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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
F1 = o 1 2 L .
2π a
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
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.