Magnetic Field, finding the current

[GDGirl]

Homework Statement

A straight 2.47 -mm-diameter copper wire can just 'float' horizontally in air because of the force of the Earth's magnetic field B, which is horizontal, perpendicular to the wire, and of magnitude 5 x 10-5 T. What current I does the wire carry? (The density of copper is 8.96 g/cm3).
HELP: The wire feels a downward gravitational force of magnitude mg, where m is mass and g = 9.80 m/s2 is the gravitational field strength near the Earth's surface.

Homework Equations

F=lIB
Gravitational force=mg

The Attempt at a Solution

Okay, I know /how/ to do this except for one step. I know that I need to find the force using the equation above. Simple enough, except that I don't know how to find the mass. I know that the mass is the density multipled by the volume. However, I don't know how to find the volume with the information I'm given. If someone could just help me out with that little bit, that would be fantastic!

 

[tyco05]

What value did you use for the length in F=lIB?

You can find the volume (assuming a cylindrical wire) by using pi*r^2*length

Be careful of your units - remember you are given 2.47 mm diameter. and the density you are given is in g/cm^3

 

[GDGirl]

Okay, I suppose you didn't understand what I said.
I haven't solved for the current yet because I don't know the force because I don't know the volume.

I don't know the length so I can't find the volume using that formula. I was hoping someone could point out to me a way ti find the mass either without using volume or a way to find the volume with the information provided.

 

[tyco05]

OK, we'll go back to the beginning.

In order for it to "float" the Upwards force needs to equal the downwards force:

lIB = mg

You know that m = rho*V

You also know that V = pi*r^2*l

Do a bit of simple algebra and you'll see that you don't need to know a length - it cancels out.

Rearrange what you have and solve for I.

Once again, be careful with units.

 

[LowlyPion]

Okay, I suppose you didn't understand what I said.
I haven't solved for the current yet because I don't know the force because I don't know the volume.

I don't know the length so I can't find the volume using that formula. I was hoping someone could point out to me a way ti find the mass either without using volume or a way to find the volume with the information provided.

Simply choose 1 m as the length. That should give you a force / meter.

 

[GDGirl]

that worked out perfectly, thank you! :)