But this is not all kids. We are just getting to the good parts here… it turns out that the change in current is also important since it creates electric waves and electric waves create magnetic waves
and magnetic waves create electric waves
and electric waves create magnetic waves
and magnetic waves create electric waves
and electric waves create magnetic waves
and magnetic waves create electric waves
and electric waves create magnetic waves

sorry for this wave propagation

The beauty of electromagnetism is that the entire theory can be resumed in four equations:

Spoiler: At some point in relativity theory we will see that the electric field $\vec{E}$ and the magnetic field $\vec{B}$ actually depend on the point of the observer. Observer 1 (let's call her Alice) could see a purely electric field with zero magnetic field and observer 2 (Bob let's say) will see the some physical phenomenon but explain it as a purely magnetic event with zero electric field. This will happen if Alice and Bon are moving with the speed of light relative to each other…

For all the hipsters who have come here to learn physics to try to look “knowledge geek cool”, you can go home now and tell this story about the relativity of E and B. It is good stuff…. even better than this quantum consciousness shit that people have been polluting the media with…. E and M is actually as fascinating if not more than all of quantum theory.

Care to join us? Do you WANT to be part of this course?
No seriously… this isn't going to be easy. We are talking physics 2 now.
Second level. Only for dedicated …. pfffff… nah man I'm kidding you. This is easy shit too.

Ok ok… enough joking around. I know you have a final coming up so I better get on with the teaching.

Charles-Augustin de Coulomb figured that out in 1786. He also figured out the one-over-r relationship of the electric force between charges. We give props to the man, by calling the electrostatic force the Coulomb force.

Did you know: Since both gravitaiton and the electrostatic law are “one over r squared” laws, we can look for analogies between them. Indeed since

$\vec{F}_e=q\vec{E}$ (charge times electric field gives Electric force)

and

Weight$=\vec{W}=\vec{F}_g=m\vec{g}$

this means that $\vec{E}$ and $\vec{g}$ are analogues.

Now it just happens that in most gravitational phenomena that we are used to $\vec{g}$ is pretttt constant. (since we stay around $r=$radius of the earth and $M$ the mass of the earth stays constant so $F_g=\frac{GMm}{r^2}=\frac{GM}{r^2}m=\vec{g}m$. This is why we are just used to the constant value $\vec{g}=9.81$ towards centre of earth.

For electric things though there are many potentials $V$ and thus the effects are much more varied. E M waves …. coool…. that is what you get when you have opposites…

alike and different…

A homopolar motor is built from a permanent magnet and a battery. The permanent magnet creates a magnetic field $\vec{B}$ everywhere in space and then the current $I$ that the battery produces along the wire feels that magnetic field \[ F_{current} = \mu \]

There is a cross product going on: $\vec{I}\times\vec{r}$. If the current is flowing in the positive $z$ direction $(I_x,I_y,I_z)=(0,0,I)$, then the resulting magnetic vectors will have components only in the $xy$ plane, since the cross product of $\vec{I}$ with anything is guaranteed to return a vector perpendicular to $\vec{I}$.

Ok. I know I may be throwing too much at you all at once, but I wanted to get the real idea out first so you know where this is going. We will use the cross product geometry and the vector functions later, but to understand everything about the magnetic fields you just need the first right-hand rule and the Ampere's law.

You might not see the point of combining the two forces together into a single equation. I mean how often are they going to give you a question with both an electric field and a magnetic field? Point granted. For this course, you can think of them as separate, but in more advanced physics we will actually see that the electric field and the magnetic field are all one.

(move to own section) Two windings, one on top of the other.

 current one -->  magnetic flux -->  - current two 

By the Lechatelier principle the second winding will try to pass a current in order cancel the magnetic field

Let's make this more precise. You have winding one which has radius $R_1$, and $n_1$ turns.

If there is a constant current (DC) that is flowing int the wire then the magnetic field created inside will be: \[ \vec{B}_{inside}(r) = \] where $r$ is the

We call magnetic flux or $\Phi$ the total amount of magnetic field that goes through some surface. Let S be the inside of the winding – it has area $\pi R_1^2$.