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Magnetic force due on current

Problem 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)
243775

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

Mentor
20,487
2,608
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:

243779


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

Mentor
20,487
2,608
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.
 
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.
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

Mentor
20,487
2,608
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.
 
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
 

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