 Now we look at the Bio-Savart law. Now Bio and Savart were two scientists who were looking at the source of the magnetic field. And experiments showed that electric currents can create magnetic fields. But it depended on a few things. It depended on how much current you had, depended on how far away you were from that current, and it also depended on other geometry factors. Now the Bio-Savart equation is kind of complicated. So let's take a few minutes here to sort of break this down. First off, we have the current I. We know that the magnetic field from a current has to depend on how much current we have, so that's our I in the equation. All of this stuff over here with the integral, well that describes our geometry and our distance. And this little guy over here is our magnetic constant. Let's look at that a little bit more closely. So this magnetic constant, well it's given this symbol here, and that's actually the Greek letter mu with a subscript of zero, so that's a mu naught. And its name is the permeability of free space. As a value, this is a constant 4 pi times 10 to the minus seventh tesla meter per amp. You could also multiply that 4 pi out, and you could write mu naught as 1.257 e to the minus 6 tesla meter per amp. Now you remember we had an epsilon knot back from electrostatics, which was the permittivity of free space. And epsilon naught and mu naught together are related to the speed of light. So now back to our equation, and let's focus in now on the side where we're talking about geometry and distance. To help explain this a little bit clearer, let's actually give ourselves a diagram. So imagine you've got some wire. It can be curvy, it could be straight, whatever, out in space. And we want to find the magnetic field at some other point in space separated from that wire. Well the ds part of our integral over here stands for a line segment. And we're going to have little line segments all up and down this wire. And notice that each one of these little line segments is the same length, but they could point in different directions. Now the R here on the bottom represents the distance. And it's specifically the distance from a line segment to the point P in space. And again each different little line segment may have a different distance from that segment to our point in space. The R hat part here is a radial direction, and the hat lets us know that it's a unit vector. So it points in the same direction as this radial distance, but it's only indicating the direction, it doesn't go all the way there. And again each point along our line may have a different R hat radial direction being shown. Now the top part of this integral here is a cross product. And it's the cross product between these two vectors for the line segment and the radial distance. So when you take that cross product that also helps determine the direction of the magnetic field. We can do that for each individual segment, but the integral tells us that what we really want to do is we want to sum up the contributions over all of those different line segments. And that will give us the overall magnetic field at our point P out in space. So while the equation itself is a little bit complicated, it helps to break it down into things that we can understand from a picture of geometry. Now let's take a look at the equation from the standpoint of units. Well we said our mu naught had a constant of Tesla meter per amp. Current we know has units of amps. 4 pi doesn't have any units. The ds part of our integral has units of meters while the R squared part has meters squared. And my R hat, you might think it's meters but it's a unit vector so again no units there. So once we've collected all these together what we see is that we have an amp on the bottom and the top of the equation which are going to cancel each other out. And then I've got two meters on the top and a meter squared on the bottom which will also cancel each other out. So everything from my right hand side all I've got left is Tesla, which is the unit I expect for the magnetic field. So every time we've got a current carrying wire we're going to end up having something of this form which ends up having a units of Tesla. So that's the end of our introduction to the Biosovart law.