Question

Two long, parallel, current-carrying wires lie in an xy-plane. The first wire lies on the line y = 0.350 m and carries a current of 34.0 A in the +x direction. The second wire lies along the x-axis. The wires exert attractive forces on each other, and the force per unit length on each wire is 285 µN/m. What is the y-value (in m) of the line in the xy-plane where the total magnetic field is zero?

Answer 1

Answer:

y = 0.105 m

Step-by-step explanation:

Given:

First wire: y = 0.350m & Current, I = 34.0A

Force per unit length on each wire = 285 µN/m

Required:

What is the y-value (in m) of the line in the xy-plane where the total magnetic field is zero?

First find the current in the second wire:

$\frac{u_0 I_1 I_2}{2\pi d} = 285*10^-^6$

$\frac{2*10^-^7 * 34 * I_2}{0.35} = 285 * 10^-^6$

$I_2 = \frac{285*10^-^6 * 0.35}{2*10^-^7 * 34} = 14.67$

Current in wire 2 = 14.67 A

Let y distance have zero magnetic field

Take the formula:

$\frac{u_0 I_2}{2\pi y} = \frac{u_0 I_1}{2\pi(0.35 - y)}$

$= \frac{2*10^-^7 * 14.67}{2\pi y} = \frac{2*10^-^7 * 34}{2\pi(0.35 - y)}$

[

$= 14.67 * (0.35 - y) = 34y$

$= 5.1345 - 14.67y = 34y$

Collect like terms

$= 34y + 14.67y = 5.1345$

$48.67y = 5.1345$

$y = \frac{5.1345}{48.67}$

$y = 0.105 m$