Current needed to keep coil levitating

[hopkinmn]

Homework Statement

A horizontally oriented coil of wire of radius r=5.00cm and carrying a current I, is levitated by south pole of a vertically oriented bar magnet suspended above center of coil. If magnetic field (B) on all parts of the coil makes an angle θ=45.0 with the vertical, determine the magnitude and direction of the current needed to keep the coil floating. B=0.0100T, number of turns in the coil is N=10.0, and the total coil mass is m=10.0grams

Homework Equations

Magnetic field equation for a solenoid: B=μ(N/L)I
Force of magnetic field: Fb=ILB
Force of gravity: Fg=mg

The Attempt at a Solution

To keep the coil floating, magnitude of Fg=magnitude of Fb

Bcosθ=μ(N/L)I since Bcosθ is the vertical magnetic field
so mg=ILB=I(2∏R)(μNI/(Lcosθ)) where L=2∏R

I think I'm using L wrong when finding Bcosθ. But the problem doesn't give the height of the coil. Am I approaching this wrong?

 

[anathema]

Thank you for your post. It seems like you are on the right track with your approach. However, there are a few corrections and clarifications that I would like to make in order to help you solve this problem.

Firstly, when finding the magnetic field at the center of a coil, you should use the equation B=μ(N/L)I, where N is the number of turns in the coil and L is the length of the coil. In this case, L would be equal to the circumference of the coil, not its height.

Secondly, the angle θ represents the angle between the magnetic field and the vertical, not the angle between the coil and the vertical. This means that Bcosθ is not the vertical magnetic field, but rather the component of the magnetic field that is acting in the vertical direction.

Lastly, in order to find the force of the magnetic field on the coil, you should use the equation Fb=ILBsinθ, where θ is the angle between the current and the magnetic field. Since the current in the coil is perpendicular to the magnetic field, θ=90° and sinθ=1, so the equation becomes Fb=ILB.

Using these corrections and clarifications, you should be able to solve the problem. Remember to set the force of gravity equal to the force of the magnetic field in order to find the current needed to keep the coil floating.

I hope this helps. Good luck with your calculations!