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:
[tex] \frac{u_0 I_1 I_2}{2\pi d} = 285*10^-^6 [/tex]
[tex] \frac{2*10^-^7 * 34 * I_2}{0.35} = 285 * 10^-^6 [/tex]
[tex] I_2 = \frac{285*10^-^6 * 0.35}{2*10^-^7 * 34} = 14.67 [/tex]
Current in wire 2 = 14.67 A
Let y distance have zero magnetic field
Take the formula:
[tex]\frac{u_0 I_2}{2\pi y} = \frac{u_0 I_1}{2\pi(0.35 - y)}[/tex]
[tex]= \frac{2*10^-^7 * 14.67}{2\pi y} = \frac{2*10^-^7 * 34}{2\pi(0.35 - y)}[/tex]
[
[tex] = 14.67 * (0.35 - y) = 34y[/tex]
[tex] = 5.1345 - 14.67y = 34y [/tex]
Collect like terms
[tex] = 34y + 14.67y = 5.1345 [/tex]
[tex] 48.67y = 5.1345 [/tex]
[tex] y = \frac{5.1345}{48.67} [/tex]
[tex] y = 0.105 m [/tex]
