Answer to Question #320687 in Electric Circuits for John

Question

Two long, parallel wires are attracted to each other by a force per unit length of 440 𝜇𝑁/𝑚

when they are separated by a vertical distance of 0.80 m. The current in the upper wire is

13.0 A to the right. Determine the location of the line in the plane of the two wires along

which the total magnetic field is zero.

Answer 1

Explanation

$\qquad\qquad \begin{aligned} \small \frac{F}{\Delta L}&=\small \mu.\frac{i_1i_2}{2\pi d} = F_{given}\\ \small i_2&=\small F_g.\frac{(2\pi d)}{\mu.i_1}\\ \\ \small B_{total}&=\small \mu.\frac{i_1}{2\pi x}+\mu.\frac{i_2}{2\pi(d-x)}= 0\\ \small \frac{i_1}{x}&=\small \frac{i_2}{x-d}\\ \small x&=\small \frac{i_1 d}{(i_1-i_2)} \end{aligned}$

• Here $\small i_1$ is the 13 A current on the top line and the current on the other line can be calculated.
• $\small d$ is the separation between the wires.
• Then the distance to the layer where the magnetic field is zero can be calculated.
• $\small i_2>i_1$ should be as the wires are held by an attracting force meaning that both currents are along the same direction.
• Then probably the x should receive a negative value meaning that it is not in between the wires but outside of them.