Magnetic field pattern in a hor. plane, wire force direction

[moenste]

Homework Statement

A current of 3 A flows down each of two long vertical wires, which are mounted side by side 5 cm apart. Show on a diagram the magnetic field pattern in a horizontal plane, indicating clearly the direction of the magnetic field at any point. What is the magnitude and direction of the force on a 25 cm length of a wire?

Answer: 9 * 10^-6 N.

2. The attempt at a solution
I did get the correct answer: F = B I L, where B = (μ₀ I) / (2 π a) = (4 π * 10^-7 * 3) / (2 π * 0.05) = 1.2 * 10^-5 T. F = (1.2 * 10^-5) * 3 * 0.25 = 9 * 10^-6 N.

In terms of other requirements I am not sure.

I see the situation like this:

Though the current goes downwards ("current flows down") and it is presented horizontally and vertically.

Is the image correct? ("Show on a diagram the magnetic field pattern in a horizontal plane, indicating clearly the direction of the magnetic field at any point.")

How do we find the direction of the force? The left-hand rule can't be applied here -- the field is in a circle, we don't know it's direction

 

[David Lewis]

The magnetic fields of the two wires will interact with each other. That's where the force would come from.
Are the currents flowing in the same direction, or opposite directions?

 

[moenste]

The magnetic fields of the two wires will interact with each other. That's where the force would come from.
Are the currents flowing in the same direction, or opposite directions?

Like this? We have two wires with current flowing downwards in a horizontal plane.

 

[David Lewis]

Diagram seems to show current flowing to the left?
Problem statement does not say whether both currents are in same direction. Be sure to confirm this first.

 

[moenste]

Problem statement does not say whether both currents are in same direction. Be sure to confirm this first.

How can we do that?

 

[David Lewis]

My bad. Problem clearly says both currents are flowing down along vertical wires.
You could rearrange your drawing to more closely follow post #1 format. It shows the wire oriented vertically. You would have to reverse the polarity of current, though.

 

[moenste]

My bad. Problem clearly says both currents are flowing down along vertical wires.
You could rearrange your drawing to more closely follow post #1 format. It shows the wire oriented vertically. You would have to reverse the polarity of current, though.

I though that we are required to draw a horizontal picture...

Here it is:

 

[David Lewis]

"I thought that we are required to draw a horizontal picture..."

No. They mean the plane is horizontal, not the picture.
Your second diagram is more accurate. Note picture in post #1 shows a perspective drawing of the magnetic field in the horizontal plane. That's basically what you are going for, but you can rotate the plane of the magnetic field into the plane of the paper to make the magnetic field easier to draw.

 

[moenste]

That's basically what you are going for, but you can rotate the plane of the magnetic field into the plane of the paper to make the magnetic field easier to draw.

That means I need to draw two circles (like I am looking from the top to the bottom)? What shall I do with them? The direction of the field is changing (it's a circle)...

 

[David Lewis]

The field of each wire is actually depicted by concentric circles. The circles represent lines of force, so you would add them vectorially. The field is static, and the directional sense (symbolized by arrowheads) of the field will not change because it's being created by direct current.

 

[MartinCarr]

Well something like this?

 

[moenste]

The field of each wire is actually depicted by concentric circles. The circles represent lines of force, so you would add them vectorially. The field is static, and the directional sense (symbolized by arrowheads) of the field will not change because it's being created by direct current.

I think I got it (also checked this video):

We have B going into the paper and going out of it from the left and right sides respectively. The smaller circles represent the field of the other wire on that wire.

F₁ = I₁ * L₁ * B₂ and F₂ = I₂ * L₂ * B₁.

If we then take our right hand and the first finger will be in the direction of the current and the middle finger will be in the direction of the field of the other wire then we'll get our forces by the thumb. In both cases the forces are pointed towards the middle.

I think this should be correct.

 

[David Lewis]

Refer to the illustration in post #1. Direct your attention to the purple concentric rings with the arrowheads. Each of those rings represents a line of magnetic force. The network formed by lines of force is a magnetic field. Your assignment is to draw a horizontal cross section through the composite magnetic field when the two vertical wires are next to each other 5 cm apart.

 

[moenste]

Refer to the illustration in post #1. Direct your attention to the purple concentric rings with the arrowheads. Each of those rings represents a line of magnetic force. The network formed by lines of force is a magnetic field. Your assignment is to draw a horizontal cross section through the composite magnetic field when the two vertical wires are next to each other 5 cm apart.

I did that. My drawing is the same, I only used circles that represent field going in and out of the paper. If you don't understand me, just skim through the video in my previous post : ).

 

[David Lewis]

The problem asks you to show on a diagram the magnetic field pattern in a horizontal plane.
You drew a diagram in the vertical plane.