00:02
Okay, so this is a fun conceptual problem here.
00:05
So i have a couple things written already.
00:08
So i have the magnetic field.
00:10
We're given in two directions.
00:14
One of the directions is in the negative y component.
00:17
The other one is in the positive x component.
00:19
Then we have in blue, we have the velocity of the particle traveling in the positive z component.
00:25
So this is what it will look like in three dimensions.
00:29
Three dimensions can be something that can be sometimes a little bit difficult to, conceptualize but imagine this x -axis as coming out of the page and then z and y are the planes of the page so you can imagine the negative x direction would go into the page this way and then z would just continue down or negative z so this is in three -dimensional space we want to find the magnetic force at a location here it can be anywhere along this blue line here we're just just going to make it right here for simplicity.
01:09
It doesn't so much matter the distance for what we're trying to calculate.
01:13
So we want the force here.
01:15
So you have two components of force now that are affecting that location.
01:20
One here from this component of the magnetic field and one here.
01:29
So this is coming up towards it and this is coming to the right diagonally.
01:34
So we'll need to do two separate equations.
01:38
So we'll do the math over here.
01:39
So to get force, we use the equation f is equal to the magnetic field times the charge, times the velocity.
01:59
Now, this typically has a sign of the angle between the force and the velocity, but as we can see, all three directions here, both red arrows and the blue arrow are all perpendicular to each other, where this is a right angle and this is a right angle.
02:21
So it'll be sign of 90 degrees or sign of pi over two in radiance, which is just one.
02:27
So we don't need to keep that into consideration here.
02:31
So this is the first one.
02:35
We'll say this is from the one in the positive.
02:37
We'll call positive x direction f1 and the negative y direction f2.
02:53
F2 is negative y, f1 is positive x.
02:55
So for the positive x direction, plugging in we have the values for b, q, and v, plugging all of those in, we find that this force is equal to 0 .004.
03:12
And it's important to note everything we're given is to two significant figures, so we'll want to keep the zero.
03:20
Everything is an si unit, so we'll be in newton's here.
03:23
You can also write this in scientific notation as four.
03:28
We want to keep the zero.
03:30
That zero is accurate, so it needs to see.
03:32
Stay there.
03:34
This is times 10 to the minus third.
03:42
And that's the force from the positive x direction component of the magnetic field in newton's.
03:48
So we'll need to do it again for the second part of the magnetic field, f2.
03:56
Same equation, same thing, just different numbers.
03:59
You plug in those numbers and you'll get 5 .5 times 10 to the minus 3.
04:09
Exact same process as the first one.
04:12
But these now what we'll want to do is go and look and see what direction this force will be in.
04:20
That means we get to use the handy -dandy right -hand rule.
04:26
So let's go back and look at f1 to start.
04:28
So we have a force.
04:30
Using the right -hand rule, you want the force to be your middle finger or your palm, depending on which version of the right -hand rule you're using.
04:37
So typically i like to start and point my pointer finger in the direction of the magnetic field, which would be the red arrow here.
04:44
So that's your pointer finger.
04:45
Your thumb, you want to go in the direction of the velocity, which is the blue arrow.
04:51
So right now your hand should kind of look like a gun symbol.
04:53
You have your pointer finger pointed out in the negative x direction and your thumb pointing up in the z direction.
04:59
Now, if you point to your middle finger the direction your palm is facing.
05:03
So all three fingers are perpendicular to each other.
05:05
It's going to point straight out this way, which means that for f1, our force is in the positive x direction.
05:16
Or if you have experience with vectors, this would be in the positive i -hat direction, the unit vector i.
05:29
But we can just say it's in the positive x direction here if you don't have any vector experience.
05:35
Oh, i'm sorry, that's for f1, not f2.
05:43
So f -1 is in the positive x direction, or i -hat.
05:50
Because this is three -dimensional space, you really need to keep track of your direction.
05:57
They're very important, especially for equations like this, where you have three different variables that are all pointing perpendicular to each other.
06:05
So that's f1.
06:07
So i'm going to draw the force in green...