Homework Help: Caculate the force between to anti-parallel wires

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

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

2. Relevant equations

B=μ₀I/2∏R

Force between two parallel wires = μ₀LI_aI_b/2∏d

3. 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.

 

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