# Find the force between two wires

Tags:
1. Mar 23, 2016

1. The problem statement, all variables and given/known data
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.

2. Relevant equations
F=(I1*I2*μ0*l)/(2*pi*d)
3. 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.

2. Mar 23, 2016

### BvU

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

3. Mar 23, 2016

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

4. Mar 23, 2016

### Staff: Mentor

Yep. So what force would that generate?

5. Mar 23, 2016

I can't find an argument for that.

6. Mar 23, 2016

### Staff: Mentor

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?

7. Mar 23, 2016

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

8. Mar 23, 2016

### Staff: Mentor

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...

9. Mar 23, 2016

Yes. I have learnt 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.

10. Mar 23, 2016

### Staff: Mentor

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.