Calculating Magnetic Interactions in Parallel Wires

[choco_moo]

Homework Statement

Shown at right is a cross-sectional view of two long straight wires that are parallel to one another. One wire carries a current out of the page; the other carries an equal current into the page. I don't know how to show the diagrams, but the current into the page is at (3,0), the current out of the page is at (8,5) and P is at (8,0). I'm judging this by their locations in the diagram.

a. Draw a vector on the diagram to show the direction of the magnetic field, if any, at point P. Explain your reasoning.

b. Suppose that a third wire, carrying another current out of the page, passes through point P. Draw a vector on the diagram to indicate the magnetic force, if any, exerted on the current in the new wire at P. If the magnitude of the force is zero, indicate that explicitly. Explain your reasoning.

c.Suppose instead that the third wire (carrying the same current out of the page) is placed such that the magnetic field at point P has zero magnitude. Determine the location of the third wire. Clearly indicate on the diagram at right the correct location of the new wire. Explain how you determined your answer.

Homework Equations

?

The Attempt at a Solution

a. I drew the vector at point P 45 degrees southeast because the B-field from the wire with the current into the page is flowing clockwise, while the B-field from the wire with the current out of the page is flowing counter-clockwise. By using the right hand rule, the fields are pointing right and down at P respectively. When I add the two vectors, the resultant vector is 45 degrees to the bottom-right.

b. For this, I used F = I x B and the right hand rule. I is out of the page at P and the direction of B is the same as in part a. By doing the cross-product, I said that the force must point upward.

c. I have no idea how to do this part. If anyone can explain how I'm supposed to go about this, I really appreciate it!

Also, if anyone can verify my answers for the parts a) and b), that would be great!

 

[Redbelly98]

The Attempt at a Solution

a. I drew the vector at point P 45 degrees southeast because the B-field from the wire with the current into the page is flowing clockwise, while the B-field from the wire with the current out of the page is flowing counter-clockwise. By using the right hand rule, the fields are pointing right and down at P respectively. When I add the two vectors, the resultant vector is 45 degrees to the bottom-right.

b. For this, I used F = I x B and the right hand rule. I is out of the page at P and the direction of B is the same as in part a. By doing the cross-product, I said that the force must point upward.

c. I have no idea how to do this part. If anyone can explain how I'm supposed to go about this, I really appreciate it!

Also, if anyone can verify my answers for the parts a) and b), that would be great!

(a) Looks good.

(b) Hmmm, the force F should definitely be at a right angle to B, since you must take a cross product involving B in order to get F. B points diagonally downward-rightward, so F cannot be pointing straight upward.

(c) Think of it this way: B due to the first two wires points downward-rightward. What direction must B from the 3rd wire point, in order to cancel the other B to get zero magnetic field?

 

[choco_moo]

(a) Looks good.

(b) Hmmm, the force F should definitely be at a right angle to B, since you must take a cross product involving B in order to get F. B points diagonally downward-rightward, so F cannot be pointing straight upward.

(c) Think of it this way: B due to the first two wires points downward-rightward. What direction must B from the 3rd wire point, in order to cancel the other B to get zero magnetic field?

so for (b), if F must be perpendicular to B, then would F be pointing out of the page?
in (c), would B be going in the opposite direction (upward-leftward)? If so, would the wire be at (3, 5)?

 

[Redbelly98]

so for (b), if F must be perpendicular to B, then would F be pointing out of the page?

No, F must be perpendicular to both I and B, since you are taking the cross-product IxB. Perpendicular to I means that it is in the plane of the paper.

in (c), would B be going in the opposite direction (upward-leftward)?

Yes.

If so, would the wire be at (3, 5)?

That would produce an upward-rightward direction of B at (8,0).

 

[joeyjokester]

can someone help me with part b) So for wires into the page the field lines go clockwise, otherwise they go counter clockwise.

My thoughts on this where that since the top and bottom rightmost wire are both out of the page, field lines from the top one would go counterclockwise, as well as those from the bottom one.

however, right in between the 2 wires, the lines are in the opposite in the opposite direction of one another and cancel each other out horizontally, and so the only field lines from either of these would be in the downward direction.

Looking at the leftmost wire going into the page, we see that its field lines are in the counter clockwise direction and so the field lines would point in the downward direction.

Using superposition then tells me that the force is in the downward direction?

for part c) I want to say that we need the point to be placed 4 squares down and 4 squares to the right of p, as this would give us a net of 0, but i don't really know how to justify this, or if i am even on the right track.

 

[anneli5417]

That would produce an upward-rightward direction of B at (8,0).

If 3,5 produces an upward-rightward direction of B at 8,0 where else should the third wire be?
I think it has to be to the right of point P to get the upward-leftward B to counteract from the first two wires but I'm not sure if I'm on the right track or not.

 

[Redbelly98]

Welcome to Physics Forums.

Here are some questions to help you think about it:

The current of the third wire is ____ (up out of the page, or down into the page)?

Therefore, the magnetic field around the third wire is ____ (clockwise, or counterclockwise)?

So, if the third wire is to the right of P, it would produce a field that points ___ (up, down, left, or right)?

 

[anneli5417]

Welcome to Physics Forums.

Here are some questions to help you think about it:

The current of the third wire is ____ (up out of the page, or down into the page)?

Therefore, the magnetic field around the third wire is ____ (clockwise, or counterclockwise)?

So, if the third wire is to the right of P, it would produce a field that points ___ (up, down, left, or right)?

The third wire is up out of the page.
The magnetic field will be counterclockwise.
So the field will point left and down? Or maybe just left?

 

[Redbelly98]

The third wire is up out of the page.

Yes.

The magnetic field will be counterclockwise.

Yes, correct.

So the field will point left and down? Or maybe just left?

No. Does this help?:

[PLAIN]http://wshs.wtvl.k12.me.us/~physics361/elecmag/ab5.jpg[/INDENT][/INDENT]​

 

[anneli5417]

No. Does this help?:

[PLAIN]http://wshs.wtvl.k12.me.us/~physics361/elecmag/ab5.jpg[/INDENT][/INDENT][/QUOTE]

Based on that picture, if point P is to the right of the wire wouldn't the tangent line pointing downward be the force on point P?​

 

[Redbelly98]

Based on that picture, if point P is to the right of the wire wouldn't the tangent line pointing downward be the force on point P?

Almost, but there are a couple of problems with what you are saying here (perhaps you meant one thing and wrote something different?):

1. You were saying before (in post #6) the wire is to the right of P, not the other way around.

2. Then tangent line pointing downward is the magnetic field at point P, not the force.

In other words: if the third wire is to the right of P, then the field at P (from that wire) is downward.

However -- we want the field from the 3rd wire to point upward-and-leftward, not downward. So you still have to figure out in what direction that wire is from P. (Hopefully the figure I posted earlier helps. The dot in the middle of the circle represents the third wire.)

 

[anneli5417]

I just had a lightbulb moment. So the direction needs to be up and to the left, as in the upper right side of the diagram you showed me. So the third wire has to be down and to the left of point P.

My next question is if it has to be down and to the left of point P, how far from point P should it be? I know that the magnetic force from the wire gets weaker the further you get from the wire. Should it be the same distance from P that the first two wires are? Or because there are two wires creating that first magnetic force down and to the right, should it be closer?

 

[Redbelly98]

I just had a lightbulb moment. So the direction needs to be up and to the left, as in the upper right side of the diagram you showed me. So the third wire has to be down and to the left of point P.

Yes! You're right

My next question is if it has to be down and to the left of point P, how far from point P should it be? I know that the magnetic force from the wire gets weaker the further you get from the wire. Should it be the same distance from P that the first two wires are? Or because there are two wires creating that first magnetic force down and to the right, should it be closer?

Hmm, I think it should be closer too, but I haven't worked that part out. For this part, you can use the equation that relates the magnetic field to the distance away from the wire.

 

[anneli5417]

Thanks so much! I did the math and figured out how far away it should be.