00:02
In this question we are given two parallel wires carrying currents in opposite directions and a couple of points at different distances from these wires.
00:12
We're asked to find both individual magnetic fields and total magnetic fields for these wires.
00:23
To find the magnitude and direction of the magnetic field at point p, do only to the wire on the right.
00:31
Let's first apply our right hand rule to get the direction.
00:39
That's where we put our thumb in the direction of the current, which in this case will be down, and then we curl our fingers around as if we're grabbing the wire to show the direction of the magnetic field.
00:51
So the right hand rule says that this field will be out of the page at point p.
01:02
I'm going to call this br by the way because it's the right wire and the other will be l.
01:10
It'll have some sort of l later.
01:13
So br will be equal to mu -naught i over 2 pi r and i is the current, which is just i in this case, and 2 pi times r, r is the distance from the wire to the point, which is d.
01:37
And now we can find part b, the magnitude and direction of the magnetic field at point p2, do only to the wire on the right.
01:49
And again, applying that right hand rule, now it's going to show that this field is into the page at point p2.
02:06
And again, this is going to be a br because it's from the right wire, always mu -naught i over 2 pi r.
02:16
Well, mu -naught i, that's unchanged, but now the distance to this one is d plus 2d or 3d.
02:29
You can leave it like this if you want to make it mu -naught i over 6 pi d, you can, but you can also leave it.
02:38
And in fact, i like to leave it in that form we just wrote with a 2 pi times 3d in the bottom because it makes it easier to compare to other fields, like the one in part a.
02:55
C asks us to find the magnitude and direction of the total field due to both wires at point p1.
03:07
All right, so b total will be equal to b left plus b right, accounting for direction.
03:24
So our right hand rule, well, we already know at point p1 that br is out of the page.
03:33
And so the right hand rule says bl is into the page at p1.
03:46
So that means we can subtract its magnitude from that of br.
03:56
So i'm going to write it as br minus bl...