# Magnetic Field, finding the current

## 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!

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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

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.

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
Homework Helper
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.

that worked out perfectly, thank you! :)