How Can Visualizing Magnetic Forces on Current Enhance Understanding?

[fight_club_alum]

Homework Statement

Three long, straight, parallel wires all lie in the yz plane and each carries a current of 20
A in the positive z direction. The two outer wires are each 4.0 cm from the center wire.
What is the magnitude of the magnetic force on a 50-cm length of either of the outer
wires?
answer is 1.5 mN

Relevant Equations

f12 (l) = (uo * i1* i2)/(2pi * r)

This is how I visualize the problem (of course I am drawing this as if it is in the z-y axis); I don't know what will be the next step. Anyone please help me.
Thank you

 

[gneill]

I don't see how the wires could be in a triangular arrangement if they all lie in the same plane. I'd imagine it'd something more like this:

Edit: By the way, your Relevant Equation, as stated, gives the force per unit length of the parallel wires.

 

[fight_club_alum]

hey, thank you for replying to my question
If I put them that way they won't give 1.5 mT and I don't think we can use the cosine law in that case

 

[gneill]

hey, thank you for replying to my question
If I put them that way they won't give 1.5 mT and I don't think we can use the cosine law in that case

No need to use the cosine law. Check out my edit to my post above.

 

[fight_club_alum]

Aren't those wires parallel, and the length is 50 cm?

 

[gneill]

Aren't those wires parallel, and the length is 50 cm?

The wires are "long" and parallel. You're only concerned with a 50 cm segment of each of the outer wires.

 

[fight_club_alum]

The wires are "long" and parallel. You're only concerned with a 50 cm segment of each of the outer wires.

does it give that answer if you do so? if Yes, can you tell the difference between this question and that question, please: Three long, straight, parallel wires each carry a current of 10 A in the positive x-direction. If the distance between each wire and the other two is 10 cm, what is the magnitude of the magnetic force on a 20-cm length of either of the wires?
Because that way doesn't give the answer in both and I, honestly, can't find a difference?
(note: for the second question, I had to draw an equilateral triangle and use the cosine law)

 

[gneill]

does it give that answer if you do so?

Yes.

if Yes, can you tell the difference between this question and that question, please: Three long, straight, parallel wires each carry a current of 10 A in the positive x-direction. If the distance between each wire and the other two is 10 cm, what is the magnitude of the magnetic force on a 20-cm length of either of the wires?

There they specify that the distances between all the wires is the same: 10 cm. That forces a triangular arrangement and they will not all lie in the same plane.

 

[fight_club_alum]

Yes.

There they specify that the distances between all the wires is the same: 10 cm. That forces a triangular arrangement and they will not all lie in the same plane.

Yes, I understand now what is happening
Thank you so much for clarifying; after the first couple of questions, all involved a triangular arrangement I thought these questions can't be solved without the cosine law!
Thank you so much again for clarifying

 

[gneill]

Glad I could help!