00:01
Okay, so we have a current loop that's partially immersed in a magnetic field.
00:06
Current i, magnetic field b, and then this angle theta zero represents that angle measured from the vertical that defines where the edge of the magnetic field is.
00:22
And i'm going to call theta the angle from the vertical out to some arbitrary line.
00:28
Okay? and then my dl is a vector of, it's our differential vector that points along the direction of the current.
00:41
Because we know that the force, df, is i times dl cross b.
00:54
Okay? and i'm going to define these carefully, x and y.
01:13
But then z is going into the board, or into the screen, so that zb is minus b times the z unit vector.
01:36
Okay? so dl, this is the crucial thing.
01:50
Let's see.
01:51
So dl is x, excuse me, yeah, it's x, no let's be more careful about it than that, it's r times i cosine theta minus j sine theta.
02:35
If we think about that carefully, we can see that this is correct.
02:38
So when theta is zero, it points in the x direction.
02:43
When theta is pi over two, then it points in the negative y direction, etc.
02:54
So that's what it is, written in terms of theta.
02:59
Okay? and we're going to integrate theta all the way around.
03:04
Okay? so, df is our i times r times, i suppose i should use x and y since i used z up there.
03:28
And that's crossed into minus bz.
03:35
Okay? and so we get irb, bring all that out in front.
03:46
Then x cross z is i, excuse me, it's y cosine theta.
04:00
And then y cross z is x.
04:12
X cross z is minus y, so that's a plus.
04:17
Because there's a minus sign there...