# Calculate the required current flow in the suspended wire

Tags:
1. Feb 17, 2016

### Taiyen

1. The problem statement, all variables and given/known data

In the figure, the top wire is 1.5 mm diameter copper wire and is suspended in air due to the two magnetic forces from the bottom two wires. The current flow through the two bottom wires is 70 A in each.

Calculate the required current flow in the suspended wire.

2. Relevant equations
F=(I1I2μo*length)/2πr
F=(r2πρ)/length

3. The attempt at a solution
I cancelled length and now have combined:

(r2πρ)=(I1I2μo)/2πr

I1 = 70A
ρ (density of copper) = 8.92g/cm2
μo = 4π*10-3
r (on the left side) = .15cm/2
r (on the right side) = 3.8cm

I just plug these in and find I2....?
I have tried to, but I keep getting the wrong answer.. maybe my r's are mixed up? I tried switching them, but still wrong.. I think I am missing something, maybe my wrote down the equations incorrectly.. please help! I don't need the final answer, I'm more interested in learning how to do this type of problem.

2. Feb 17, 2016

### TSny

Welcome to PF!
Did you mean for the length in the second equation to be in the numerator? Does the acceleration due to gravity play any role here?

Think about the direction of the magnetic force on the the top wire due to each of the bottom wires.

Since you didn't show your calculation, we can't tell if you did the unit conversions correctly. (Your units for the density of copper are incorrect.)

What units are you using for expressing μo?

3. Feb 17, 2016

### Taiyen

Oh, yes! The length on the left side is supposed to be in the numerator to cancel. That is my mistake!

I thought that I could calculate mg (in the equation F=mg) by using r2πρ*length, but I really am not sure that this is correct..
Would the direction be downward?

μ0's units are Wb/m2.

And again, my mistake, the density of copper's units are in kg/m3 not g/cm2.

4. Feb 17, 2016

### Taiyen

Here's what I have after I converted everything to meters:

(0.0015m/2)2*π*(8.92kg/m3) = [(70A) * I2 * (4π*10-3 Wb/m2)]/(2π*0.038m)
and I found I2 to be 4.27*10-6, so I am doing something very wrong...

5. Feb 17, 2016

### TSny

Your value for the density in kg/m3 is incorrect. Be careful with converting cm3 to m3. Also, your value for μo in the SI system of units is incorrect. Check your textbook or notes.

There are two magnetic forces on the upper wire; one force from each of the lower wires. These forces are vector quantities and so you need to consider the directions of these forces.

6. Feb 17, 2016

### TSny

What happened to the "g"? Yes, the direction is downward.

These are not correct units for μ0.

7. Feb 17, 2016

### Taiyen

OHH! Okay okay! I think I get it!
Sorry for the many mistakes in values and units, I looked back in the textbook and corrected everything.
μo = 4π*10-7 Tm/A
density value is 8960 kg/m3

And then with 2*Fcos(30) = ρπr2*length*g, I can cancel lengths, the "2", and put it back into the other equation to get:

ρπr2g = [I1I2μocos(30)]/(πr)

I got my correct answer with this, thank you so very much for your help! c: I really appreciate it!

8. Feb 17, 2016

### TSny

Great. Good work!