Flux and Gauss' Law (11th Day)

Spring 2015
Professor Mason
March 31 class

Flux
The first thing we needed to do in class was to type "Caltech E field" on Google, and the link is shown in the picture attached. On the website, it showed us how flux would work and what it would like in Java.

Relationship between Net flux and Net charge is they are proportional to the charge enclosed, [flux = charge/ epsilon] or [flux = integral of E dA cos (theta)].

Gauss' Law
After we were done playing with flux, we did an experiment, which included a cylinder with a piece of paper attached, and we plugged it in to the electrical field machine. When we turned on the machine, the outside part of the paper attached to the cylinder moved, while the inside part of the paper did not.

Next, we needed to think about the maximum possibilities when we have eight positive charges to be attached to a ring, and it would look like this.

It has to be no charges at all in the inner radius of the ring in order to have its maximum distance from each other. 

Then, the professor asked us what we were going to do if there was a lightning storm in the middle of nowhere, and we picked an option, which was to stay under the car because electricity is inductive to the ground. One of ideal conductors is metal object, which has excess charges that are free to move around inside or outside of the conductor, which is one example is car. 

The Gauss' Law conductor is [E = omega / epsilon], which will lead to [flux = polar integral of E da = q in / epsilon]. The charge density is defined as [rho = dq/dv] and [q = integral from 0 to r of rho dv]. If it is sphere, it becomes [q = integral of 4 pi rho r^2 dr from 0 to r] or [rho = 3Q/4pi R^3], and the electric field calculation is [E = q/4pi ^2 epsilon] or the short form of that calculation is [kq/r^2].

Microwave experiment
In class, we did an experiment which includes disc, steel wool and a light bulb. First, we started off with the steel wool. We put the steel wool in the microwave, and then we turned it on; it would light up and show a spark inside the microwave. Next was the compact disc, we also put it in the microwave and turned it on, and it showed us a spark as well. The next one was light bulb, it showed us different color, and it lights up in the microwave.

The picture attached above is a compact disc after it was put in the microwave, it has some scratch or crack mark on the disc. 

The two pictures attached above are the equations for electrical field for cylinder. We know that the surface area of the cylinder is [2 pi r L + 2 pi r^2] (the surface area of the rectangle and 2 circles when we break it apart). Therefore, the equation becomes [E = lambda/ 2 pi r epsilon] as shown above. 

Gravitational Field

We learned gravitational field in class, which has an equation of [F/m = Y] thus, it would become [integral of Y dA = m/G]. Then, we can break the equation down again to [y = mG/ (Re + h)^2] and finally to [Gm/r^2].