[Music] I talk a little bit more about ga's law and if you'll remember from the last lesson I introduced G's law as being this equivalence between the flux out of a surface and the charge enclosed inside it that the flux is equal to the charge divided by Epsilon KN and what I said was if there's a symmetry to our situ and we can take advantage of this to make the problem solving pretty easy I'm going to give you an example of that here today I worked through two already that that kind of uh I went through them backwards instead of forwards but let me let me point out to you there's only a couple of situations where I can really take advantage of this because I have to have symmetry to make it work the first of these we already saw was the idea of a spherical symmetry that if I have a say for instance a point charge or a ball of charge or something like that I can draw a sphere around it the sphere the gray sphere being what I refer to as my gaussian surface I'm not really putting a sphere there it's just sort of imaginary construct that I can calculate the electric field on the surface of that sphere because it's everywhere equal and always pointing outward and therefore the e. da is easy to figure out for that guy the way we motivated this to begin with was talking about a cylindrical surface and there what we had was we could draw a toilet paper tube if you will around it so that there was no flux coming in or out of the ends of it and the flux all went out the sides and again would all be the same magnitude everywhere around the surface of that that that tube and always pointing outwards so the e. da is once again pretty easy to figure out the other situation that I can use though is a planer surface and I'm going to make this an infinite plane so i' can't draw on infinite plane of course but imagine that pink surface actually extends out to infinity and I'm going to use a gaussian surface here that is kind of like a tuna fish can cut in half so I've got the top half of the can above the plane and the bottom half of the can below the plane and there's a circle there in the middle that's cutting through it and my reason for doing this is because if I look at the field lines that ought to come out of this plane they should point away from the plane and they actually are going to be perpendicular and straight up everywhere because this thing's infinite there's no reason any one of those guys should be tilting to the left or right or to the front or back so all of the field lines here are going to be in the Z Direction which again is going to make me c my calculation of the flux pretty easy here if I set the cap of that can and the bottom of that can equal distances away from the surface then what I can say is the field strength should be the same on the cap everywhere around the cap and the area of the cap is just P pi r s where R is the radius of that Circle so let's walk through this and see what happens first I'm going to calculate what the flux is through the top there and that's going to be the field strength times the area and since the field is perpendicular to the area everywhere it points straight out of that can lid then we'll have is EZ * a is equal to EZ pi r 2 the flux through the bottom is pretty much identical except just in the opposite direction but the surface is the opposite direction as well so therefore what I get is the same amount of flux EZ * pi r 2 the charge that's enclosed is all in that little ring right there and if this surface has a charge density of Sigma then the total charge in there is going to be Sigma time a and the a is PK R 2 so let's put these together and say that the flux the total flux 2 * EZ pi r s the top and bottom added together must be equal to the charge and Clos / Epsilon Sigma * r^ 2 Epsilon if I divide out the P pi r squ and divide through the two what I get here is that the field strength above and below this infinite sheet of charge is Sigma over 2 Epsilon KN now it's kind of a curious thought here that this doesn't depend on distance but on the other hand what I've got is a situation where this field the sheet of charge goes to Infinity so being twice as high as kind of the same as being three times as high or 10 times as high when something's infinitely wide anyway so that kind of makes sense if you wrap your head around it the other thing about it is the field points in uh in in the negative Direction below the sheet and the positive direction above the sheet so it's pointing away from the positive charges if I flip the sign on this make the sigma negative it will point back inward