Electromagnetic Waves

Prerequisite: physics, algebra 2

Maxwell came up with a couple equations pertaining to light:

1) some kind of charge-field relation that involves calculus.. not in the scope of AP
2) magnetic fields have no beginnings or ends, whereas electric fields do
3) change in magnetic field generates an electric field
4) a current or change in electric field generates a magnetic field

An electromagnetic wave is essentially energy transmitted through fields. Change in magnetic field causes change in electric field by Faraday's Law, then the change in electric field causes a magnetic field by Ampere's Law, that may change the existing magnetic field or not.

I forgot to label the third picture; the vertical waves are electric fields and the horizontal waves are magnetic fields.

Since light rides on electromagnetic fields, it does not rely on a medium, thus explaining how it can travel through a vacuum. The constancy of the speed of light also relies on this fact; light is not something that you actively move, but rather it is something you send through a field.

If the speed of light is your cake, the derivation of Lorentz Transformation might be of interest.

Early Atomic Models

Prerequisite: physics, algebra2

First two equations are for the cathode ray experiment, which sets magnetic force equal to the centripetal force. The cathode rays then became known as electrons. The third is the oil drop experiment, in which the electron's electric force is equal to its weight. Simple and elegant.

Scientists then became interested in why elements only emit certain wavelengths. They came up with various mathematical models for the hydrogen atom, in which the Balmer series describes visible wavelengths, the Lyman series UV, and the Paschen series IR. All three combined shows the emission spectrum for hydrogen. Rydberg's constant R is 1.0974 E7 /m.

The orbit radius then became of interest. The second step of the derivation is electric and centripetal force. The Bohr radius is the inner orbit of a hydrogen atom.

The energy of light emitted is the energy it takes for an electron to jump levels. The quantum condition is interesting where the angular momentum L is.. quantized. The integer n refers to the orbit level, or principal quantum number. The most amazing thing is probably how the angular momentum reduces to an integer and some constants.

The total energy is the kinetic energy minus the potential energy. Substitute v from angular momentum and r from radius. The ground state of a hydrogen atom is 13.6eV. The second set of equations describe the wavelength associated to an electron skipping energy levels, as Balmer, Lyman, and Paschen had previously attempted.

To explain the quantized energy levels, the Broglie wavelength of an electron must fit the circumference of its orbit by an integer n. The equation can then derive angular momentum as in the quantum condition, thus verifying its legitimacy.

Except that physics likes to be counter intuitive. It continues to boggle our minds and turn our brains inside out..

Genesis 9:3

"Every moving thing that lives shall be food for you. And as I gave you the green plants, I give you everything"

Meat consumption has become a topic lately. It is destructive in every way, from deforestation to water shortage, to ocean pollution, to greenhouse effect, to animal cruelty, to obesity, and the such. I would say that meat makes about one sixth of my diet, which is a small portion of an already minute appetite. Still working on minimizing the consumption~

And my pastor brought up this interesting topic to light: people before Noah were vegan. Our sins collected over many generations to the point where meat consumption is necessary and God must allow it. Not sure how it came to be biologically, but sin is as physical as it is spiritual, in the same way that Adam and Eve became mortal.

Today the crave for meat is greater than ever. Despite all the notices for environment, humanity and health, very little people are ready to give it up. In fact, most people are in denial at the severity of its effect (especially when shutting the livestock business is not quite economical). Sin is so deeply rooted in our flesh that meat has become an artificial necessity.

The more I think about it, the more I realize that God really has provided everything for us. Skeptics point at the starving people of today and ask: "Where is God?". God has already given, but we meat eaters have taken more than our share. We give crops to livestock when crops could easily feed the world. There is in fact plenty for all if we would give up our cravings for meat.

Let me clarify: the wrong is not in the meat itself but in how we came to want meat, and in recent times, how we disregard immoralities that come with our meat. If meat was sinful, God would not have permitted it.

Meat is economical. Meat is sociable. Meat is not environmental. The social and economical interest often outweighs the environmental concern, and that is the way I often thought of this. But meat consumption is a spiritual fight as well. Only when we are alleviated of our sins are we freed from our bondage to meat. Nobody is going to be immaculately clean of sin, but it will take more than campaigns and reforms to cut meat consumption to a significant minimum. It takes God.