[Music] I want to say one last thing about G's law here in this lesson and and is to get you an idea of a fundamental meaning of this I've written up top there ga's laws we've done it using the integral of e. da uh the flux is equal to Q over Epsilon KN uh those of you who had some Vector calculus might might recognize it as in a slightly different form as What's called the Divergence dell. e is equal to row over Epsilon KN where row is the density and I I don't expect most of you to recognize that second equation you may someday if you're lucky but one way or another what what this represents to us is something kind of fundamental about what the flux uh and what this Divergence of e what this this spreading out of the field lines really means so let me think for a second if I have a field line that comes into my box and goes out of it that as shown there the flux on the way in is going to be equal and opposite to the flux on the way out the field points inward on one side and outward on the other and this is true no matter what line I draw through the box if it goes in it it comes out somewhere else I have an expectation if a line goes in it's going to come out somewhere and therefore the flux that passes through this box the total flux on the box is going to add up to zero because every field line that comes in goes out somewhere else and therefore there's no charge inside this box that's what the meaning of ga's law up top there is is the total flux is zero there's no charge inside the thing or at least there's no net charge there may be positives but they're offset by negatives this is different than the case where if I have a field line that comes into the box and then never comes out in which case the total flux for the box is less than zero it's negative or a field line that starts in the box after having never coming in in which case the total flux through the the surfaces of the box is greater than zero recognize each one of these the the first one it must mean that there's a negative charge somewhere inside and the other one means there's a positive charge somewhere inside finally I could I can have an exotic situation here where I have a field line that wraps around and never gets out of the box in which case there's there's no charge no charge necessarily inside or no no net charge there can be a plus or minus in there but they're offset from each other the the whole idea here is is that what this flux is really representing to me is how many sources and how many sinks there are in that box the field lines must start on a charge and must end on a charge because after all if I have a field line that comes out of the box without having gone in somewhere that means there was a charge somewhere inside that so this start must have been at that charge and this charge is is in some way you can think of it as a source or a sync of the field lines what a positive charge really represents is a place where an electric field starts and where a negative charge represents is where an electric field ends and this is kind of a subtle philosophical way of looking at it but I want to have it in your head even if this doesn't relate to a specific problem that we're solving so much is just so you understand why physicists are so interested in this idea of flux and what it means to us