What is the Direction of Current Flow in a Parallel Conducting Wire?

[eps1lon]

Homework Statement

There an electron and its moving parallel to and above a horizontal conducting wire. When A current is allowed to pass through the wire the electron is seen to move towards the wire. The direction of current flow is...

Homework Equations

None/hand thumb rule

The Attempt at a Solution

We weren't really taught other ways to approach the problem other than using the right hand rule where we use the 1st,2nd and 3rd fingers to view the direction of the current. Please note that this is an enrichment problem and so we weren't really taught much background to this problem. I'm not very good with the concept and often find my hands hurting after trying to do it lol... I'm starting to think that the scenario is impossible since we need to know which direction the current is actually flowing in (parallel or anti parallel) to do this problem. Please help!

 

[berkeman]

Hands hurting, LOL.

Have you learned the equation F = qV X B, where V is the velocity, B is the magnetic field vector, and X is the vector cross product operator?

Also, do you know what the B-field looks like around a current carrying wire?

 

[eps1lon]

lol my hands hurt whenever I try the right hand rule. We just learned it recently and I always look twisted/demented whenever the field direction changes and I have to move the hand around.

I was given no other information for the question and frankly I don't even know what the B field is :S we were simply taught the rhr to find out the directions usually. Any ideas with the given information?

 

[berkeman]

lol my hands hurt whenever I try the right hand rule. We just learned it recently and I always look twisted/demented whenever the field direction changes and I have to move the hand around.

I was given no other information for the question and frankly I don't even know what the B field is :S we were simply taught the rhr to find out the directions usually. Any ideas with the given information?

Well, you can use the RHR to determine the B-field direction generated by a current on a wire -- see the drawings part-way down this wikipedia.org page:

http://en.wikipedia.org/wiki/Magnetic_field

So that shows you the direction of the B-field around the wire. Then, you can also use the RHR to determine the direction of the force on the charged particle, using the equation:

F = qV X B

Where F, V and B are vectors, and X is the cross product (and q has a sign + or -). You use the RHR to determine the direction of the F vector by pointing your fingers in the direction of B, then curling your fingers toward the direction of qV (watch the sign), and that makes your thumb point in the direction of the force.

 

[eps1lon]

Would it be anti parallel to the velocity of the electron?

 

[berkeman]

Would it be anti parallel to the velocity of the electron?

Quite possibly. Why do you say that?

 

[KalvinDeathX]

Um, that's really weird, cause when I read the question, I assumed that it was just a random electron. So if it is, and its floating near a wire, I think that the electron would go towards the wire as soon as it is turned on, no matter what direction the current is flowing. Of course, I don't know a WHOLE lot about magnetism, especially the effects of magnetism on charged particles, other than repulsion and attraction.

 

[berkeman]

Um, that's really weird, cause when I read the question, I assumed that it was just a random electron. So if it is, and its floating near a wire, I think that the electron would go towards the wire as soon as it is turned on, no matter what direction the current is flowing. Of course, I don't know a WHOLE lot about magnetism, especially the effects of magnetism on charged particles, other than repulsion and attraction.

No, follow the links I posted and look at how the B-field circles around the wire when there is a current flowing. The force on the moving electron depends on the direction of the B-field, which reverses for a reverse current. That's why the electron is either attracted to the wire or pushed away -- it just depends on the motion of the electron in relation to the motion of the current.

 

[KalvinDeathX]

So I don't get it. Why would the MF Lines attract or repel the electron anyways? Wouldn't the electron fall into a sort of circular magnetic orbit, and then get flung away because of inertia when it tries to change direction? If I explained that badly, look at this picture courses.science.fau.edu/~rjordan/busters_22/1.14q.gif its the best illustration of what I am thinking. Stupid URL rule.

 

[jae05]

that picture represents static electricity right? that means it's an E-field rather than a B-field.

anyway, for the electron to be affected by the B-field, the electron needs to be moving perpendicular to the B-field, as given by the Lorentz force law, F = q (E + v x B). if the quantity v is zero, there is no force (and I'm assuming the E fields produced by the wire are negligable), so the electron will not fall into some circular orbit.

remember, the electron is negatively charged in the elctricity sense (i don't know how else to phrase this haha). it will follow the electric field lines when left alone alone in the presence of a field, but it is oblivious to magnetic field lines unless it is otherwise already moving.

i suppose if there were such things as magnetic monopoles, there would exist some weird magnetic-electron type particles, and they would follow the magnetic field lines, but there are no such things ($$\nabla\bullet B=0$$). oh well

 

[berkeman]

Kalvin and jae, you are kind of heading off into the weeds, there fellas. Look at the drawing at the wikipedia page that shows the shape of the B-field lines circulating around a (DC) current-carrying conductor. See how they swirl around the wire (getting weaker farther away from the wire)? The problem stated by the original poster (OP) was where an electron already had some initial velocity, in the same direction as the wire. There is no mention of any E field, so the only equation that applies is F = qV X B. Work out the instantaneous force on that electron, given that B-field (which cuts sideways through the electron's initial path), and you get a magnetic force that either pulls the electron toward the wire, or pushes it away, depending on whether the current is flowing one direction or the other in the wire.

You won't get uniform circular motion of the electron, because the B-field is not constant throughout space. If the electron is attracted to the wire, it will hit it. If it is pushed away from the wire, it will execute a more complicated motion (I think it might make oblong circles and move farther and farther away, but I'm not sure, and don't have time to work it out at the moment).

 

[jae05]

isn't that what i said? maybe i should have quoted kalvin's post. i was referring to his image, not the wiki stuff.

 

[berkeman]

isn't that what i said? maybe i should have quoted kalvin's post. i was referring to his image, not the wiki stuff.

I had problems with you saying something about the field was an E-field from static electricity (no idea what that meant), and that the electron was not moving initially, so there was no magnetic force (the OP question said the electron had an initial velocity, but wanted to know the direction).

that picture represents static electricity right? that means it's an E-field rather than a B-field.

anyway, for the electron to be affected by the B-field, the electron needs to be moving perpendicular to the B-field, as given by the Lorentz force law, F = q (E + v x B). if the quantity v is zero, there is no force (and I'm assuming the E fields produced by the wire are negligable), so the electron will not fall into some circular orbit.

remember, the electron is negatively charged in the elctricity sense (i don't know how else to phrase this haha). it will follow the electric field lines when left alone alone in the presence of a field, but it is oblivious to magnetic field lines unless it is otherwise already moving.

i suppose if there were such things as magnetic monopoles, there would exist some weird magnetic-electron type particles, and they would follow the magnetic field lines, but there are no such things (). oh well

 

[jae05]

the picture link that kalvin posted... courses.science.fau.edu/~rjordan/busters_22/1.14q.gif

i mean as far as i know, rubbing the comb gathers static charge on the comb, which then attracts the water flow.

and i was just trying to explain the v x B thing, i didn't mean the electron wasn't moving. sorry if that was misleading haha. like if it's not moving, there's no v, and electrons are then oblivious to magnetic fields. that's what i meant

 

[berkeman]

the picture link that kalvin posted... courses.science.fau.edu/~rjordan/busters_22/1.14q.gif

Ohhhh. I missed that. Thanks for the clarification.

 

[benabean]

A moving electron is a moving charge and therefore a current is flowing.
We know that conventional current is in the opposite direction to electron flow.
Also we know that 2 wires that are parallel to each other will attract each other when the currents flowing in the wires are in opposite directions.
So thinking of the moving electron as a mini-wire, the original wire and this new mini-wire will attract leading to the conclusion that the direction of current flow is in the opposite direction to the current flowing in the original wire.