# Magnetic force due on current

#### fight_club_alum

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) 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

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#### gneill

Mentor
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.

• JD_PM and fight_club_alum

#### 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

Mentor
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

#### fight_club_alum

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

#### gneill

Mentor
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

#### 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

Mentor
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

#### 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

Mentor
Glad I could help!

• fight_club_alum

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