00:01
All right, so let's say we have a wire that has a radius of r, which is five centimeters, and it's a infinitely long wire, and it has a uniform current distributed over it.
00:15
So we'll say that the current density j is just like some total current divided by pi r squared.
00:22
We want to find the magnetic field at a distance of little r, which is three centimeters from the center.
00:29
So we can use amper's law, which says that the integral of the magnetic field over some empyrian loop, which will just take to be this little circle, is going to be mu not times the enclosed current.
00:43
So the magnetic field will be constant at all points along our loop due to the symmetry of the wire.
00:49
So what we'll really have is 2 pi r times b is equal to mu not times the enclosed current.
00:54
Now the enclosed current is really just going to be the current density times the area that little region.
01:00
So it'll be i like the total current times little r squared over big r squared...