Determining magnitude of net force with three parallel wires

[mevalle]

Homework Statement

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

Homework Equations

F = ILBcosθ
B = μo * I/ 2∏r

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.

 

[Doc Al]

B = μo * I/ 2∏r

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?

 

[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?

 

[Doc Al]

The distance used with I3 would be 3r and I2 would be 2r?

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.

The Current for I3 being 3A and for I2 being 2A, right?

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.