Problem 55

  Suppose in Figure 21.31a that I₁ = I₂ = 25 A and that the separation between the wires is 0.016 m. By applying an external magnetic field (created by a source other than the wires) it is possible to cancel the mutual repulsion of the wires. This external field must point along the vertical direction. (a) Does the external field point up or down? Explain. (b) What is the magnitude of the external field?

SOLUTION:

(a) Using the right hand rule, you can see that the magnetic field at each wire due to the other wire is pointing upward. Since the current in each of the wires is the same, the magnitudes of the magnetic fields are the same. Therefore, an external magnetic field pointing downward with magnitude equal to that produced by either wire will cancel the mutual repulsion.

(b) Use the equation for the magnitude of the magnetic field produced by a long straight wire. The external field must have the same magnitude

$$B = \frac{\mu_o I}{2 \pi r}$$

$$B = \frac{\mu_o (25 A)}{2 \pi (0.016 m)}$$

$$B = 3.1 \times 10^{-4} T$$