For my experiment, I will be trying to find a relationship for the force created by these magnetic eddy currents based on the speed of the conductor and the strength of the magnetic field. I first began my experiment by logically dividing it into two parts. One, finding the strength of a magnetic field at a distance. Two, finding the relationship between the speed of a conductor, and the eddy current force created, with the conductor at set distances from the magnet.
I propose that the relationship between the magnetic field strength and distance will be of the form Ba1/r this is based on the B-field outside of a wire versus distance given by Giancoli (Giancoli, 1991: 525). However, from the physical feel of magnets, this doesn't seem to be the case. To me, the force (by definition BaF) feels as if it increases as 1/r2 (Ibid: 512). I believe that the speed of the conductor versus the eddy current force will be a linear relationship and the strength of the magnetic field versus the eddy current force will also be a linear relationship. I have based these mainly on the formula for motional emf which states that the voltage created by such a movement will be equal to the length times the velocity times the B-field strength (E=Blv) (Lehrman, 1984: 238). Although the voltage created will yield a linear relationship with the current (V=IR) and therefore force, I don't think this has to be true (Ibid: 201). In fact, from some of my previous experiments with eddy currents in fluids I have found that the relationship is not necessarily linear, but often times a power function. For example, the drag around a body falling quickly is proportional to v2, whereas at slow speeds it is proportional to v (Feynman, 1963: 12-3). To sum it up, my hypothesis is that the eddy current force will be some constant times the speed and the B-field at a distance will likewise be some constant times the distance.