Magnetic force with 2 Current Carrying Wires

1. Mar 11, 2010

mike_302

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

Two parallel loops are parallel, coaxial, and almost in contact, 1.29 mm apart. Each loop is .117 m in radius, the top loop carrying 137 A clockwise, and the bottom look carrying 137 A counter-clockwise. Calculate the force that the bottom loop exerts on the top.

2. Relevant equations

dB = (u0/4pi)(I*ds x r^)/r^2 where r^ is the unit vector.
For a long wire: B = (u0*I)/(2pi*r) where r is the distance from the center of the wire
Fb = Int(I*ds x B) for a current carrying wire

3. The attempt at a solution
So the answer works out to Fb= I^2*u0*r/d where d is the distance between the two loops.
To get this, I simply said Fb = ILB, where L is hte circumference of the loops, and then I had to say B was the magnetic field around a long straight wire... But I don't quite understand why I approximate the circle as a long straight wire? IS it because the two loops are stated as being so close together that one side doesn't affect anything except that which is directly above it?

Can someone explain this, and possibly even the math that I might have done directly from that dB equation to figure that out?

Thanks!