 After thousands of years of collective exploration of a whole variety of phenomena that were apparently very different, people realised that they were actually all electric and magnetic phenomena and that indeed electricity and magnetism were very strongly connected as well. They realised that it was all based on charge, that charges made electric fields and electric fields applied forces to charges. They realised that moving charges made magnetic fields and magnetic fields applied forces to moving charges. And Faraday found also that changing magnetic fields would make an electric field. And then James Clark Maxwell got all the data that everyone else had collected and all the laws they'd discovered and tried to make one integrated theory for electromagneticism. So we should adjust our summary here. We know that electric fields are made by charges and changing B fields. Remember Faraday discovered this experimentally but we motivated by thinking about what would happen if we had a moving coil and a stable magnet or a moving magnet and a stable coil and we thought they should do the same thing. And so we discovered there was actually a problem with electromagneticism the way it was. And in exactly the same way Maxwell looked at the equations for electricity and magnetism and put them in as detailed a form as he possibly could and he noticed there was an actual problem with them. They were definitely wrong. And in facing that problem what he did was he added the fact that magnetic fields could also be made by changing electric fields. And this had the effect of restoring the symmetry to electromagneticism and it made the theory actually self-consistent. It had an extra effect and that was he looked at those equations and he saw well if I have a changing electric field I'm going to make a B field and if I have a changing B field I'm going to make an electric field. Hey wait a minute these can propagate and so we could have an electric field make a magnetic field and then a magnetic field make an electric field and he discovered there was actually a wave solution so the fields themselves would make one another in an unending wave that would just head off into the distance. And he carefully worked out the speed of that wave and he discovered that the speed of that wave was the speed of light. Now of course that wasn't a coincidence and Maxwell was smart enough to realize that. He'd figured out the speed of these electromagnetic waves based only on properties that people discovered in lab about electricity and magnetism. So the permutivity and Coulomb's constant together would be enough to give you the speed of the wave and he found out that it came out to be the speed of light which he had not thought about at all up to that point. And so suddenly he realized oh my goodness I know what light is. I mean in fact there's the story that that's how he proposed to his girlfriend Catherine. He took her out and showed her the night sky and the starlight coming down on them and said Catherine I'm the only person in the entire world who knows what that starlight really is. Will you marry me? Now of course that could have gone two ways but fortunately history shows that in this case it was successful and she married him. His revised theory of electromagnetism was also unbelievably successful. It explained the existence and nature of visible light, infrared radiation, x-rays and more showing how they were all the same thing. It drove the discovery of special relativity and the theory lasted all the way through to the discovery of quantum mechanics and even since then it's still a great description of electromagnetism for nearly all practical purposes. So unlike most other waves you might be aware of, electromagnetic waves travel in the vacuum. They don't need any medium to travel in. It's just an electric field making a magnetic field and vice versa. They can be of any frequency or wavelength they like. Remember that the speed is related to the frequency in the wavelength in a very simple way and so the speed of all electromagnetic waves is the speed of light but they can have any frequency and then once you know the frequency you get a wavelength or vice versa.