# Current in wire that's being held up magnetic field of two others

1. Oct 25, 2008

### Sasha26

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

In the figure, the top wire is 1.1 mm-diameter copper wire and is suspended in air due to the two magnetic forces from the bottom two wires. The current is 45 A in each of the two bottom wires.

Calculate the required current flow in the suspended wire.

http://i37.tinypic.com/2u3v8sm.jpg

2. Relevant equations

F = mg
F(of wire1 on wire2) = I1 * I2 * u0 * length of wire2 / 2*pi*r
(second equation derived from equation from B, u0 * I / 2pi r)

3. The attempt at a solution

I've drawn a FBD with two forces going up (sin(60)* force from each of the two lower wires), and one force going down (that of gravity). I've set the two up equal to the one down.

(Force down = mg, and I calculated mg by using r^2 pi * length * density of copper (8.92 g/ cm^2) ). This allows the "length" factor to cancel out, since we're not told what it is.

Then I solved for the second current (since the first one is given as 45) ... unfortunately I'm not getting the right answer.

Any tips? Thank you!

2. Oct 26, 2008

### merryjman

I don't see anything wrong with your method. This may be too easy to be the problem, but I notice that you are using grams and centimeters for your units - have you converted these into kg and m? Because the acceleration by gravity and the permeability constant are in m and kg units...

3. Oct 26, 2008

### Sasha26

I did convert the density into kg/m^3 and got 187 A for the current, which is still wrong. I'm really stumped since I've redone it several times now and still gotten the same answer.

4. Oct 26, 2008

### merryjman

I got 186.6 A, the same answer as you, but if you are doing this as a web-based problem maybe rounding is the issue? For example, the program I use with my students (webassign) would want the answer as 186.6 rather than rounded to 187, since it's halfway between 186 and 187. If that's not it, I'm stumped!

5. Oct 27, 2008

### Sasha26

Hi everyone,
It looks like there was a bug in the coding and they had programmed it with the wrong answer ...the right answer is 187. Stupid computer Thank you so much for your help!