00:02
So we have some information on two current carrying wires, and the information includes a graph as well as current ratio in the two wires.
00:15
What we'll be using is amper's law, which works for very long wires, which says that the magnetic field of a long straight wire carrying a current is mu not times that current over 2 pi times the distance from the wire, which we'll call r.
00:39
We also know that magnetic fields add.
00:43
So here we have two magnetic fields, and we are adding them together to figure out the total at any given point.
00:55
So if we look at the graph, what we can tell is that the stronger current, while you're closer to it, is creating a negative b -y.
01:08
And if we use our right -hand rule, we can tell then that i -1 is into the page, into the direction of the negative z.
01:24
And because the weaker current will eventually overcome the stronger one on the side in the positive x, that tells us that i2 must be opposite.
01:40
So i2 is out of the page, and that is a big clue.
01:51
So the two magnetic fields, we can just draw them at any position in the positive x, side of the axis, b1 will be down in the negative y, and b2 at that same position will be up.
02:17
And at some point, the b2 will overcome the b1.
02:22
Now, what is helpful in the graph is we have some information about where they are actually equal.
02:30
And what we will use that for is to find the unknown length l.
02:38
That separates the two wires because there will be a unique position where that magnetic field strength total is zero.
02:51
So what we'll do is we'll go ahead and write b1.
02:56
And here we're really looking at the positive y component.
03:06
So b1 will be minus.
03:11
And in the plus x region of the graph and space as well.
03:21
So b1 will be negative and it will be minus mu not i1, 2 pi x plus l.
03:35
B2 in contrast is mu not i2 over 2 pi x.
03:48
And when those two equal each other in magnitude at the special zero position, so p total is equal to zero, when x is equal to, let's take a look at the graph, 10 centimeters or 0 .1 meter.
04:14
And so we will have mu not, and here we'll use the proportions, so some nice things will cancel, and that should equal.
04:30
Mu not i2 over 2 pi times 0 .1.
04:44
And a lot of things will cancel here.
04:48
The unknown current, the 2 pi, etc.
04:53
And so eventually we get l plus 0 .1 is equal to 0 .4.
05:04
And so l is 0 .3 meters.
05:07
And that will be very helpful because what we are after is where is the maximum in the magnetic field? we can't tell from the graph.
05:25
It's kind of leveling out, but we don't know where the maximum is and what value it has.
05:35
Okay, it's definitely in the positive y direction, but where is it? so our second step is now find the b max position and b max...