Calculating Conservation of Energy for Magnet Dropping Through Coil

[Redro]

Hi

I am trying to understand the effect of dropping a magnet through a single coil of wire. If there is one turn of wire, connected to a resistor, and a magnet with known mass and flux density is dropped vertically through the coil, a current will be induced in the coil. The forces acting on the magnet will be gravity, and a magnetic force. This force will be proportional to the current induced in the coil, such that

F = NBI*pi*(coil diameter)
where
N = number of coils
B = flux density

Lenz's law will also apply, giving the induced voltage as a function of the change of flux per unit time.

So, if a magnet is dropped from a known height above the coil, it will have a known potential energy. The motion through the coil will induce a current in the wire that will be dissipated as heat in the resistor. Using the conservation of energy principle, the kinetic energy and the dissipated energy will equal the initial potential energy (assuming the reference point is at the base of the coil, therefore potential energy at the final position can be ignored).

When I try to calculate the velocity of magnet at the end of the coil I end up with two unknown variables, the current and the velocity.

This seems like it should be a simple case of conservation of energy but it only seems solvable if one of these variables is held constant eg. the current. I can then solve it incrementally in excel. This is not an adequate solution to the problem as I believe it should be possible to solve it using the eqations above and the standard equations of motion using Newton's Second Law and a summation of the forces acting on the magnet.

Any ideas will be welcome.

Thanks

 

[eljose79]

for your post. It seems like you have a good understanding of the principles involved in this scenario. To answer your question about solving for the velocity of the magnet at the end of the coil, it is important to consider the factors that affect the induced current in the wire.

Firstly, the rate of change of flux through the coil will depend on the speed of the magnet as it passes through the coil. This means that the velocity of the magnet is not a constant, but will change as it moves through the coil. Secondly, the number of turns in the coil and the strength of the magnetic field will also affect the induced current.

To solve for the velocity of the magnet at the end of the coil, you will need to consider the motion of the magnet through the coil and how it affects the induced current. This can be done by using the equations you mentioned, along with the equations of motion and the principles of electromagnetism.

One approach could be to set up a differential equation that takes into account the changing velocity of the magnet and the changing current in the coil. This would require some simplifications and assumptions, but it could provide a more accurate solution than using a constant current.

Another approach could be to use experimental data to determine the relationship between the velocity of the magnet and the induced current, and then use that relationship to solve for the velocity at the end of the coil.

I hope this helps you in your research. Keep exploring and experimenting to find the best solution for your problem. Good luck!