00:01
Hi there, so for this problem, let me just draw first the axis for this.
00:08
We have the vertical axis and the horizontal axis.
00:12
And then we have a positive charge about this point in here.
00:21
It is a positive charge, okay? and it is moving to the right with some speed that we are given.
00:28
So the magnitude of the speed is equal to 2 times 10 to the 7 in units of meters per second.
00:39
Okay? now, and this is the charge of this corresponds to the charge of a proton that is 1 .6 times 10 to the minus, to the 7, sorry, no sorry, is 1 .6 times 10 to the minus 19 that is the charge of a proton and it is at this position that is 1 1 1 in here and 1 in here and the point at which we want to measure this magnetic field is it is at a point minus 1 minus 1 in here so the the point is about here.
01:33
So we need to determine this distance in here.
01:44
Okay, so first let's find how is the magnetic field produced by a moving charge.
01:53
So the magnetic field produced by a moving charge is mu sub zero divided by four times pi.
02:01
The charge involves the cross product between the velocity and the position and this position is and is the unit vector in that position and then this divided by the separation distance to the square so let's find first the separation distance we know that in here we go from the the point minus one.
02:40
Well, let's obtain first the position vector, okay? so that will be this position vector in here from the charge to this point.
02:57
Okay, so then we know that the initial point is at one, one.
03:07
So we will have, and the final point is minus one, minus one.
03:13
So that will be minus 1 in the x -direction minus 1 in minus 1 in the y -direction so then this minus the initial point so that will be minus 1 in the x -direction in minus y in the y -direction simplifying this this will give us just simply 2 times minus so as you can see this is just 2 times this...