Question

According to Ampere, which of the following sets of current-carrying wires would repel each other? The arrow point indicates the direction of the current in each wire.

Answer 1

a
b
c
d

Answer 2

There should be no force between either of the crossed pairs. Source: Ampere's Law:

\({\vec {F}}_{12}=-{\dfrac {\mu _{0}}{4\pi }}\int\limits _{L_{1}}\int\limits _{L_{2}}{\dfrac {(I_{1}d{\vec {\ell }}_{1}\ \mathbf {\cdot } \ I_{2}d{\vec {\ell }}_{2})\ }{|r|^{2}}} {\hat {\mathbf {r} }}_{21}\)

Because \(d{\vec {\ell }}_{1} \perp d{\vec {\ell }}_{2}\), the dot product is zero

For c, they are anti-parallel so the negative signs cancel,...., repulsion

vice versa for a.