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# 7.2: Force Between Two Current-carrying Wires

• • Contributed by Jeremy Tatum
• Emeritus Professor (Physics & Astronomy) at University of Victoria

In Figure $$VII.1$$, we have two parallel currents, $$I_1$$ and $$I_2$$, each directed away from you (i.e. into the plane of the paper) and a distance $$r$$ apart. The current $$I_1$$ produces a magnetic field at $$I_2$$, directed downward as shown, and of magnitude $$B=\mu I_1/(2\pi r)$$ where $$\mu$$ is the permeability of the medium in which the two wires are immersed. Therefore, following Equation 7.1.1, $$I_2$$ experiences a force per unit length towards the left $$F'=\mu I_1I_2/(2\pi r)$$ You must also go through the same argument to show that the force per unit length on $$I_1$$ from the magnetic field produced by $$I_2$$ is of the same magnitude but directed towards the right, thus satisfying Newton’s third law of motion. $$\text{FIGURE VII.1}$$

Thus the force of attraction per unit length between two parallel currents a distance $$r$$ apart is

$F' = \dfrac{\mu I_1I_2}{2\pi r}$

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