Final answer:
The force between two long straight and parallel conductors separated by a distance r can be found using the formula F = IlB.
Step-by-step explanation:
The force between two long straight and parallel conductors separated by a distance r can be found by applying the formula F = IlB, where I is the current in the wire, l is the length of the wire, and B is the magnetic field created by the other wire. In this case, we are considering the force exerted by wire 1 on wire 2. The force per unit length, F1, is given by F1 = I1lB1.
We can express this force in terms of the variables a, b, and r by substituting the expression for B1 into the equation for F1. The expression for B1 depends on the distance r and the dimensions of the wires a and b. The calculation of B1 involves integrating over the length of wire 1.
Therefore, the component of force along the line connecting the two atoms, Fr(r), on one atom can be found by substituting the expression for F1 into the equation for Fr(r). This will give us a function of r in terms of a, b, and r.