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What is the force between two perpendicular wire carrying current, one to the north and one to the east?

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What were you thinking? – user12345 Mar 14 at 9:38
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closed as too localized by Ϛѓăʑɏ βµԂԃϔ, Manishearth♦ Apr 16 at 6:12

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2 Answers

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Hints:

  1. The magnetic field due to a current-carrying wire circulates around the wire, in other words, the magnetic field vectors point tangent to circles whose planes are perpendicular to the wire and whose centers are intersected by the wire.

  2. The magnetic force experienced by a moving charge $q$ (like those in line currents) with a velocity $\mathbf v$ in a field $\mathbf B$ is given by $$ \mathbf F = q\mathbf v\times\mathbf B $$

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If the wires were parallel, the force per unit length of wire is given by $F =\frac{\mu_0I_1I_2}{2\pi r}$. In the case that both wires have the same magnitude of current, but in opposite directions, the equation becomes: $F =\frac{\mu_0I^2}{2\pi r}$ and the force causes the wires to repel.

If the wires are perpendicular however, the force between them is 0.

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