Caculate the force between to anti-parallel wires

[LBP]

Homework Statement

I am trying to figure out how the formula for the force between two anti-parallel wires differs from the formula for parallel wires.

Homework Equations

B=μ₀I/2∏R

Force between two parallel wires = μ₀LI_aI_b/2∏d

The Attempt at a Solution

I understand that d is the hypotenuse made by the x and y distances between the two parallel wires.

I also understand that if the two currents run in parallel they will attract, but if they run anti-parallel they will repel.

What I don't understand is how to manipulate the formula to calculate the anti-parallel force. At first I thought it would just be the negative value of the attractive force, but I am unsure. My other thought was that the repelling force would be based off of the net magnetic force between the two wires.

I am very lost. If anyone felt like clearing this up for me I would very much appreciate it.

 

[I like Serena]

Welcome to PF, LBP!

The anti-parallel force is just the negative value of the attractive force.
It follows from the same equation if you let one of the currents have a negative sign.

FYI, your formula for the force follows from your first formula, combined with the formula for the Lorentz force: F = B I L.
The direction of the magnetic field in the first formula and the force in the second formula, follows from applying the right hand rule twice.
Regardless of this direction, the magnitude of the force is the same in both cases.

 

[LBP]

Thank you so much! I had a quiz on this yesterday and I am pretty sure I nailed it! So thank you again!

 

[I like Serena]

Good!