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

[Sasha26]

Homework Statement

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

Homework 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)

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!

 

[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...

 

[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.

Thanks for your response though!

 

[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!

 

[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!