Magnetic Field, finding the current

In summary, the copper wire feels a downward gravitational force of mg, where m is mass and g = 9.80 m/s2 is the gravitational field strength near the Earth's surface.
  • #1
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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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  • #2
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
 
  • #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.
 
  • #4
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.
 
  • #5
GDGirl said:
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.
 
  • #6
that worked out perfectly, thank you! :)
 

What is a magnetic field?

A magnetic field is a region in space where a magnetic force can be detected. It is created by moving electric charges, such as electrons, and can be represented by magnetic field lines that indicate the direction and strength of the force.

How is a magnetic field measured?

A magnetic field can be measured using a device called a magnetometer. This device detects the strength and direction of the field and can be used to calculate the current flowing through a wire.

What is the relationship between magnetic fields and electric currents?

Magnetic fields and electric currents are closely related. Whenever an electric current flows through a wire, it creates a magnetic field around the wire. Similarly, a changing magnetic field can induce an electric current in a nearby wire.

How can you find the current in a wire using a magnetic field?

To find the current in a wire using a magnetic field, you can use the right-hand rule. Point your right thumb in the direction of the magnetic field, and the fingers of your right hand will point in the direction of the current. You can also use the formula I = Bdl, where I is the current, B is the magnetic field strength, and dl is the length of the wire.

What are some applications of magnetic fields and current measurement?

Magnetic fields and current measurement have many practical applications. They are used in devices such as generators, motors, and transformers. They are also used in medical imaging techniques, such as magnetic resonance imaging (MRI), and in navigation systems, such as compasses and GPS devices.

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