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Transcript

Magnetic Force Between Two Parallel Conductors This is a short direct application of what we’ve learned so far about magnetism. Given two long straight parallel wires separated by a distance a and carrying currents I1 and I2 in the same direction, let’s find the force each exerts on the other. The force on a length L of wire 1 is given by F1 = I1 LB2 , where B2 is the magnetic field produced by wire 2 at the site of wire 1. But this magnetic field is given by µ I B2 = o 2 2π a and so we can write the force on length L of wire 1 as µII F1 = o 1 2 L . 2π a G G The direction of the force follows from L × B2 (see Figure 30.9) and is toward wire 2. If you were to re-do the above calculations to find the force on wire 2, the result is equal in magnitude and opposite in direction. The two wires attract each other with a force per unit length given by FB µ o I1 I 2 = . L 2π a Note that if the two currents are in opposite directions in the two parallel wires, then the magnitude of the force remains the same, but the direction becomes mutually repulsive.