Answer to Question #314220 in Physics for mcc

Question

Two parallel straight wires 10.0 cm apart carry currents in opposite directions. Current I₁ = 5.0 A is out of the page, and I₂ = 7.0 A is into the page. Determine the magnitude and direction of the magnetic field halfway between the two wires.

Answer 1

The net magnetic field

$$B=B_1+B_2=\frac{\mu_0 I_1}{2\pi r_1}+\frac{\mu_0 I_2}{2\pi r_2}$$ $$r_1=r_2=d/2$$

$$B=\frac{\mu_0 (I_1+I_2)}{\pi d}$$

$$B=\frac{4\pi\times 10^{-7} (5.0+7.0)}{\pi \times 0.10}=4.8\times 10^{-5}\:\rm T$$

The field is directed upward in the plane that is perpendicular to the plane where lying the wires.