00:01
Okay, so we want to find the magnetic field at the origin of this with this current carrying wire.
00:10
So i'm going to call this red section of the wire section 1, the green section of the wire section 2, and then i'm going to call this side section section 3 and this side section section 4.
00:24
Now we know by biot -savart that the magnetic field is given by mu nought i times the length cross -producted with the radius vector divided by 4 pi r squared, where r is the distance from the point at which you're measuring the magnetic field, little r hat is the vector pointing from where you're measuring it to the wire.
01:06
So for instance if we've got this scenario the vector r hat points along here, it has length big r, l is, well really it should be, this is a infinitesimal point, dl is this little vector here pointing along the length of the wire, i is the current flowing through it and the rest are defined.
01:36
So what we're going to say is we're is equal to the magnetic field from section 1 plus that from section 2 plus that from section 3 plus that from section 4.
01:52
However on section 4 and 3 the current is parallel to the radial vector to the origin, or anti -parallel in the case of wire 4, and so the cross product between l and r is going to be zero and so these guys are going to give zero.
02:18
So let's just worry about sections 1 and 2...