00:01
Look at newton's second law of motion in the presence of magnetic and electric forces.
00:08
And oftentimes that motion can get rather interesting, let's say.
00:14
But in our example, we have a charged particle at t equals zero.
00:19
And it is moving along the x direction to the right with a certain velocity.
00:25
And it is experiencing both a magnetic field and an electric field.
00:30
Field that are perpendicular to its motion out of the page, and what i'm calling the z direction.
00:38
And our goal is to find the position of the particle.
00:41
We know it's an initial position, its initial velocity.
00:46
We want to know its position a little bit of time later.
00:50
And we're going to have to use the sum of the forces on the particle is equal to its mass times its acceleration.
00:59
And use that acceleration then with some kinematics to figure out the position.
01:06
Now, the way to handle this is to realize that there are really two types of motion that are going on.
01:13
In the xy plane, the magnetic field force is equal to qv cross b, and i'm going to write that as explicitly, v0, cross b.
01:32
And we notice that this force is always perpendicular to the velocity.
01:38
So what's going to happen in the x, y, plane is that the particle is going to experience a circular motion because of the fact that the force is always perpendicular to that initial velocity.
01:58
In the z direction, however, we have an electric field that is going to accelerate the particle.
02:08
And so we're going to have to use f equals qe and figure out the acceleration in that z direction.
02:19
Since the e is in the z direction, we can figure out the force in that z direction.
02:34
And this is, the force is equal to the mass times the acceleration in the z direction.
02:42
So this is going to reduce to a fairly simple kinematic situation.
02:49
Q, e, z over m equals az.
02:55
And since the electric field is constant, we can determine that we can use some simple kinematics, that z is going to be equal to z -0 plus v -0, z times t, plus one -half 8 z t squared.
03:23
And fortunately, many things inside of that equation are zero.
03:29
So i'm going to work on that simple part first.
03:37
Doing a calculation, we find that the acceleration by plugging in the charge and the mass of the electric field of 60 newtons per column, it's a fairly simple calculation to do.
03:52
We find that a z is 450 meters per second squared, and we can simply solve for the z with the 0 .02 in it for the time.
04:12
And we can dispense then with the z direction.
04:18
So the final z coordinate we already have as, let's see if we can move the board here, 0 .09 meters.
04:34
And i'm saving the best for last, which is the circular motion.
04:39
And a reminder how circular motion works.
04:43
The v and the b are perpendicular, and we can use the right -hand rule to figure out the direction initial on that particle.
04:58
So right -hand rule.
05:01
So the way i usually use my right -hand rule is take the fingers on my right hand and let them point in the direction of v, and then let them curl in the direction of b, which is out of the page.
05:22
And in this instance, i have to have my palm facing up out of the page, and my thumb points down.
05:31
So the particle is going to execute a clockwise, with the magnetic field remaining perpendicular to that...