Project Proposal 2 | Modeling and Experimental Tools with Prof. Magnes

For my project I will attempt to model the magnetic field from a magnet as it interacts with a wire coil. I will make an interactive model that can vary speed, distance of coil to magnet, magnet intensity, and number of turns among other things. My first attempt at the animation can be seen below.

And here it is to illustrate the movement:

As is evident by this picture, I still have yet to add the magnetic field lines, and that is where the bulk of my project will be. I will be using our Griffiths textbook, The Art of Electronics by Horowitz & Hill, The Handbook of Tables for Applied Engineering Science, and Engineering Circuit Analysis by Hayt and Kemmerly. I also have collected a few journal volumes that I will use as I see which are the most useful.

I will be using the equation

(1) $\begin{equation*} B=\frac{\mu _{0}2\mu^{2}}{4\Pi d^{3}} \end{equation*}$

as well as

(2) $\begin{equation*} \Phi ^{_{B}}=Ba \end{equation*}$

and

(3) $\begin{equation*} \epsilon =-n\frac{d\Phi _{B}}{dt} \end{equation*}$

Where $\mu$ is the Magnetic Moment, $\epsilon$ is the electromotive force, and $\Phi^{_{B}}$

Since I will have the magnet moving over a stationary wire coil, we will see that electric fields (not magnetic forces) are responsible for setting up the emf. Although the electric and magnetic fields are inextricable linked, it is useful to note that because stationary charges can’t experience magnetic forces, there has to be another explanation.

The unanswered question is how to mathematically model the magnetic field due to these magnets. I currently will be simplifying each magnet to a magnetic dipole, as opposed to a more complex magnet. I would hope to have their intensities change as I change the magnetic moment, and I would also like to see what kind of feedback the solenoid would produce. In order to simplify this process the next iteration of my animation will be a square magnet and a square coil. This should hopefully make the modeling easier, as their seems to be more information on that kind of a set-up.