Charge movement in a magnetic field along the z-axis (into page/out of page)

[pinkenergy]

Homework Statement

: VIEW ATTACHMENT FOR JPEG IMAGE of a) and b). Predict the direction of the charge (into the page or out of the page) for a) a proton moving into the page in the (-)z-direction when the B field is in the (+)x-direction, and for b) an electron moving into page in the (-)z-direction when the B field is in the (+)x-direction.

Homework Equations

: As far as I know, I must open my hand with my fingers stretched towards the particle's velocity, then position my hand's fingers so that they curl/close toward the magnetic field and then, the thumb will indicate a clockwise/counterclockwise direction for a + charge...BUT how can i use this rule for into the page/out of the page movement? i can't really curl my hand in a B field that is on the x or y axis...it seems to only work if the B field is in the +/- z axis...?

The Attempt at a Solution

: i am guessing that for a) force is in the (-)y-direction and the proton is moving out of the page and for b) the electron, force is in the (+)y-direction and the electron is moving into the page...but this is a guess and I am sure how to do it with my right hand or do it again without memorizing it. :(

 

[amolv06]

I'm not a big fan of the right-hand rule; it always confuses me. The system I use, which works pretty well for me, is that since you're looking for the cross product, why not just take the determinant?

We know that F = q\vec{v}\times\vec{b}. For both problems, we have the particle moving in the \hat{-k} direction and the magnetic field in the \hat{i} direction. Knowing this, we can set up the determinant as such:

<br /> \begin{vmatrix} \hat{i} &amp; \hat{j} &amp; \hat{k} \\ 0 &amp; 0 &amp; -v \\ B &amp; 0 &amp; 0\end{vmatrix} = vB\hat{j}

From this, I would say that your force << complete solution deleted by berkeman >> direction.

 

[pinkenergy]

hey there, thanks so much for your reply.
im so upset to say it, but i never learned cross products and nor do i know of the k and j direction. :(
the "determinent" you set up is beyond anything i know at this time.

help.
is there any way to solve it with the RHR? or anything easier?

 

[pinkenergy]

help please? :)

 

[Nabeshin]

RHR will work in all three dimensions. With a right hand outstretched, point your fingers in the direction of the particle's velocity. Now, turn your hand so you can curl your fingers in the direction of the B-field, and thumb points in the direction of force. Knowing two of these three should allow you to figure out what way your hand must be oriented! Additionally, the same applies to negative charges except with your left hand (or opposite the result obtained by the right hand rule). Hope that clears it up.

 

[pinkenergy]

i think you meant thumb points in direction of charge. isn't my force the direction from my palm?

anyhow. i still can't get how to do this when v and b exist on the same plane as they do in my pic.

 

[Nabeshin]

No, I meant the direction of force.

Using the alternate RHR with VxB, with fingers in the direction of velocity, curling into B-field again yields a thumb in the direction of force. The only thing is when v and b exist in the same plane, the force will be out of that plane (It always will be out of the plane of the other two components: such is the definition of the cross product).

 

[pinkenergy]

oh! i see what you're saying. i was told that the thumb would indicate the charge's movement...but ok. that works too. but I am not trying to get the direction of force. I am trying to get the direction of the charge's path. (?)

 

[Nabeshin]

Well experiencing a force the charge will accelerate in the direction of the force via Newton's 2nd.

 

[pinkenergy]

ohhh! is that regardless of it being a positive or negative charge?
if that's true, then is the direction of the charge's path...
a) = into page
b) = out of page?

 

[Nabeshin]

ohhh! is that regardless of it being a positive or negative charge?

No. What I have described in relation to RHR applies to positive charges. To consider negative charges you can do one of two things. You can either follow the same steps, but with your left hand, or do a RHR and reverse the resulting vector. I find it easier to use my left hand just so I don't confuse anything!

 

[pinkenergy]

ok, to verify and solidify all of this.
Magnetic force, acceleration, and charge path all point in the same direction for positive charges only?

were my answers correct?
a) into page
b) out of page?

 

[Nabeshin]

I'm sorry if you misunderstood, but they will all point the same direction for negative charges too. Just opposite of what it would be for positive charges ^^.

Looking over the diagram you posted (Which is extraordinarily confusing, let me tell you) I think I agree with your answers!

 

[pinkenergy]

ahhhhh...YAY! that's what i thought you were saying! :)
hehehe...you made me laugh bc i swear I am getting delerious just looking at it myself. i just learned how to use RHR when v and B exist on opposite planes, but geez, when they are in the same plane as in the picture...that just sucks for me. and yea, i actually had to put my hand up against the computer screen to do it. i just hope i did it right.

im so glad you agree. if anyone else is reading this, please, please just take a second to tell me if you agree as well. PLEASE?

 

[pinkenergy]

anyone want to verify
a) into page
b) out of page

 

[pinkenergy]

please please can someone verify my answer, i want to make sure I am getting this.

 

[pinkenergy]

HEEEEEEEEEELLLLLLLP? did i do it right?