Review Conceptual Example 2 as an aid in understanding this problem. A velocity selector has an

step 1 All right. First part for this problem is a little tricky. We're going to try and visualize ever

Review Conceptual Example 2 as an aid in understanding this...

Key Concepts

Velocity Selector

A velocity selector is a device that uses perpendicular electric and magnetic fields to filter particles by velocity. Particles with a specific speed experience forces from both fields that cancel out, allowing them to pass through undeflected. This concept is crucial in instrumentation that requires precise control over particle speeds, such as in mass spectrometry and particle accelerators.

Lorentz Force

The Lorentz force is the total force acting on a charged particle moving in the presence of both electric and magnetic fields. It is expressed as F = q(E + v × B), combining both the electric and magnetic contributions. This principle is central to the study of electromagnetism and is used to predict and explain the motion of charged particles in various devices and natural phenomena.

Magnetic Field

A magnetic field is a vector field that exerts a force on moving charges through the magnetic force, which is given by F = q(v × B). The strength and direction of the magnetic force depend on the velocity of the charged particle and the orientation of the magnetic field. This concept is critical for analyzing the motion of charged particles in magnetic environments.

Electric Field

An electric field is a vector quantity that represents the force experienced by a unit charge at any point in space. It acts on charged particles by exerting an electric force given by F = qE, where q is the charge and E is the electric field vector. This concept is foundational in understanding how charges interact with their environment in electromagnetism.

Transcript

00:01 All right.

00:03 First part for this problem is a little tricky.

00:05 We're going to try and visualize everything that's happening here.

00:09 So i have this compass because we're given compass directions for some of our quantities here.

00:15 So to best visualize this, draw this on your page, the compass, north, south, east and west, north facing up, east -facing to your right, west -facing to your left, and south -facing down.

00:29 And then lay your paper flat on your side -east -and -west -facing -down.

00:32 Your table or desk.

00:34 So compasses are two -dimensional but we're working with three -dimensional quantities here.

00:43 So with your paper or your notebook laid flat on your table or desk, we have two other directions besides these four.

00:51 We have out of the page which with it flat on your desk should be straight up and then you'll have into the page which would be down.

01:02 So this is three -dimensional.

01:04 So like this you'll have another one coming out of the page and another one going into the page.

01:13 This would be up and this would be down.

01:17 That's what they mean when they say the electric field is facing up.

01:21 It's coming out of the page.

01:23 With your paper laid flat, that would be pointing straight up.

01:27 Now, we are told the magnetic field is facing south.

01:34 Now the first part here, let's let's start with once again writing down everything that we are given, everything we know.

01:43 So we have the electric field.

01:47 We have e.

01:49 We have the velocity for the first particle.

01:54 I'm going to call velocity one.

01:56 We have the charge for the second particle that comes through because we have two different particles that come through.

02:01 That's going to be charge 2 and we have the net force for the second particle and we call that f subnet the net the net force okay let's do some more visualizing here so we have that the electric field is up so once again lay your paper flat on your table we're going to try to use the right -hand rule here so we know that the velocity goes in the direction.

02:45 That would be to your right.

02:47 So you want to point your thumb in that direction to the right, your thumb's pointing to your right.

02:53 You want to point your index finger in the direction of the magnetic field, which is south, which means you have to tilt your right hand up so that your pointer finger is pointing directly at yourself.

03:06 And then your middle finger points down, which is the direction of the force, which makes sense.

03:13 If we have e up, the force of the electric field is up, then the force of the electric field and the electric field itself are in the same direction, as opposed to the magnetic field where they're at 90 degrees to each other.

03:26 They're perpendicular to each other.

03:28 In this case, we have the magnetic field south, and with the right -hand rule, you get that the force of the magnetic field is down, which is opposite e, which is good for the first part of this problem.

03:40 Once again, the right -hand rule, you have your thumb point in the direction of the velocity, which is east to the right.

03:46 You have your index finger point in the direction of the magnetic field, which is to the south, which with your paper on your desk, would be right back at yourself.

03:55 And then you stick out your middle finger, and it would be in the direction of the force, which in this case is down.

04:04 All three fingers are perpendicular to each other.

04:08 So we have b is down, or the force of b is down and the force of e is up, which is good because they'll cancel.

04:17 Because we're told in the first part that the particle, particle 1, passes through unfazed.

04:22 So because of that, we know that the force of the electric field e is equal to the force of the magnetic field.

04:34 And we know equations for both of these.

04:37 We have f sub e is equal to simply the charge of the particle times the electric field and we know f sub b is equal to the magnetic field times charge and you can write these in any order it doesn't matter the multiplication you can just move them around it doesn't change any of the numbers so you can write q times b or b times q it doesn't change any of the numbers if you've seen it in a different form before.

05:20 And this is times velocity.

05:22 And we're called velocity is east.

05:24 Magnetic field is south, so they are perpendicular.

05:27 So we don't need to worry about the sign of theta because it would be sign of 90 degrees, which is just one.

05:32 Now we know that the particle doesn't change its direction, which means these two forces have to be equal to each other.

05:41 That's the physics of this problem, or at least of this first step, is to know that because the particle, doesn't change its trajectory, the forces cancel on it.

05:51 Because if you have a force passing this way, or if you have a particle moving in this direction, you have two forces acting on it, one in this direction, and one in this direction.

06:03 If they didn't cancel, the particle would either shoot up or shoot down, depending on which one was farther.

06:11 But it doesn't do either of those...

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