Maxwells-Equations.com Presents: Maxwell's Equations

okay in this video we want to discuss what Maxwell's equations are so in textbooks or university these equations are often described in very mathematical terms and as a result a lot of times you come out knowing how to manipulate very complicated equations but you don't really know what they mean or how to ever use them in real life so the purpose of this video is to give an intuitive minimal math explanation of Maxwell's equations that will be useful to practicing science scientists and somebody who just wants to know what these equations mean so here are Maxwell's equations they're a set of four somewhat complicated looking equations vector equations actually and these all just govern the way that the electric and the magnetic field exist in nature so these four equations describe how the electric and magnetic field can distribute themselves what configuration they can take and they describe what types of physical phenomenon can give rise to electric and magnetic fields and then so just a brief aside the D and B are pretty much the same as the electric and magnetic field governed by just material parameters so sometimes most of the time you see the equations written by this but really all we're talking about is the electric and magnetic field okay so what are these equations we start with the first one Gauss's law so this first equation is equivalent to saying charges of the same sign repel each other so if you have two positive charges which are just things that exist in nature they will repel so if you have two negative charges they push away if you have one positive charge one negative charge they're going to be drawn together opposites attract so that's where this comes from what this actually means is this symbol means the divergence it means the feel builds around a point so in this case D which is basically equivalent to the electric field the divergence is equivalent to the volume charge density so this is how much charge which is measured in coulombs exist over a given volume so if we have a small point charge is saying that divergence is equal to the amount of charge here so that means the fields go away from the charge so the charge was negative the electric fields must point in and finally that says if there is no charge of the divergence is zero then we cannot have a field distribution that looks like this like if the electric field goes like this there has to be a charge here second of Maxwell's equations this one which is Gauss's law for magnetic fields says something basically the divergence of the magnetic field or the magnetic flux and density the same thing is zero so this means basically there is no isolated magnetic charge which means you cannot find a magnetic monopole that's going to have this type of distribution this also says you'll never find magnetic fields that diverge away from a point like this so this equation is kind of simpler than the electric Gauss's law so there is no magnetic monopoles that attract each other as in the electric field case okay the third of Maxwell's equations is known as Faraday's law so this one starts the left-hand side here's the curl of e so this symbol del cross means curl so as the divergence is a measure of how much fields flow away from something the curl is a measure of how fields wrap around something so for instance if we look at a point here and we imagine this is an e field then the curl here would exist there's a flowing of electric field here the curl is zero because the fields just move out in a way that has that virgins here the divergence is zero but we do have a curl so the curl of e the rate at which an electric field swirls around something is equal to the rate of change of the magnetic field so this means two things one is if we have a time changing magnetic field so if the magnetic field is changing within this loop here it's going to give rise to an electric field that swirls and similarly if we have an electric field that swirls this way we're going to have a magnetic field through this loop that's changing in time so this originally was done Faraday's law they had an experiment where they changed the magnetic field through an electric circuit and measured the current that was coming out I found that when the magnetic field was changing within a loop there would be this flow of current depending on whether the magnetic field was increasing or decreasing so this is an experimentally found law that's somewhat simple to understand that manifests itself by this pretty complicated equation the curl of the electric field is equal to the time rate of change of the magnetic field okay the last of Maxwell's equations is this which is known as amperes law so this says the curl of the magnetic field is equal to the time rate of change of the electric field plus the electric current density so if we just start with the curl of H equals J this is electric current density so if you think about current flowing on a wire you know you have current usually represented by amps here it's current density so you know the units are amps per square meter if you have current flowing through a wire then this says the magnetic field circles around the wire by the right hand rules of current is flowing this way the magnetic field wraps around it so that's the first interpretation so if we and the second term the curl of the magnetic field is equal to this this is known as the displacement current density so this was Maxwell's great contribution that really made Maxwell's equations a whole and make sense and describe the electric and magnetic fields so this term is known as displacement current density and the easy way to think about it is it's the measure of the current through a capacitor so if you think about this circuit and you know the AC voltage source you're still going to have current flowing but if you think about between a parallel plate capacitor you have nothing of error banking or whatever you want but no conduction path so how does the current get through here so max will introduce this term which is the rate of change of the electric field perspective time and NAT says that if we have this describes current going through a non conductive path as in this case and when this current in here also gives rise to a circulating magnetic field so we have two different phenomenon that can give rise to a circulating magnetic field and current density which is conductive current density as opposed to a displacement current density is equal to Sigma e so if you have an electric field in a conductor then you'll have current flows that's we can actually get rid of this J term and write partial D with respect to u plus Sigma E and again we're back to just electric field and magnetic field so as a whole we have a bunch of equations that describe what gives rise to electric and magnetic fields you know the electric charge gives rise to you know a diverging electric field flowing electric charge gives rise flowing electric charges current that gives rise to a rotating magnetic field and then how they all interact is governed by these equations so one thing you note is that if we have a changing magnetic field that to a curling electric field and if we have a changing electric field in time that gives rise to a rotating electric field so these equations if you want to go through a bunch of complex math you're going to end up with what's known as the wave equation which for instance I'll just write is so this says the rate of so if we have an electric field you know traveling in the Z direction the rate of change of the electric field in the Z direction actually the second derivative it's kind of an acceleration if you want to think of that is equal to the rate of the acceleration in time of the electric field so the second derivative with respect to time so that comes directly from here you know a time change electric field gives rise to a rotating H field this is rotating so it's changing in time that means that's going to give rise to a rotating field and on and on and on we have a wave equation and one of the big things about Maxwell's equations is that this is derived directly from here and these are all experimental results but this says that any shape electric field can travel in space and also says that no matter what frequency or what shape it is they all travel at C the speed of light and that is one of the big consequences of Maxwell's equations okay so anyway that's a brief overview of what Maxwell's equations are what they mean and I know I went through some of that kind of quick like for instance I didn't say anything like what is Epsilon that's permittivity but if you go to I made this website Maxwell's - equations calm and you can go through and like you I know I put all of Maxwell's equations right here and then I made it so you can click on you know any single part it's like oh what's the divergence I click there oh it tells me that's cool or what's D I click on that and figure it out or what is this partial B it explains it so you can kind of go through and figure what everything is I think that's kind of cold and then so I basically go through and give more description of what everything is like Faraday's law I can actually describe the experiment here and go through and you know the wave equation that I briefly went over I explained it there then just a lot more information if you really want to understand what's going on so I hope that gives you a little bit of an idea of what Maxwell's equations are

Channel: Pete's Free Info Center

Views: 180,090

Rating: 4.8898849 out of 5

Keywords: Maxwell's, Equations, Electric, and, Magnetic, Fields, Gauss', Law, Faraday's, Ampere's, The, Wave, Equation

Id: kGia0ngFq0o

Length: 11min 32sec (692 seconds)

Published: Mon Aug 13 2012