00:02
Okay, so this is the setup that we have for our situation here.
00:05
We have two intersecting wires that are completely perpendicular to each other.
00:10
Then we have points b and points a here.
00:15
So we have these points are a distance x from the wire, from the vertical wire.
00:24
I'll call this one.
00:25
This is the vertical wire and this is the horizontal wire.
00:30
So x and y are distances from the vertical for x and the distance y from the horizontal wire h.
00:43
And we have the same thing on the side.
00:47
X and y are equal to each other.
00:54
And we want to know the net magnitude of the net force acting on, or the net magnetic field acting on these points.
01:04
So let's do, let's start with this top one here.
01:07
So we have two wires.
01:09
Each are going to have their own equation for magnetic field.
01:15
B, we have our equation.
01:18
The magnetic field is equal to mu not, the permeability of free space, times the current divided by 2 pi, times the distance from the wire, also called r.
01:41
So, we have two cases.
01:46
We'll need to do this twice.
01:48
One for bv and one for bh.
02:00
So bh is going to be the same equation.
02:04
Mu not times the current, times 2 pi times the distance.
02:23
So let's look at the equation for bv first.
02:27
So the wire v here on point a.
02:36
So v is a distance x from a.
02:40
This is point a here.
02:43
So we could replace r in this case with x because x is our distance and we know what x is.
02:52
That's a good point.
02:54
We can keep track of everything we're given.
02:56
So we're told that both of the wires have the same current and we're given the current.
03:02
We're given the values of x and y.
03:13
So at point a, we found we can get rid of the r and put in x for r.
03:19
We can do the same thing for bh, but instead for bh, it's a distance y at point a.
03:25
So we can put in y for r here.
03:32
And we can use those two to calculate the two values here, bv and bh.
03:37
Now, let's use the right -hand rule because we need to find direction.
03:41
So bv, if you curl, point your thumb in the direction of the flowing current, which is up in this case.
03:47
Your thumb, your fingers will curl around.
03:51
They'll be going around this way.
04:01
Here, let's do a little bit better.
04:05
So they're going to curl round like that.
04:15
So over top here and then it goes under.
04:18
Or you can do a reverse and then it comes back over.
04:25
So at point a, these lines are going to be pointing directly down into the page.
04:32
So here we have our magnetic field i'll draw it in green, see if that makes it a little bit easier to see.
04:39
So here, our magnetic field is going to be pointing into the page.
04:48
So this is bv points into the page...