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]. 

Electric Dipole and Torque (10th Day)

Spring 2015
Professor Mason
March 26 class

Electric Dipole
In class, we needed to draw an electric field horizontally and give the direction of where it will go in between two bars containing one negative bar and one positive bar, [a = qE/m].

As for electric dipole, the dipole moment [p = 2aq].

We needed to sketch the forces on each particle on the picture with three lines shown. After that, we found out there was a torque, and we needed to calculate it by using torque equation shown below.




Torque
We found out that torque has positive and negative forces, which could be combined into [T net = 2Fa sin theta] or [T = pxE] and [Uf = -pE cos theta] or [ Uf = p . E (dot product)]. Other equation that we used was [W = pE (cos theta i - cos theta f)].

Flux

Flux is defined as [Flux = EA cos theta], which E is electrical field and A is area. Net flux = Rate in - Rate out = 0. We were given a positive charge in between the flux lines, and we needed to find which direction it would go. In the end, we needed to do coding in VPython, which requires a lot of work, but we did not take any pictures of it.

Electric Field (9th Day)

Spring 2015
Professor Mason
March 24 Class

Definition of Electrical Field

 The first thing we learned in class was to define Electrical Fields. The picture attached shows the four definition of electrical fields along with the equation, which is [E = kq/r^2].
There are four steps to help remember the calculation/equation of electrical fields, which is shown in the picture attached below.

 Force on charged particle in an electric field, [F = qE].

Electric Field has field lines; field lines point out of positive charges and into negative charges (infinite lines on the charge). It uses the lines on charge to calculate the magnitude.






Super Position Principle
Super Position Principle is the complicated version of defining waves, which means that two waves that added together, and it works in electric fields (vector sum of the forces), [E = E1 + E2].

In class, we did some calculations about this equation, and some of them requires Microsoft Excel in order to do the calculation to make them easier to calculate. We used [r hat = vector r2 - vector r1 divided by magnitude of r2-r1 that will equal to just r], so it becomes [E = kq(vector r2 - vector r1)/ r^3]. The picture attached below is the calculation we did on Microsoft Excel.

VPython

In class, we were given a code from the lab book or we could also find it on profmason.com, and we needed to draw the diagram based on the code. The picture attached shows the diagram we made based on reading the given code.

VPython Assignment

Spring 2015
Professor Mason
VPython assignment

In class, Professor Mason, gave us an assignment, which involves VPython program in order to do 3D modelling. The steps are:
1. Go to vpython.org
2. Download and install Python 2.7 and Vpython by the "Windows" tab.
3. Open VIDLE for Vpython in my directory to start the program.

The first assignment I need to do is to code vectors of sphere and give them arrows, such as:

Next, I need to add # before "arrow" and pick one arrow length to be shorten by half. (*Note: Due to the unseen arrows because it was too short, I put more length to all of the arrows).

Next in the assignment, I need to do a 3D model, which I need to name the variables on each sphere.

Next, I was asked to add twice of one of the y-axis in the vector to the code.

The last part of the tutorial was about placing the  [print] command, which is written as print(variable,attribute).

Electrostatic Forces (8th Day)

Spring 2015
Professor Mason
March 19 class

Static with Balloon and Charge
Firstly in class, we learned about static that involves with a balloon. The first experiment was  to rub balloon on hair, then it sticks to the glass because it produces statics. The next experiment was to rub the balloon on silk, then sticks it to the glass; as a result, it sticks just for a while because there is no as much static as while rubbing on hair. Next, we needed to define charge for 7-years-old student; the example of charge is magnet: one side of the magnet can stick with the different side of the other magnet.













Electrostatic on Scotch Tape

In class, we did another experiment including electrostatic; however, this time we did it with scotch tape. First, we need 4 scotch tapes with approximately 10 cm long. First experiment: put a strip of scotch tape on the table with the sticky side down, then curl over the end of each tape to make a non-stick handle. Then, we peel the tape off the table and bring the non-sticky side of the tape toward another tape. As a result, the tape sticks to each other.
Second experiment: we place two strips of tape on the table sticky side down and we label them "B" for bottom. We press another strip of tape on top of each of the B pieces; then, we label these strips "T" for top. We pull each pair of strips off the table and we pull the top and bottom strips apart; then, we put one "T" strips of tape toward another tape. As a result, they're both attracted.

Next, we put one "B" strips of tape toward another tape, and the result was they move away from each other. The same result goes with the interaction between a "T" and a "B" strips.
The idea is that the interaction between objects that have been rubbed is due to a property of matter that we called it charge, which contains negative and positive charge. Charge moves readily on certain materials, known as conductors, and  not on insulators. In conclusion, metals are good conductors, while glass, rubber, and plastic tend to be insulators.




Forces between Two Balls

In class, we did an experiment of two balls moving toward another involving electrostatic force. We were supposed to do this experiment on Logger Pro and analyze it based on the video given from the professor. The free body diagram of forces of the balls give us an equation of [Fx = F- T sin(theta)], which will equal to [T = W/cos(theta)]. There is also an equation which involves gravitational force between two masses m1 and m2 separated by a distance r, and that leads to an equation of [F = G (m1 m2)/r^2]. The F vs r graph is shown on the picture attached.

 We can compare when the ball move away from each other with the mathematical formulation of coulomb's law, which is [Fe = K r12 (q1 q2)/r^2], which r12 is a unit vector from q2 to q1, r^2 is the square of the distance between the two charged objects in meters, K is a constant that equals to 9x10^9 Nm^2/C^2, and q is the charge in coulombs. We used this formula to define the two balls as charge in coulombs as they move away from each others.

The next experiment after we analyzed the balls' movement was to make a graph out of it by making an equation by using manual fit.

Electrostatic Experiment

 In class, we did another experiment involving electrostatic machine. Professor placed some strips of paper on the machine to show that the machine is producing electrostatic if the machine is turned on. The strips of paper sorts of hovering in the air when the machine is turned on because there is a static on the machine. If we placed our hands on the machine, it would produce a static noise. The next one is that the professor place a rods that spins when the machine is turned on because the machine produces statics and it is conducted to the metal rods, so it spins.