Determining magnitude of net force with three parallel wires

1. Jul 5, 2012

mevalle

1. The problem statement, all variables and given/known data
Three parallel wires carry a current of I 1 = 3 A, I 2 = 2 A, and I 3 = 1 A, respectively. They are arranged as shown. If r = 2m and L=5m,what is the magnitude of the net force on the bottom wire?
<------------------------- I1
r
-------------------------->I2

2r

<--------------------------I3

I1 = 3A I2 = 2A I3 = 1A r = 2m L = 5m
They show the radius from I1-->I2 as r and the radius from I1-->I3 as 3r

(a) 0 N
(b) 5×10−7 N
(c) 2×10−7 N
(d) 3×10−7 N

2. Relevant equations
F = ILBcosθ
B = μo * I/ 2∏r

3. The attempt at a solution

I feel like I am missing a concept here.

B = (1.257e-6)(1A)/2(Pi)(2) = 1.00028e-7
F = ILB = (1)(5)(1.00028e-7) = 5.0014e-7

The answer is supposed to be 0N. I was thinking the first two wires might cancel out, but I am really not too sure. I don't see any other concepts. I also tried the right hand rule to determine the direction of Force. I feel pretty lost at this point.

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Last edited: Jul 5, 2012
2. Jul 5, 2012

Staff: Mentor

This, with the right hand rule, is what you need.

Hints:
When figuring out the B field at I3 due to I1, what distance will you use? What value of I?

When figuring out the B field at I3 due to I2, what distance will you use? What value of I?

3. Jul 5, 2012

mevalle

The distance used with I3 would be 3r and I2 would be 2r? The Current for I3 being 3A and for I2 being 2A, right?

4. Jul 5, 2012

Staff: Mentor

I'll reword that. We want to calculate the B field created by I1 at the position of wire 3. So we need the distance between wire 1 and wire 3, which is 3r.

And we also want to calculate the B field created by I2 at the position of wire 3. So we need the distance between wire 2 and wire 3, which is 2r.
When finding the B field due to wire 1, we use the current I1 (which is 3 A). When finding the B field due to wire 2, we use the current I2 (which is 2 A).

So find the magnitude and direction of those two B field contributions. Then you can add them up to find the net B field at wire 3 due to the other two currents.