How Is Magnetic Force Calculated on a Cylinder in a Gradient Field?

[ramez]

I am a chemistry student that is trying to calculate the magnetic force on a cylinder due to a gradient produced by sitting in an annulus. The annlus is a cylinder of height h with outer radius ro and inner radius ri. The other cylinder has height h and radius r such that a gap exists with width ri-r. This gap produces a field gradient on the centered magnetic. I am not too sazy with E&M and would appreicated any assistance. Thanks in advance.

 

[brucedog]

I think if you assume you have two current carrying rings and calculate the force of one on the other it will work. Does everyone agree?

 

[Graeme Robinson]

The magnetic force on a cylinder can be calculated using the formula F = BIL, where B is the magnetic field strength, I is the current, and L is the length of the cylinder. In this case, we can consider the cylinder to be a loop of current, with the current flowing in one direction along the length of the cylinder.

To calculate the magnetic force on the cylinder due to the gradient produced by the annulus, we first need to determine the magnetic field strength at any point in the annulus. This can be done using the formula for the magnetic field strength of a current-carrying wire, which is B = μ0I/2πr, where μ0 is the permeability of free space, I is the current, and r is the distance from the wire.

In this case, the annulus can be treated as a series of concentric wires, each with a different radius. The magnetic field strength at any point in the annulus will be the sum of the magnetic field strengths of all the wires at that point. This can be calculated using the principle of superposition.

Once we have determined the magnetic field strength at any point in the annulus, we can then use the formula F = BIL to calculate the magnetic force on the cylinder at that point. The force will vary depending on the location of the cylinder within the annulus, as the magnetic field strength will be different at different points.

If you are not familiar with E&M, I would recommend seeking assistance from a physics or engineering student or professor who is more familiar with this topic. They can guide you through the calculations and help you understand the concepts involved. Good luck with your calculations!