Find the force between two wires

[zade70]

Homework Statement

Two rectilinear wires with length 100 m have the intensity 2 A. The wires in are perpendicular directions with distance 5 meters from each-other. Find the force they interact.

Homework Equations

F=(I1*I2*μ0*l)/(2*pi*d)

The Attempt at a Solution

F=(2*2*4*pi*10^-7*1)/(2*3.14*5)=1.6*10^-7
The solution in my book is 0 N.

 

[BvU]

Check the direction of the magnetic fields and the direction of the currents...

 

[zade70]

Check the direction of the magnetic fields and the direction of the currents...

I think the currents are perpendicular with each other and so are the vectors of magnetic induction.

 

[berkeman]

I think the currents are perpendicular with each other and so are the vectors of magnetic induction.

Yep. So what force would that generate?

 

[zade70]

Yep. So what force would that generate?

I can't find an argument for that.

 

[berkeman]

I can't find an argument for that.

Okay, so I'm getting the impression that you have not been exposed to the vector relationship between the current in a wire and the B-field that circulates around it, is that right? Also, have you learned how to calculate the vector Lorentz Force?

 

[zade70]

Okay, so I'm getting the impression that you have not been exposed to the vector relationship between the current in a wire and the B-field that circulates around it, is that right? Also, have you learned how to calculate the vector Lorentz Force?

I don't know what the Lorentz Force is. I know that F=B(induction)*l(length)*I(intensity)*sin alpha. I also know that the force is perpendicular with current and induction

 

[berkeman]

I don't know what the Lorentz Force is. I know that F=B(induction)*l(length)*I(intensity)*sin alpha

Do they have any diagrams in your textbook that show a current carrying wire and the B-field circling around the wire? Do they discuss and show the "Right Hand Rule" for the direction of the B-field? I'm just trying to get a feel for how the book wants you to know how to answer this question...

 

[zade70]

Do they have any diagrams in your textbook that show a current carrying wire and the B-field circling around the wire? Do they discuss and show the "Right Hand Rule" for the direction of the B-field? I'm just trying to get a feel for how the book wants you to know how to answer this question...

Yes. I have learned the Right Hand Rule. Actually I am doing some problems that are not from the book I'm studying and I don't know which is appropriate for me to do with the knowledge I have so far.

 

[berkeman]

Yes. I have learned the Right Hand Rule. Actually I am doing some problems that are not from the book I'm studying and I don't know which is appropriate for me to do with the knowledge I have so far.

Ah, that might explain it. Yeah, just using the force formula for parallel wires will not work for perpendicular wires.

The B-field for a current carrying wire looks like this:

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magcur.html#c1

And the Lorentz Force is written as the cross product of two vectors: F = qv X B Where F is the force vector, v is the velocity vector of a charge, and B is the magnetic field vector. Vectors have both a Magnitude and a Direction.

The vector cross product can be simplified if you are not familiar with it, so the Lorentz force can be re-written as magnitudes only F = qvB sin(θ), where θ is the angle between the velocity vector v and the magnetic field vector B. So the result of the cross product is maximized when v and B are in the same (or opposite) direction, and it is zero when they are perpendicular.

Does that help some? You can do more reading about this at Hyperphysics or Wikipedia.

Edit -- not sure why the image is not displaying correctly, but you can click on the link to see it.