Two Long Straight Wires Carrying Curent

[CARNiVORE]

Homework Statement

Homework Equations

B = μ₀*i/(2PI*r)

The Attempt at a Solution

First of all, if you're looking at this, that means you intend to help me study for my upcoming physics exam on a Friday night. If you fit into this category of people, then god bless your soul.

I should state that I have all the answers to these, because the solutions are posted - I just want to ensure that I understand the material. Some of the solutions are illegible, but that's not a huge deal.

So, I understand part a: I use the relevant equation that I typed and replaced 'i' with "i1" and "i2" and replaced 'r' with 'd.' After accounting for unit vectors, the correct answer is:

B(vector) = μ₀*(i1*x(vector) + i2*y(vector))/(2PI*d)

So, let's start w/ part b: I have no clue what's going on besides that we need to find the force per unit length, which is F3 / L where L is length. The formula sheet equates F3 / L = i3 * B(total). Why is this the case?

 

[drvrm]

So, I understand part a: I use the relevant equation that I typed and replaced 'i' with "i1" and "i2" and replaced 'r' with 'd.' After accounting for unit vectors, the correct answer is:

B(vector) = μ0*(i1*x(vector) + i2*y(vector))/(2PI*d)

So, let's start w/ part b: I have no clue what's going on besides that we need to find the force per unit length, which is F3 / L where L is length. The formula sheet equates F3 / L = i3 * B(total). Why is this the case?

so, what is force on a current carrying conductor in a magnetic field?

 

[CARNiVORE]

Oops, brain fart - Fm = iL x B, so Fm/L = i3*B(tot). B(tot) is equal to (μ₀*√i1^2+i2^2) / (2PI*d), so Fm/L is equal to i3 times this.

For c, if the angle is to be 45 degrees, then tan^-1(i2/i1) = 45 degrees. This would mean that the ratio of i2/i1 is one to one, so i1 would have to be the same value as i2, which is 40.0 mA. The resultant force vector would be -45 degrees because the force is perpendicular to the B-field.

I'm confident that these answers are correct. Of course, you can let me know if you see a discrepancy, though. Thanks for your help!