For electric fields, like charges repel, and unlike charges attract. We have something similar for magnetic fields: like currents attract, and unlike currents repel.

Consider two long parallel wires W₁ and W₂ spaced r apart with currents I₁ and I₂ in the same direction.

I₁ is going to produce a magnetic field of strength at W₂. W₂ is carrying a current I₂, and sitting in B₁. It thus experiences a force per unit length of

.

What about W₁? Similarly, W₁ is carrying I₁ sitting in B₂. So it experiences a force per unit length of

.

Using the FLHR, one can deduce that the two wires are mutually attracting each other if they carry currents in the same direction.  If W₁ and W₂ are carrying currents in opposite directions, then it is going to be a mutual repulsion.

Do realize that even if I₁ and I₂ are different in magnitude, the magnetic forces each wire exerts on the other are still going to be exactly equal in magnitude. This is yet another example of two objects obeying N3L.

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Concept Test

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