7.2: Force Between Two Current-carrying Wires
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In Figure VII.1, we have two parallel currents, I1 and I2, each directed away from you (i.e. into the plane of the paper) and a distance r apart. The current I1 produces a magnetic field at I2, directed downward as shown, and of magnitude B=μI1/(2πr) where μ is the permeability of the medium in which the two wires are immersed. Therefore, following Equation 7.1.1, I2 experiences a force per unit length towards the left F′=μI1I2/(2πr) You must also go through the same argument to show that the force per unit length on I1 from the magnetic field produced by I2 is of the same magnitude but directed towards the right, thus satisfying Newton’s third law of motion.
FIGURE VII.1
Thus the force of attraction per unit length between two parallel currents a distance r apart is
F′=μI1I22πr