Magnetic Interactions vector diagram

[robera1]

Homework Statement

Shown at right is 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.
Draw a vector on the diagram to show the direction of the magnetic field, if any, at point P. Explain your reasoning.
Draw a vector on the diagram to indicate the magnetic force, if any, exerted on the current in the wires.

I don't have the diagram here, but (using a coordinate system) the current going into the page is at (3,0), P is at (8,0) and the current out of the page is at (8,5).

Homework Equations

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The Attempt at a Solution

I really don't know how to do this. There are three questions like his one, so I am not looking for an answer, but more like an expiation of how to solve problems like this one.

Help I am so confused :(

 

[drizzle]

you assume these coordinations or are they illustrated in the diagram? either way you'll need to apply the right hand role

 

[robera1]

They are from the diagram.
So, that is all I do... use the right hand rule?

 

[drizzle]

then you should consider the distance of the P point from both wires, however you'll have the net magnetic force directed towards [x,-y]

 

[dx]

Find the directions of the magnetic field at P due to each wire using the right hand rule (you should find that they are perpendicular). Since the point P is equally distant from both wires, they will have the same magnitude.

 

[dx]

you'll have the net magnetic force directed towards -y

Wrong.

 

[drizzle]

Wrong.

yah, I've corrected it

 

[dx]

Ok, but please don't give away the final answer.

 

[drizzle]

Ok, but please don't give away the final answer.

I thought it was a hint, I didn't say the vector will make an angle of 45^o from the x-axis in the forth quarter

 

[robera1]

I am still really confused. If the current is going into the page, then the magnetic field could be at any angle on the page, as long as it was still perpendicular with the current.

Do I say that the current is moving from the into the out, thus moving 45 degrees to the left, and thus the magnetic field would be running 45 degrees to the right.

Is that the correct way of doing it?

 

[dx]

I am still really confused. If the current is going into the page, then the magnetic field could be at any angle on the page, as long as it was still perpendicular with the current.

You were asked to find the direction of B at the particular point P. Forget about one of the currents for now. With just the current at (3,0), what is the direction of B at P? (Use the right hand rule.)

Do I say that the current is moving from the into the out, thus moving 45 degrees to the left, and thus the magnetic field would be running 45 degrees to the right.

Is that the correct way of doing it?

No, that doesn't make much sense.

 

[robera1]

You were asked to find the direction of B at the particular point P. Forget about one of the currents for now. With just the current at (3,0), what is the direction of B at P? (Use the right hand rule.).

Just at this point... is it moving straight up? (I point my thumb (which represents the current) out of the page... and my fingers are straight out)

 

[dx]

The current is into the page at (3,0), so you point your thumb into the page. B therefore points straight down at this point.

Also, your fingers should be curled, not straight out. They curl in the direction in which B curls around the wire.

 

[robera1]

Oooh I see. Okay, that makes sense. So then at the point where the current goes out of the page B points straight up?

So, does this mean that the magnetic field at P is zero?

 

[dx]

No, the B due to the other current will point to the right. I think you're not applying the right hand rule correctly. Point your right thumb in the direction of the current, and curl your fingers into your palm. The direction in which your fingers curl is the direction in which B circles around the wire.

 

[robera1]

That does not make sense to me. When my thumb is down, B points straight down. When my thumb is up, B points to the right?
Shouldn't B be in the opposite direction, since I is?

 

[dx]

You are aware that B circles around the wires right? The position of the wires is important too, to find the field at P. Why don't you draw a picture with both the wires, and the directions in which B circles around each. It is clockwise around the (3,0) wire, and anticlockwise around the (8,5) wire.

 

[robera1]

You are aware that B circles around the wires right? The position of the wires is important too, to find the field at P. Why don't you draw a picture with both the wires, and the directions in which B circles around each. It is clockwise around the (3,0) wire, and anticlockwise around the (8,5) wire.

I feel really stupid asking this, but if B circles around the wires, how can you draw a vector and say that B is straight down, or to the right? Isn't it technically moving around the wire, and not in anyone direction specifically?

 

[dx]

This is what I mean when I say B circles around the wire:

At any given point, it has a direction. (B is a vector field, with a direction and magnitude at each point.)

 

[robera1]

This is what I mean when I say B circles around the wire:

At and given point, it has a direction.

But what determines why when the current moves into the page it has a magnetic field that is straight down, and when a current moves out of the page it has a magnetic field that is to the right?
This is so damn confusing!

 

[dx]

You are forgetting about the point P. Look at the right picture above. It shows a wire with current into the page. Take this and impose it on your original diagram. And then, at the point P, see in which direction the lines are pointing.

 

[robera1]

Oooooooh! Okay, this makes perfect sense! So, there are essentially two magnetic forces acting at P, the one straight down and the one to the right, which added together give a vector 45 degrees down and to the right.

So, now I have to find the magnetic force acting on P, and they have added a third wire, who's current is moving out of the page right at P.

So, if I am doing this correctly, the magnetic field from the third wire won't effect P, since it is at P.

As for the force, is it in the same direction as the magnetic field?

 

[dx]

Force per unit length on a wire is I x B (vector cross product of I and B).

 

[robera1]

Okay, so what does that mean in terms of vectors?

The questions asks to indicate the magnetic force on the current in the new wire (the one at P).

So, is this force in the same direction as the magnetic field created by the other two wires (the ones we've been talking about this whole time)

 

[dx]

No, it's not in the same direction. Do you know how to find the direction of a cross product? Take I in the direction of the new current, and B in the direction of the field we've found previously, and the force on the wire will be in the direction of I x B.

 

[robera1]

The current is moving counter-clockwise. The magnetic field is 45 degrees down the right. How do you cross-product this?

 

[dx]

The current is out of the page. See this if you don't know how to find cross products: http://en.wikipedia.org/wiki/Cross_product