be content with one section in the particle physics chapter.
There are two answers to that question:
- Electromagnetism has the most practical applications. From generating and transporting industrial power to long distance communication, the study of the electromagnetic force gives rise to much of the infrastructure we take for granted today.
- Electromagnetism is the "middle" force. The strong and weak nuclear force are only relevant on a very small atomic scale. Gravity is ignored unless the objects involved are massive. However, electromagnetism has applications on both the atomic and stellar scale. More importantly, it has an impact on the everyday scale of people and things and so is the most relevant to us, who also exist in this middle scale.
Properties of Fields.
If you asked a physicist and a farmer what a field is, you would get two very different answers. The physicist would say something along these lines:
"A field is a region of space where a certain force acts"
There are many different types of field depending on which force governs them. In this chapter, we will discuss primarily electric and magnetic fields but the reader should be aware of gravitational, strong nuclear and weak nuclear as well as the elusive Higgs field (see the section in the particle physics chapter).
All of these fields have shared properties which we need to understand before a deeper understanding of electromagnetism can be made. Returning to our definition of fields, we described them as "regions of space where a force acts".
An important point to make here is that this definition is slightly misleading. First, a field is not made of anything, it is simply an area of the universe and as such can be made of anything.
We have therefore reached our first property of fields: fields do not need a medium to transport their forces. That is to say fields can exist in all mediums - regardless of whether they are submerged in water, are in air or in a vacuum.
The definition is again slightly misleading when it talks about a "region". In reality, all fields operate over a theoretically infinite range. A field on one side of the universe affects matter on the other side of the universe. This is due to the second property of fields: fields have an infinite range of effect but their strength is inversely proportional to the square of the distance.
This structure of one property being inversely proportional to another squared is so common in classical mechanics it is given its own name: the inverse square law. You could say that the strength of the field and the distance through which it acts obey the inverse square law.
For fields and matter interacting on opposite sides of the universe, the distance is enormous and so the observed force is vanishingly small. The region a force acts is indeed unbound but beyond a certain distance it becomes obsolete and so is ignored - depending on how you classify obsolete, you can therefore create a practical boundary of the field. Beyond this boundary, the field still has influence but it's negligible so the field may as well be finite.
We should therefore amend the definition:
"A field is an unbound region (although for practical purposes it can be contained) in which a certain force acts regardless of medium or external properties of the space it exists in."
Vector Fields.
Vector fields are an incredibly powerful tool to represent the motion of an interacting particle when placed in the field. Simply put, a vector field is lots of arrows that represent the magnitude and direction (hence all the arrows are vectors) of a given force.
The best use of vector fields in real life is modelling three-dimensional fluid flow - an example of this is wind flow. By analysing weather data, vector fields for the wind speed and direction in an area can be created and are a great way of showing how windy different parts of the region are.
These vector fields are often simplified from a three dimensional fluid flow (the wind) into a two-dimensional diagram (the bird's eye map of the area). We will also simplify the 3D world of Electric and Magnetic fields into a 2D model but the reader should be aware that they represent a 3D region of space. In our 2D models there are 2 rules:
- The direction of the arrow drawn is the direction of the force at the point where the arrow starts. Obviously if every single particle of air had it's own individual arrow in the weather map, it would be unreadable. We too will simplify this mess of arrows by only drawing the necessary ones to give the overall shape of the field.
- The length of the arrow represents the magnitude of the force at the point where the arrow starts. In many vector field diagrams, the varying magnitude of forces would make it difficult to read, so the length of the arrow only show's it's magnitude compared to the other vector's around it.Therefore the smallest arrows may be larger than their actual represented magnitude and the largest arrows may be smaller than their represented magnitude. In short, the extreme values of magnitude are not proportional to the arrow lengths but length is an indicator of magnitude.
Drawing Fields.
When representing fields, we use pole-line diagrams. This models the field as having a point of origin called a pole and by drawing lines that show how a particle would behave under the influence of that force.
In fields there are two types of pole - sources and sinks. A source-pole is one in which the field lines are generated by it - they all point away from it. Each field line represents the force on a particle in that position (assuming it interacts with the force of that field).
This means that source-poles repel any interacting particle near them. On the other hand, a sink-pole is one where the field lines converge on it and all point in towards it - therefore interacting particles feel a force towards sink-poles.
Traditionally, sinks are represented with a - sign and sources with a + sign. This is very confusing for electric fields as an electric source has negative charge!
From pole-like diagrams arise two properties of fields that are measurable and so merit their own names and symbol:
Divergence.
Represented by div or a downward pointing triangle and a dot: ∇.. It is a measure of how many field lines emerge or converge in on a specific point.
A field with high divergence has many field lines entering or leaving a pole whilst a low div field has very few. This is represented in the diagram above left and is essentially a measure of the strength of the field. A sink with lots of lines pointing into it pulls in interacting particles more powerfully than one with fewer lines.
Divergence is also a way of knowing whether a point in the field is a source or sink as it can be negative or positive: positive div = the pole is a source, negative div = the pole is a sink. For areas in the field where it is neither obviously a sink or source, a value of divergence can still be generated. Consider a scnerio where the field lines on the left of the point were weaker than the ones on the right as pictured below left. This would still imply that the flow out of the point was greater than the flow in and so it's divergence is positive.
Curl.
Represented (imaginatively) by curl. It measures how much the field lines swirl around the pole.
A high-curl field looks like a bullseye with lots of rings. As the curl gets lower, the rings become larger and more spaced out as seen above left.
A good visualisation of curl is to imagine what would happen if you dropped a pencil into a moving river and somehow held the pencil's centre still. As the river rushes by, the pencil rotates around its centre. The faster the pencil rotates, the greater the curl of the river at that point. The same logic applies to fields: curl of a point measures how a particle would spin if placed there.
Like div, curl can take positive or negative values. Negative curl = anti-clockwise rotation and positive curl = clockwise rotation. The common misconception of curl is that all the field lines must be pointing anti-clockwise to generate a negative curl value and vice versa for positive curl.
Consider however, a field with changing strength as seen in the diagram below right. If the field lines are stronger below the point and weaker above the point then the net effect will be a clockwise rotation as pictured. Despite the arrows all being straight, the field still has curl.
Uniform Fields.
2. Maxwell's Equations.
James Clerk Maxwell was a Scottish physicist and mathematician who lived in the late 1800s. He is best known for his discovery and classification of electromagnetic radiation and his 4 laws of electromagnetism. They mathematically govern the behaviour of electric and magnetic fields and, like all the best parts of physics, they are beautifully simple:
Note: in electromagnetism, E represents an electric field whilst B is used to show a magnetic fields presence.
1. DivE = ρ / ε0.
ρ is the density of electric charge (the amount of electric charge per unit volume, measured in coulombs/m^3). ε0 is the electric constant, sometimes known as the permittivity of free space. The permittivity of a substance is it's resistance to an electric field passing through it and so the electric constant is how much free space resists having an electric field run through it. It is 8.854 x 10^-12 Fm^-1.
Maxwell's first law therefore tells us that the divergence of the electric field is proportional to the charge density of the field at that point.
2. DivB = 0.
The divergence of any magnetic field is always zero. Magnetic field lines are always continuous and closed (just like in the high/low curl diagram). Experimentally this was observed through the phenommena that single magentic poles do not exist. In other words, a magentic field will never touch a pole, whether that be a sink or source.
Warning: Maxwell's third and fourth law require an understanding of basic calculus. The reader can explore this powerful mathematical tool in the 'Maths in Physics' chapter.
3. CurlE = - ∂B / ∂t.
4. CurlB = (μ0 J)+ (1 / c^2 ∂E / ∂t)
3. Consequences of Electromagnetic Fields.
4. The Elusive Aether.
Towards the end of the 19 century, scientists (mostly astronomers) began to collectively ponder a question:
How did light waves travel from the sun to the earth through the vacuum of space?
The understanding of waves at the time was based purely off of mechanical waves like sound and water which require a medium to move through - you can't have a water wave without any water! The vacuum of space contain nothing that light can use as its medium, or does it?
In 1704, Isaac Newton first proposed the Aether model in his ground-breaking book Opticks. The aether model suggests that a frictionless, massless, uncharged superfluid exists in space and indeed in all of matter. This fluid, called the aether, was the proposed medium of light waves. Scientists at the time couldn't imagine a wave existing without a medium and so it was widely accepted and its elegance applauded.
However, the aether model was ultimately wrong as light is not a mechanical wave but an electromagnetic wave (much more on this later) and so does not require a medium to move through but is self-propagating.
Despite being well received and accepted, there remained no cold, hard proof for the aether until the Michelson Morley experiment (which ultimately disproved it!). The scientific community became so attached to the idea of the aether they refused to believe other better models. Even after the aether was disproved, nutty physicists would cling to their old Aether books and call Michelson and Morley heretics! This is one of the earliest examples of an important lesson in physics; chasing elegant solutions over the truth leads to pseudoscience.
The idea behind the Michelson Morley experiment was in theory watertight. It was first reasoned and performed by two American scientists, Albert Michelson and Edward Morley, in 1887.
The idea behind the experiment is as follows:
If an aether exists in space and the earth moves through the aether then we on earth could detect an "aether wind" as we move through space. Detecting this aether wind would be the equivalent of sailing in a boat and putting your hand over the side to feel the "water wind" move past your fingers.
Rather than stick their hands into space, Michelson and Morley conducted an experiment to see if the earth had different measures of the aether depending on the season (more accurately the position of the earth relative to the sun).The logic used by the two Americans can be simplified into an analogy that can be explained using simple mechanics:
No wind present.
Imagine two planes. Plane x will fly due east from the point of origin towards town X, whilst plane y flies due north to town Y. Both town X and Y are exactly 500 miles from the origin and both plane x and y travel at exactly 500mph. Therefore, if there is no wind acting on the planes, the planes would fly to their respective towns and back in exactly 2 hours.
x=2 hours
y=2 hours
Wind present.
But suppose that on the day of flying, there is a 100mph westward wind. For plane y this wind would mean that it would be blown off course at and angle and so it takes longer to both go to and return from town Y. Using trigonometry we can deduce that the total time for plane y goes up to 2.041 hours. For plane x this would mean that on the outbound journey it would fly slower (against the wind) but fly faster on the home journey (with the wind). Again we can deduce that plane x would now take 2.083 hours.
x=2.083 hours
x=2.041 hours
The Michelson Morley experiment is fundamentally the same as the planes, but rather than have two planes flying in normal wind, two waves of light were used - flying in "aether wind"? The logistics of the experiment is as follows:
These beams of light travel at equal speed and both mirrors are placed the exact same distance from the half-silvered mirror. This means that unless some external force was at play, La and Lb would return to the half-silvered mirror at the same time.
Because they are approaching from the opposite side, both waves come together and move towards the observer's microscope. Two waves of equal frequency, wavelength and speed (such as La and Lb) can come together and add to each others amplitude, this is known as constructive interference.
A good way of visualising this is to imagine the two waves side by side, with each trough and peak lining up. In the experiment, the practical outcome of this constructive interference is that La and Lb come together to form a new wave L (which is identical to the wave first emitted by the light source assuming the mirrors are perfect) and has a brighter light than La or Lb
However, if La and Lb do not enter the observers microscope at the same time, that is to say one enters slightly before the other, then the troughs and peaks of the two waves will be offset and so no constructive interference will be seen. In fact if the the waves are offset by exactly half their wavelength (so troughs line up with peaks and vice versa) then complete destructive interference occurs and L is not formed at all.
If La and Lb are only partially offset, partial interference occurs which causes L to have a slightly less than expected intensity and therefore be less bright.As discussed earlier, according to the design of the experiment and the nature of light waves, La and Lb should come together at the same time and form L through constructive interference. La + Lb = L.
Now remember the plane analogy from earlier. Plane y represents wave Lb and plane x is La. In the plane scenario when there was no wind, they arrived back at the origin at the same time but if there was wind present, they arrived offset from one another.
The same reasoning can be applied to the light waves. If an aether wind existed, it would interfere with the movement of La and Lb and cause partial interference as oppose to constructive interference. This would mean that the observer looking through their microscope would see L as less bright than expected.
The Michelson Morley experiment was repeated in different orientations and at different times all over the planet. Every experiment showed the same results: La and Lb always returned at the same time and formed L out of constructive interference. The only conclusion was that the Aether did not exist.
The arguments that put the final nail in the Aether's coffin are as follows:
- As seen in the Michelson Morley experiment, there is no such thing as aether wind. Either the aether does not exist or is stationary in space.
- If the Aether was stationary it would provide a universal constant reference frame which contradicts Einstein's theory of relativity (see the relativity chapter).
Conclusion - THE AETHER DON'T EXIST HUN.
5. What is Light?
6. The Fourth State.
As the monotone drone of key-stage three science tells us, there are three states of matter:
Solid - the molecules are bound close together and have minimal vibration.
Liquid - with greater separation and vibration, the molecules in liquids are free to move past each other.
Gas - with huge separation between high-energy molecules, gases hold no definite shape.
However, this rudimentary model of matter leaves out the fourth (and most exciting) state: Plasma.
What is Plasma?
Plasmas are formed when a gas is subject to either extremely high temperatures or strong magnetic fields. This causes the gas to ionise which gives it a unique property - plasma are sensitive to changes in external electric and magnetic fields (including their own!) due to their composition of charged particles.
The gas ionises when exposed to these extreme temperatures because the particles have such huge kinetic energies that when they collide, they cause electrons to be knocked out of their shells - leaving a melting pot of positive ions and electrons.
The name plasma was first coined by Irving Langmuir (a Nobel laureate in plasma physics) and it is derived from a Greek word meaning "a mouldable substance" - referencing their sensitivity to both electric and magnetic fields.
Although most of the matter we interact with on an every-day scale is of the first three states, plasma is surprisingly widespread. Examples of plasma include:
- Stars - nothing more than huge spheres of super-heated ionised gases, stars are primarily composed of plasma.
- Man-made plasma - in the laboratory setting, plasmas are vital in many kinds of manufacturing and research.
- Lightning - the air immediately around lightning strikes is superheated to around 5x the temperature of the sun's surface, easily enough energy to produce a temporary plasma about the lightning.
- Auroura Borealis - also known as the northern lights, they are produced from high-energy interactions between charged particles from the sun and the Earth's upper atmosphere. This interaction causes excited atoms to emit flashes of light which we observe as the multicoloured ribbons of light in the night sky - who says physics is not romantic??!!
Graphing Plasma.
The other surprising thing about plasma is the range of conditions that produce them. It turns out that on the cosmic scale, solids, liquids and gases are vanishingly rare due to how picky they are in forming. Plasma's have no such limitation and so are the most abundant state in the universe. We can visualise this characteristic through a graph of density against temperature:
As seen in the graph on the left, solids, liquids and gases occupy a very small area. They are contained in the bottom left - this represents high density (in the range of 10^20 - 10^30 particles/m^3) but low temperature (in the range of 10 to 10^4 kelvin).
Other types of plasma display different temperature/density characteristics:
- Interstellar space - with low temperature and low density, interstellar space (the space between solar systems) is simply a very diffuse, low-energy plasma.
- Solar Wind and Nebular - with low density but rapidly rising temperatures, these exotic stellar phenomena can be found in the top right of the graph.
- Solar Corona and Core - both the core and corona (surface) of stars are composed of plasmas. The solar core is slightly denser and hotter but both types have extreme temperature and density.
- Fusion - nuclear fusion (the high energy production of larger atomic nuclei by combining multiple smaller atomic nuclei) occurs when the system is in the plasma state. The ultra high energy of these systems leads to both high temperature and high density - placing these rare plasma in the top right of our graph.
- Fluorescent Lamps - fluorescent lamps are ones in which a small electrical current causes the release of UV rays in mercury vapour which in turn produces visible light when in contact with the lamp's inner surface. This creates a temporary plasma with great density - similar to that of the solar corona but at much lower temperatures - bottom right of the graph.
7. Modelling Plasma.
Your Title
This is where your text starts. You can click here and start typing. Sed ut perspiciatis unde omnis iste natus error sit voluptatem accusantium doloremque laudantium totam rem aperiam eaque ipsa quae ab illo inventore veritatis et quasi architecto beatae vitae dicta sunt explicabo nemo enim ipsam voluptatem.