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.

 

[Nickie]

I would like to first clarify the setup of the problem. Are the wires all in the same plane or are they stacked on top of each other? This information is important in determining the direction of the force.

Assuming the wires are all in the same plane, we can use the right hand rule to determine the direction of the force on the bottom wire. The magnetic field created by the current in the top wire (I1) will be directed into the page (using the right hand rule). The magnetic field created by the current in the middle wire (I2) will be directed out of the page. These two fields will cancel each other out, resulting in a net magnetic field of 0 at the location of the bottom wire. Therefore, the net force on the bottom wire will also be 0 N.

To further clarify, the right hand rule states that if you curl the fingers of your right hand in the direction of the current, your thumb will point in the direction of the magnetic field. So for the top wire (I1), the magnetic field will be directed into the page, and for the middle wire (I2), the magnetic field will be directed out of the page. Since these two fields are equal and opposite, they will cancel each other out.

In summary, the answer to the question is (a) 0 N. It is important to understand the concept of magnetic fields and how they interact with each other in order to solve this problem correctly.