# Calculation of conservation of energy of a magnet falling through a coil of wire.

1. Jan 25, 2012

### 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