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Electromagnetic Waves

Teacher/Instructor Jonathan Osbourne
Jonathan Osbourne

PhD., University of Maryland
Published author

Jonathan is a published author and recently completed a book on physics and applied mathematics.

Electromagnetic waves are waves that take place in electromagnetic fields. When looking at electromagnetic waves in a vacuum, change in magnetic flux generate electric field and change in electric flux generates magnetic field. Alternating magnetic or electric field result propagation in vacuum in form of electromagnetic waves. The speed of the electromagnetic wave was found to be 3 x 10^8 m/s. Basic properties of electromagnetic are electric field and magnetic field perpendicular to one another in plane waves, the direction of propagation of is given by electric field x magnetic field, and the speed is calculated as wavelength times frequency.

So let's talk about electromagnetic wave well what is an electromagnetic wave? Well it's a wave that takes place in the electromagnetic fields. Now this was something that actually follow from an addition to electricity and magnetism that was first discovered by James Clerk Maxwell in 1864 so let's go through how this works. When we look at electromagnetic fields in a vacuum we find that because of the Kirchhoff Faraday Lenz law if I change a magnetic flux I will generate an electric field. So if a magnetic flux is changing like this then the electric field will circulate around that changing magnetic flux. Now what Maxwell did was he modified Ampere's law and said that a change in electric flux will generate a magnetic field. So what this does, well first off it changes the name of the Ampere's law to the Ampere's Maxwell law and together with that all 4 of the previous laws were brought together and were all refereed to as Maxwell's laws so James Clerk got a lot out of that discovery.

But anyway what it also does is that it says that when you change a magnetic field you generate an electric field. You change an electric field you generate a magnetic field. So what that does is that it says that anytime you got an alternating magnetic or electric field you'll generate the other ones and then that thing that you just generated will generate the other guy again and so it just kind of propagates away from there in the form of a wave an electromagnetic wave. Now the beautiful thing about this is that this was taking place in vacuum. So in vacuum with no medium there we can still have an electromagnetic wave and in fact we will always have an electromagnetic wave, we can't avoid it if we start off with an alternating electric or magnetic field. We can do that just by having positive and negative charges switch places back and forth. That's going to generate a changing electric field that continues to change. Doesn't change once it continues to change over and over and over again and now will generate a changing magnetic field which generates a change in electric field so on and so forth giving us this nice electromagnetic wave.

Alright the speed of the wave can be determined from the standard constants in electricity and magnetism. The speed is given by the square root of 1 over mue 0 times epsilon 0, mue 0 is the permeability of free space and is associated with magnetic fields whereas epsilon 0 is the permittivity of free space and is associated with electric fields, so we can see them both together generating the speed of electromagnetic waves. Numerically this turns out to be 3 times 10 to the eighth meters per second or about 300 million meters per second, 300,000 kilometers per second 186,000 miles per second. Put in another way it's about seven and a half times around the equator of the earth in 1 second. So no wonder people weren't able to measure how fast that was in the 1500s the first actual measurement didn't happen until the 1800s. Alright so let's see what makes electromagnetic waves different from mechanical waves. The big thing is that you've got propagation in vacuum, remember that mechanical waves require a medium. They represent a disturbance in a medium like water or air or rock or something like that.

In vacuum you can't, what are you disturbing? Electromagnetic waves have an answer, we're disturbing the electromagnetic field we don't need a medium for that, we can do that in vacuum because electric and magnetic fields exist in vacuum. Now what people used to say is that "there's the medium we just can't see it." The problem is that the way that speeds work with mechanical waves this aether that was proposed to carry electromagnetic waves or light would need to be both very very light and very very rigid to support such a high wave speed. So to put it in another perspective sound waves propagates through aluminum at about 5,100 meters per second. So we're going to need a material that's so much lighter than aluminum and yet so much more rigid that it supports speed not 5,100 meters per second 300 million meters per second.

And that's just unrealistic and furthermore all of the times that we've tried desperately to observe this aether we haven't seen anything. And so what that leads us to believe is that this really is a disturbance in the electromagnetic fields and not a mechanical wave at all. Alright some basic properties of electromagnetic waves, when you have a plane wave and that means that it's just coming like this not like a light source that goes out all like that but just kind of a plane wave like that always associated with an electric field and a magnetic field that are perpendicular to each other. So if the electric field is going back and forth like this, the magnetic field will go back and forth like this alright. The direction of propagation of the wave is always given by e cross b so it's perpendicular both to the electric field and to the magnetic field. In that previous example the electric field was like that, magnetic field just like that the wave will be going that direction, perpendicular to both the electric and the magnetic fields.

Alright as with all waves the wavelength times the frequency equals thee speed. In this case the speed is really, really big. Now most of the time we're looking at mechanical waves the frequencies can't get too big because it's associated with the medium having to respond to being disturbed and that takes a little bit of our time. But with electromagnetic waves this is just associated with disturbances and the electric and magnetic fields which are not media. So that means that the frequency can be very high, it's limited only by how quickly we can move charges back and forth. So there're electromagnetic waves that are known with frequencies up to like 10 to the 22, 10 to the 24 oscillations per second which is way higher than any physical medium could sustain. So anyway that's electromagnetic waves.