Covering Laws and Terms

There are many laws that apply to my project, mostly having to do with how magnetic fields interact with my system. These laws include Faraday's and Lenz's Law, which are commonly grouped together as they were based on one another, Earnshaw's Theorem about magnetic levitation, the concepts surrounding Eddy Currents, and other electrical terms such as resistivity and magnetic permeability.
Faraday's Law and Lenz's Law are very important to my project because they explain how moving electricity through a coil of magnet wire will create a magnetic field. This is important because these two laws explain how my non-contact motor-generator can utilize the magnets on my axis to get my FES spinning. Faraday’s Law explains how the movement of coils along a magnetic field produces a current in the wire. The three ways are to move a magnet through a coil, to move the coil in the x- and y- directions in relation to the magnetic field, or to rotate the coil perpendicular to the magnetic field. The coil will not generate electricity if it is not moving along rings of the magnetic field (if it is in line with the magnetic field). <See the picture on the right from hyperphysics.phys-astr.gsu.edu>. In simpler terms, a current is produced if a magnet is passed over multiple lines of the magnetic field produced by the coil.
Lenz's Law builds off of the concept of Faraday's Law. Lenz's Law states that if a magnetic field causes a current to flow through a coil, then the coil will generate its own magnetic field. This magnetic field resists the original magnetic field in an effort of resisting change, causing a lower energy output than input. However, if the magnetic field that acts on the coil is decreasing, then the magnetic field of the coil will add onto the original magnetic field in an attempt to keep equilibrium. This concept is seen in the efficiency of the motor-generator of my project, which will vary depending on the core implemented in each coil of magnet wire.
Earnshaw's Theorem is quite different from Faraday's and Lenz's Law, as it deals with the whole design of my FES rather than how the system works. Earnshaw's Theorem is quite simple, as it states that any object can never reach equilibrium by only utilizing magnetic levitation. After hearing about this theorem, I added an important feature to my design: the small point on the end of my shaft that pushes into the glass. Although this point results in a point of contact, which causes a frictional force to slow down the FES and lose efficiency, this point is very important at keeping the FES balanced and levitating.
Going back to electrical properties, probably the most confusing electrical property in my project are Eddy Currents. Eddy currents are reverse currents created on the surface of metal conductors by a changing magnetic field. The intensity of the current is based on the strength of the magnetic field and is inversely related to the resistivity of the material of the core. Eddy currents are problematic since they cause a loss of energy in the form of heat. This concept is important because Eddy currents will be present in all of my cores except the air core, which will be interesting to see how the absence of Eddy currents will affect the air core, even though the air core produces much weaker magnetic fields due to the lack of a metal core to stimulate the magnetic fields.
Resistivity and magnetic permeability relate back to the electrical laws already discussed in this post. Resistivity is a measure of the resisting power of a specified material to the flow of an electric current. In my project, each of the different cores are made of unique materials with different levels of resistivity, which will change the efficiency of the coil. The other major term is magnetic permeability, which is how a specific material changes the intensity of a magnetic field. Similar to resistivity, the different cores will have different levels of permeability, which will increase or decrease the strengths of the magnetic fields, which will change the amount of time it takes that coil to get the FES spinning.

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