Understanding Right Hand Rules - Namely w/ parallel wires

[orb]

Homework Statement

There seem to be three right hand rules for dealing with magnetic field, current, and force, and I don't quite understand how to use them.

Namely, I'm having trouble understanding why two parallel wires with current flowing in each of them attract if the currents are in the same direction and repel if they are in opposite directions.

Homework Equations

RHR-1 says that if I "wrap my hand" around the wire where the magnetic field is, my thumb points in the direction of the current. That's all well and good. Both of the wires,next to each other , have current flow upward and, according to RHR-1, a magnetic field "counterclockwise" relative to the current.

The Attempt at a Solution

But I can't figure out how to use the other right hand rule(s) to figure out the direction of each force. The textbook says that the force exerted on the 2nd wire's current I₂ by the first wire's current I₁ is to the left, and that the force on the 1st wires current I₁ by the 2nd wire's current I₂ is to the right, making them attract. But how do they know which "direction" the force is going? Is the force centripetal? Or does it go in a definite direction?

I think I might be looking at the problem incorrectly..

Thanks in advance for any help. :)

 

[Mindscrape]

So you understand how you can tell which direction the magnetic field is in? You figure out the force by using the Biot-Savart law. F = qv x B. This requires the right hand rule again! :)

 

[Chi Meson]

Biot-Savart is not helpful if you haven't studied "cross-products" yet.

When using RHRs # 1&2, choose one wire to "produce" the magnetic field, and the other wire to "feel" the magnetic force. Call the first wire the top wire. The wire underneath will be in the field of the first wire.

Read this next line carefully: Use RHR #1 to determine the direction of the field of the first wire in the location of the second wire. Then, with the direction of the field determined, use RHR #2 to determine the direction of the force on the second wire.

 

[orb]

Biot-Savart is not helpful if you haven't studied "cross-products" yet.

When using RHRs # 1&2, choose one wire to "produce" the magnetic field, and the other wire to "feel" the magnetic force. Call the first wire the top wire. The wire underneath will be in the field of the first wire.

Read this next line carefully: Use RHR #1 to determine the direction of the field of the first wire in the location of the second wire. Then, with the direction of the field determined, use RHR #2 to determine the direction of the force on the second wire.

So by my understanding, that's what you mean, right?

If so, I understand what you're saying up to actually using the RHR#2 as your last instruction. I can't see how that makes sense. How do you know where the red arrow points? The thumb is the force, right? How can I get the magnetic field to be circular? (Besides, the RHR#1 and #2 seem to be different depending on which textbook) :/

Thanks again.

 

[Mindscrape]

I didn't realize right hand rule was, or even could be, taught without cross-products. Hmm.

So, from your diagram the wire with the red arrow creates a magnetic field that points down. The opposite wire sees a magnetic field pointing down, and because its current goes into the page, the right hand rule will show that a force causes the wire to go to left.

Now repeat the process for the opposite wire creating a magnetic field that the wire with the red arrow sees. It will see a magnetic field pointing field pointing up, and so you take your hand and point it in the direction of the current (into the page) and curl your fingers towards the magnetic field (up). Your thumb will point in the right direction, and so the force goes to the right.

Both forces point towards the opposite wire, which shows that the wires are attracted to each other.

 

[Chi Meson]

So by my understanding, that's what you mean, right?

If so, I understand what you're saying up to actually using the RHR#2 as your last instruction. I can't see how that makes sense. How do you know where the red arrow points? The thumb is the force, right? How can I get the magnetic field to be circular? (Besides, the RHR#1 and #2 seem to be different depending on which textbook) :/

Thanks again.

No, the thumb is the direction of "I" the "conventional current" (opposite the electron flow).

Looking at the left wire which is in the magnetic field pointing up (just forget the "clockwise" designation--where the wire is, the B-field is pointing UP).

fingers in the direction of the B-field, thumb in the direction of the current, Palm is Pointing in the direction of force on the wire. Try it.

 

[orb]

Thanks :) I've worked it out.

 

[Chi Meson]

I didn't realize right hand rule was, or even could be, taught without cross-products. Hmm.

This indicates you never learned magnetism in high school

OR

You had one heck of a math program in your high school.

 

[Mindscrape]

I guess so. When I went through high school I took IB Physics, and I always assumed (apparently falsely) that they taught right hand rule with the cross product in all the classes. In my class, if we ever had vectors we were supplied with the i, j, k, determinate formula, but I thought the more general sine rule was always taught with cross products.

I don't mean to be belittling at all, but I just don't see how the right hand rule makes any sense without a cross product and don't understand why they don't teach it in all classes.

P.S. Glad you see you got it worked out, Orb.