# Magnetic Field's Effect on a Charg[ed Particle]

1. May 6, 2007

### mbrmbrg

1. The problem statement, all variables and given/known data

A magnetic field CANNOT:

[a]exert a force on a charge
accelerate a charge
[c]change the momentum of a charge
[d]change the kinetic energy of a charge
[e]exist

1a. Question

I found that the answer was [d] (see bottom for my fun, tedious thought process), but I'm not sure why that must be so.

Given a three-dimensional system, with a magnetic field acting along one of the axes, say the x-axis, and a moving charged particle.
Any x-component of velocity will not affect the magnetic force, so let's forget about the x-component (possibly a dangerous thing to forget about, but I will disregard it nonetheless).
A y- or z-component of velocity will produce a force along the z- or y-axis respectively.
If the velocity vector has one non-zero component that points along either the y- or z- axis, then the magnetic field will indeed affect only the direction of the velocity, and not its magnitude. This is consistent with magnetic field not affecting (scalar) kinetic energy.
But if velocity has both y- and z- components, then the resulting force has both y- and z- components, as well. Thus, the force should change both the direction and magnitude of velocity, and thus kinetic energy as well.

So is my reasoning flawed, or is the problem incorrect/imprecise?
*********************************************************

HOW I GOT PART D AS THE CORRECT ANSWER
2. Relevant equations

$$\vec{F_B}=q\vec{v} \times \vec{B}$$ (equation 1)

$$\vec{F}=m\vec{a}$$ (equation 2)

$$\vec{a}=\frac{\Delta \vec{v}}{\Delta t}$$ (eqation 3)

$$\vec{p}=m\vec{v}$$ (equation 4)

$$K=\frac{1}{2}mv^2$$ (eqation 5)

3. The attempt at a solution

Radio buttons tell me that there is one (real), unique correct answer. None of the options (with the exception of [e]) make sense unless there is an implicit "ed particle" after the word "charge"--so I inserted it and analyzed as follows:

[a] False. Equation 1 says "insert magnetic field (and non-zero velocity) and get a force."
False. We have concluded that a magnetic field produces a force, and equation 2 says that a force produces acceleration (assuming a non-zero mass. Which I am.)
[c] False. Since there's an acceleration, equation 3 states that the velocity much change. If the velocity changes, then by equation 4 the momentum changes.
[d] Process of Eliminatin. See a, b, c, and e.
[e] Ummmm... Well, I wouldn't know, really. But seeing how my entire study of magnetism seemed to be predicated on the existence of magnetic fields, I'll assume that a magnetic field is a useful model, and as such, exists.

Last edited: May 6, 2007
2. May 6, 2007

### rootX

non- uniform B can cause the particles to accelerate

"The charge will be decelerated and and reversed as if reflected from a so-called magnetic mirror" -- my book

This causes Auroras. (you may wish to confirm this though)

so, that means it can change the kinetic energy!!

I would say [e], provided that you haven't learned about non-uniform magnetic fields; through process of elimination lol, and also because it only exists when there is something to experience it

- a newbee

3. May 6, 2007

### mbrmbrg

:rofl: Yeah; I was trying to avoid the problem of existence. Hell, does it think? Then since I want to use Descartes' axes, the field's existence really is called into question!

OK, so a non-uniform magnetic field can change a charged particle's KE. Since we only learned about uniform magnetic fields, so I'll assume that the question is overall sloppy: in addition to implying that charge=charged particle, it implies that the field is uniform. Not nice, but probably what 'they' mean.

Why can't a uniform magnetic field change a charged particle's KE?

Last edited: May 6, 2007
4. May 6, 2007

### jackiefrost

You could say [e] if you can count the line of logic whereby a magnetic field can be shown to be a relativistic manifestation of the electric field.

5. May 6, 2007

### mbrmbrg

To clarify:
[d] "A magnetic field CANNOT change the kinetic energy of a charge" is the correct answer (at least according to WebAssign).

I just don't understand why a magnetic field cannot change a charged particle's speed (see first post).

6. May 6, 2007

### rootX

How force is related the velocity of the charged particles, and the B field?
Because there is no parallel component, so no change in speed!

7. May 6, 2007

### rootX

anyhow, from do you get these questions
I searched a lot, but never found mc's

8. May 6, 2007

### mbrmbrg

Oh. Good Lord. Right. Thenk you. No need for crazy thinking, just look at the cross product operator.

huh?

9. May 6, 2007

### rootX

was just wondering what is that "WebAssign" from where you got this question. because I really want these type of multiple choice questions.

10. May 6, 2007

### mbrmbrg

Oh-- I know of mc as in Master of Ceremonies!

Actually, WebAssign is the website that my physics professor uses to post homework for us (in this case, review for the final). If you want, I bet I could copy and paste it into a file and PM it to you. (But if you want it with an answer key, you'll have to wait a week or two until the answers go up.)

11. May 6, 2007

### rootX

Thanks so much
I do not have enough knowledge(i'm just a high school kid) to be much helpful, but I would try to.
I think I need them urgently, have a unit test coming this friday.
Anyhow, I still have like two-three books, but would be really glad to have the questions even without answers.

12. May 6, 2007

### mbrmbrg

The computer that I'm using now doesn't have the capabilities to do what I'm trying to do. I plan on going to the school building tomorrow and saving my WebAssign as a file there and attatching it to this thread (rather than PMing it to one, then two, then a gazillion people ).

The questions in the assignment that I plan on attatching are for the last chapter of electricity that we did, and the first three chapters of magnetism.

13. May 7, 2007

### Staff: Mentor

Before I approve these copies, are these questions copyrighted? Like, when you start up the webassign pages, is there a copyright notice, or any other terms & conditions that you need to agree to in order to use their software and website?

14. May 7, 2007

### Staff: Mentor

I checked the Terms Of Use at webassign, and it looks like it's up to the individual professor whether their questions can be freely copied out of the online assignments and passed around:

mbrmbrg, is it okay with your prof for you to distribute the copies? If so, I'll approve them. If not, you should delete them or I can.

15. May 7, 2007

### mbrmbrg

Thanks for the heads up, Berkeman. I'll send my professor an e-mail now.

edit: My professor was quite clear that posting the files would be copyright infringement, so I've deleted them. Thanks for catching that, Berkeman!

Last edited: May 7, 2007
16. May 7, 2007

### Staff: Mentor

No worries, mbrmbrg. Thanks for taking the time to follow-up.

17. May 7, 2007

### rootX

anyways, thanks for the effort, and spending all that time =P.