Predicting path/direction of a charge in a magnetic field (drawings included

[pinkenergy]

[SOLVED] predicting path/direction of a charge in a magnetic field (drawings included

Is there any convention to go by when trying to predict the path of a charge in a uniform magnetic field?

I know that a charge makes a circular path upon entering a magnetic field, but that's all. I am not sure how to get the charge's actual direction within a B field: clockwise, counterclockwise, into the page, out of the page...etc.? (I am currently using RHR in which my palm = force, fingers = B field, thumb = velocity.)

example 1: if i am told to steer a PROTON through chambers I, II, III, IV which differ in magnetic field (see link with picture below), can the charge's initial path differ from the resulting velocity vector? yes, right?? In that question, I am given the path (red) of the charge and I am told to draw in the magnetic field, the force vector, and velocity vector in each of the four quadrants. did i do this correctly and why? please see my drawing and help. please. like in chamber I, if i did my drawing correctly then why is the path clockwise, and then in chamber II counterclockwise?

example 2: i am told to steer an ELECTRON through chambers I, II, III, IV, and again label B field, F and v. is my drawing correct? again, in chamber I, why is the path clockwise, and in II counterclockwise? I find that labeling F abd v for chamber III to be especially difficult. :(

thank you for all your help. this is my 1st post. you guys are awesome.

image of examples 1 and 2.
http://i5.photobucket.com/albums/y173/trick_ass_annie/annie1.jpg"


key: red = path of charge, aqua = direction of force, orange = velocity

 

[rock.freak667]

Is there any convention to go by when trying to predict the path of a charge in a uniform magnetic field? /QUOTE]

You use the Left hand rule for that. For a positive charge, the direction of the current is the direction of its motion.
For a negative charge, it is in the opposite direction.

 

[pinkenergy]

thank soooo much you for your reply, but are my picture images correct? there is no wire/battery present so I am not sure how current is involved? if you're saying that the charge's path always follows current, then where would current go in my picture?

 

[Dr. Jekyll]

thank soooo much you for your reply, but are my picture images correct? there is no wire/battery present so I am not sure how current is involved? if you're saying that the charge's path always follows current, then where would current go in my picture?

Lorentz force points to center of circular motion.
So, your picture is not quite correct (left one). The directions of magnetic fields should be like this (to get the drawn path):
ox
ox (just invert the directions).

The picture on the right is correct, but I don't understand the red vectors.

 

[pinkenergy]

hey! :)
when you said "like this: ox" i didnt understand what you menat by "ox"...and "invert the directions"...invert the directions of which vector?

red= the steer path of the electron/proton...
orange= the velocity vector upon changing, in the new magnetic field of the chamber. is it correct? i feel like i don't know what's going on. this isn't a homework problem for me, I am just trying to grasp the concept. i wasnt taught to this extent. :(

 

[berkeman]

hey! :)
when you said "like this: ox" i didnt understand what you menat by "ox"...and "invert the directions"...invert the directions of which vector?

red= the steer path of the electron/proton...
orange= the velocity vector upon changing, in the new magnetic field of the chamber. is it correct? i feel like i don't know what's going on. this isn't a homework problem for me, I am just trying to grasp the concept. i wasnt taught to this extent. :(

Hi pinkenergy, Welcome to the PF. The Homework Help forums are used for both homework and coursework, so since this is coursework that you are using to study for an exam, it qualifies for the Homework Help forums.

The image is a bit fuzzy, but I agree with rock.freak that the force directions seem wrong. Force points toward the center of uniform circular motion, which is what a charge in a uniform magnetic field exhibits (well, it can be a spiral if there is an initial velocity parallel to the magnetic field, but it still looks like a circle when viewed from above).

The o and x notation that he was using is similar to how vectors are drawn in some texts. x means pointing away from you, and o (or a dot) means pointing at you.

The fundamental equation you should be using for this type of problem is just:

F = qV X B

Where F, V and B are vectors, and the X is the vector cross product. Are you familiar with the vector cross product? That should give you what you need to solve this type of problem.

 

[pinkenergy]

hey, so, for the proton, (example 1 on the LEFT of my image) i did what you told me...
ox
ox
and i see that it works! :)

but 1.) i don't get why my initial drawing of
xo
xo
doesnt work...? to me, they both work? how can i tell that
xo
xo
is incorrect?


also...my "red"/orange vectors were supposed to be velocity. are they wrong? if so, does velocity always follow the charge "path" despite the B field?

 

[berkeman]

hey, so, for the proton, (example 1 on the LEFT of my image) i did what you told me...
ox
ox
and i see that it works! :)

but 1.) i don't get why my initial drawing of
xo
xo
doesnt work...? to me, they both work? how can i tell that
xo
xo
is incorrect?


also...my "red"/orange vectors were supposed to be velocity. are they wrong? if so, does velocity always follow the charge "path" despite the B field?

Sorry, the scan is a bit too fuzzy for me to be able to see the B-field directions.

The velocity vector will always be tangent to the path, pointing in the direction of motion. The acceleration (force) vector for a charged particle moving in a uniform B-field will always be determined by the equation F = qV X B, so the acceleration will always be orthogonal to both V and B.

 

[pinkenergy]

Ok. I totally get it! :) I will post in coursework! Thank you for all your help! This site is such a relief!

when you said, "Force points toward the center of uniform circular motion, which is what a charge in a uniform magnetic field exhibits"...
i still don't get how i would be able to know whether the circular motion is clockwise or counter clockwise. i included corrections of my work below. :) please help.

new image: http://i5.photobucket.com/albums/y173/trick_ass_annie/IMG_0458.jpg

1. are the "ox" B fields labeled correctly?
2. are the velocity (green) vectors drawn correctly for all quadrants?
3. are the force (blue) vectors drawn correctly in all quadrants?
4. is the charge moving clockwise (cw) in quadrant a?
counterclockwise (ccw) in quad b?
ccw in quad c?
cw in quad d?
ccw in quad e?
cw in quad f?
ccw in quad g?
5. is there some generalization i can make about cw/ccw movement in a B field? is it safe to say that any charge (+ or -) will always move clockwise in a "o" B field?
and any charge (+ or -) will always move counterclockwise in a "x" B field?

 

[pinkenergy]

http://i5.photobucket.com/albums/y173/trick_ass_annie/IMG_0458.jpg

 

[pinkenergy]

hi berkeman! thank you soooooooooooooooo much. now, i understand velocity entirely! i included a new redrawing of the image with corrections. :)
if you could just please verify my image and accuracy as well as the clockwise and counterclockwise directions, i would be ever so thankful. i think this is finally coming together for me.

 

[berkeman]

http://i5.photobucket.com/albums/y173/trick_ass_annie/IMG_0458.jpg

Hey, good job! That looks correct to me. Glad that F = qV X B is finally starting to click for you. It's a very useful concept to have straight in your mind.

 

[pinkenergy]

hey I am so very appreciative of your help. i swear this will be the last question for a while... :)
but can you verify the charge path as
clockwise for quadrant a, counterclockwise for quadrant b...
counterclockwise for quadrant e, clockwise for quadrant f?

if this is correct (which it probably isnt), can i say that a charge (whether + or -) will always move clockwise in a "o" (out of page) B-field?

and a charge (whether + or -) will always move counterclockwise in a "x" (into page) B-field?

 

[berkeman]

hey I am so very appreciative of your help. i swear this will be the last question for a while... :)
but can you verify the charge path as
clockwise for quadrant a, counterclockwise for quadrant b...
counterclockwise for quadrant e, clockwise for quadrant f?

if this is correct (which it probably isnt), can i say that a charge (whether + or -) will always move clockwise in a "o" (out of page) B-field?

and a charge (whether + or -) will always move counterclockwise in a "x" (into page) B-field?

Your drawing is correct, but your words above seem a bit mixed up. You switched the B-field direction for the quadrants in Example 2, so that is why the motion is the same for the + and - charges. Given a magnetic field direction, the force will be opposite for a + and a - charge.

 

[pinkenergy]

ahhhhh...ok...ok! now, it makes sense!
YAY, i came up with this as per our discussion and all of your help...(lol, you're probably thinking "finally...") :)

1. positive charge will always move clockwise for an out of page/toward you B field

2. negative charge will always move counterclockwise for an out of page/toward you B field

3. positive charge will always move counterclockwise for an into the page/away from you B field

4. negative charge will always move clockwise for an into the page/away from you B field

 

[berkeman]

ahhhhh...ok...ok! now, it makes sense!
YAY, i came up with this as per our discussion and all of your help...(lol, you're probably thinking "finally...") :)

1. positive charge will always move clockwise for an out of page/toward you B field

2. negative charge will always move counterclockwise for an out of page/toward you B field

3. positive charge will always move counterclockwise for an into the page/away from you B field

4. negative charge will always move clockwise for an into the page/away from you B field

I believe that is correct, based on the vector cross product, F = qV X B.

Good job!

 

[pinkenergy]

YAY! thank you! i know, i know...it took a lot. i am just getting used to seeing things in 3 dimensions... so cool of you to help! :)