(9/30/14) Electric Fields

Today we go further into the life of electricity and discuss Electric Fields, flux, and start understanding the complexity that is Gauss's Law

Class Activity - Relating Torque and Potential Energy to Electric Dipole

Deriving pxE

By understanding the idea of torque, used all the way back from 4A as a way to calculate rotation, we can then rebuild the equation τ = r x F (a cross product), we can then use the idea of work, and obtain the new equation τ =pEsinθ, knowing that sinθ creates a cross product, obtaining
τ = p x E

Deriving p·E

Similarily we can do the same thing that we did for torque with potential energy, obtaining the equation pEcosθ, which we know it to be a dot product U = p·E







Class Activity - E-field in a metal canister

Set up of experimentation

In the next activity, we were to place a metal canister (shown on the right) next to a Van De Graaff (shown on the left). The canister contained 3 tin foils inside and 3 tin foils outside.
The activity here was to see how the tin foils will react to the electricity produced by the Van De Graaff generator

Our initial prediction

We predicted that all 6 tin foils will react to the Van De Graaff generator and move as a result.
This prediction came as a result of what we thought we knew about E-fields, and that since its electricity and metal, they should react accordingly

A video of the experiment

A correction of our theory

We learned that in fact only the 3 tin foils outside actually reacted to the Van De Graaff generator and moved as a result.
We learned that this came to be because of the fact that while inside the metal canister, the E-field actually turns out to be zero, while an E-field is generated outside the metal canister, causing the tin foil to move.



Class Activity - Electric Field Lines
We were asked to place a single charge in this simulator in order to understand electric field lines.

When we placed a positive +1 charge into the simulator and ran it, we realized that it gave us 5 field lines. We can also see that these field lines become denser as it gets closer to the particle, most likely due to the fact that the close the lines are to the charge, the stronger the magnitude of the charge becomes. We realized that as we increased the charge, the lines increase by an increment of five.

When we placed two particles of opposite charge, we get that these five lines react to each other, the closer the lines are, the more the lines bend to the opposite charge. We also can state the same reason as before as to why the lines become more dense as it becomes closer to the charged particle.




Overall, we can state that the field lines represent our vector, the direction in which the electric field travels, with it being stronger as it get closer to the charge

Class Activity - Flux as a Function of Surface Area
In order to speed up the process of learning flux, Professor Mason taught us the idea of the proportionality between flux and angle through a simple experimentation

Fun video showing distribution of weight to a nail bed

He used the nail bed to act as a charged electric field, and a square wire to act as the area enclosed. By having the angle at 0 degrees, it is shown to have the most amount of charge enclosed. Subsequently, when the angle reaches 90 degrees, it is shown to have zero charge enclosed.







Class Activity - Flux Simulator
In our last lab, we worked on answering questions about flux within a simulator provided for us.

Answers to questions 1-4

Answers to question 6 and 7

Additional Events
On Friday, September 26th 2014, SPS (Society of Physics Students) invited a guest speaker Prof Seiji Takemae to talk about his research on Raman Spectrometers and their future usefulness. As a result, he also allowed a selected few students (myself included) to take part in his future research pertaining to this subject (Physical Chemistry).

His setup on evaluation carbon tetrachloride and Tylenol 

(9/25/14) Electric Fields

Today we focused on electric fields, going in deeper on Coulomb's Law, formulating a new formula from an old one.

Class Discussion - How does Gravity Work:
We started the class by first asking the question "How does gravity work?" As the class struggled to try to answer this, we were shocked when we were told by Prof Mason that scientist, to this day, cannot figure out how gravity works. We then went on to learn about Gravitrons and how these theoretical particles are supposedly the interaction that gravitational force uses, similar to the observed photons that electromagnetic force uses in order to interact.

We then focused on understanding the similarities between electric force and gravitational force, and how they both are dependent on the magnitude of their charge/mass respectively and their distance as well

Electric Field Simulation:
We then went online to answer questions regarding electric field as various positions

Answers to question 1 and 2

Answers to questions 3 and 4

Representaion of Electric Fields

The following video is an 3D representation of an electric field. The hill side is the positive side, while the crater is the negative side. We can then view that in for a positive charged particle, the particle will roll from the positive hill and into the negative crater

Deriving the newest expression of Electric fields

We then, after having an understanding of electric fields, were asked to derive it, knowing Coulomb's Law, and the fact that FE = qE

It is to note that we took a slightly different approach to how to find Electric Fields, yet yielding the same answer


Class Discussion- Example Problems

Solution to the problem

In order to get a better understanding of superposition of Electric Fields, we took a problem that involved using unit vectors as well.

It is to note that we took the idea of the unit vector, instead of using sines and cosines, realizing that the y-component canceled out, and gave the answer in terms of the x-component

Activity: Eletric Field Vectors from Two Point Charges:

Our next portion of the lab was a bit more challenging, using nothing more than an excel spreadsheets of the electric fields at different distances, we were asked to find the magnitude of the E fields at different positions shown below.

The points in question

Our results of each points

By using Coulomb's Law and the equation for Electric field, we were able to successfully the magnitude of the electric field, as shown to the far right

It is to note that excel doesn't really like negative numbers, in which is why the last number is in parenthesis, it is actually a negative number

As a mini activity, we were asked to show the configuration of the electrons in both a copper environment and wood environment

In a copper environment, it would create an equatorial triangle, while in a wood environment, it would stay as is.

Activity: E-Field Vectors from a uniformly Charged Rod

Once again, we were given a figure, and asked to find the magnitude of its electric field, by only using the excel spreadsheet. This time, it was of a uniformly charged rod ads shown below.

Our envision of the activity at hand

We were asked to find the electric field at two different point.

1) 5 cm across from it

2) 5 cm above it perpendicularly 

Once again, by using the unit vectors, Coulomb's Law, and the equation for electric field, we were able to find the answer, which is about 5.94x10^-6 N/C

It is to note that if we were to increase the partition from 10 to 20, the answer would become close to about 6 E-6 N/C. 

We then learned that another way that it could be solve was by taking the integral, which when we did would lead to be exactly 6 E-6 N/C. We then decided to calculate the percent difference between our answer and the answer that the integral would give us, yielding a 0.01% difference. 

Activity- Electric Field Hockey
Our take-home assignment was by looking at a simulation called electric field hockey, in which we are given a positive (or negative, if you wanted to change it) particle, and asked to use the fewest amount of negative and positive charges to send the particle into the goal line. We also learned that via experimentation, the particle cannot bounce off any obstacles, including the walls of the goal line, making the task much more complicated. Below are our solutions to each of the following scenarios  along with the amount of charges we thought were required to obtain the GOAL! 

Level one (6 needed)

Level two (3 needed)

Level 3 (7 needed)

It is to note that for level three, we learned that the particle can around the obstacles and into the background of the java, which was necessary because it was truly the only way to solve level three (Thinking outside the box)

(9/22/14) Electrostatic Forces

In this class period, we studied about electrostatic forces, focusing on repelling and attracting, Electric Force, and Coulomb's Law

Exploring the Nature of Electrical Interactions:

We started the lab with a simple experiment, by charging a balloon with two different charges, one with an animal fur, another with thin rag, we theorized what would occur to the balloon when placed on a glass object in each cases

Test one - Animal fur

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With the animal fur, we predicted that rubbing the fur on the balloon will give the balloon a charge, and in turn when placed on the glass, will stick.

Additionally, with our free-body diagram, we show that since there is a force that is sticking on the wall (Electrical) that the said force would have to be bigger than its normal force

We turned out to be correct, that the balloon will indeed stick onto the wall, due to said electrical force

Test two - Thin Rag

We stated that in this case, the same thing will occur as the animal fur case, with the only exception being that the charge on the balloon would be opposite to the charge that the animal fur gave

Again, we turned out to be correct that the balloon will again stick to the glass

Simple Definitions - Mass and Charge

From this lab, we are able to assess a definition (that a 5th grader could understand) for charge, using a similar idea for the definition of mass

Next, we were asked to use pieces of tape to conduct two experiments

Tape Test one

The first tape test required us peel two tapes of similar size from a table and bring the non-stick ends to each other. Although the picture shows the tapes attracting, we made an error and placed two different sides of tapes to each other. When we placed the two non-stick ends together, after being electrically charged due to the quickness that came by removing it from the tables, the tapes repelled each other. 

Additionally, we discovered that the farther away the tapes are from each other, the weaker the repel force was.

Tape Test two 

The second tape test required four tapes of similar size, and had us label the tape that would be on the bottom "B" while the top tape "T" as we stacked two tapes on each other. We then ripped them from the table and each other, and examined what the tapes did to each other. When we brought two tapes that were either labeled "B" or "T", they repelled each other, however, when a "B" tape and a "T" tape were placed next to each other, we observed an attracting force occurring

From this experiment, we can then concur that there are indeed two different types of charges when dealing with electrical forces, a repel charge and an attract charge. 

Electrical Force Law: Video Analysis Activity

Before we began with the second lab, we had to review a few of the things that we learned back in Physics 4A before we can successfully graph a Electrical Force vs Separation Distance graph.

Calculating for theta

First off, we were asked that given a ball  that hangs on a string of length L, along with  a vertical force that pushes the ball, to calculate for the angle of the ball. 

We derived the angle to be equal the the arcsin of the separation distance divided by its length

Calculating for the horizontal force (Electrical Force)

Using what we just calculated, we then needed to find the horizontal force that the ball experience when it is being pushed

We calculated that for to be the mass times the gravitational field strength constant of earth times the tangent of the arcsin of the distance of the ball divided by its length.of the rope

This calculation will prove useful on as we need to be able to calculate the electrical force that occurs within the lab.

First portion of the lab
 Measuring distance

We then began the lab by opening up Loggerpro and obtaining a video of what the picture to the left shows, two balls of equal mass, one hanging stationary and the other on a stick moving until both balls repel each other, forcing the second ball to move as well. Using the tools provided for us in Loggerpro, we are able to set an initial position for each ball, and give both the balls a point for each frame that the ball on the stick moves closer to the stationary ball. 

It was important to know that the mass of the ball was about 2.93 grams, while the length of the stick was about two meters.

Obtaining a Separation distance vs time graph

After some messing around with the data we got, removing the y-axis from the equation, since we mostly deal with the x-axis, and calculating the separation distance, which is the distance of the ball on the stick, minus by the hanging ball, we were able to get this clean graph of separation distance vs time graph

However, within the lab report, the question asked us to create an Electrical Force vs Separation Distance graph, meaning that we were still missing the electrical force that is required.

Electrical Force vs Separation Distance 

By recalling the equation that we found for a horizontal force in the exercise (F=mgtan[arcsin(X2/L)])

We were able to calculate for the electrical force, and by using the calculated column tool in Loggerpro, successfully plug it in to the graph to obtain an Electrical Force vs Separation Distance graph

Its to note that the graph tells us that the relation between these two functions are inversely proportional.

CONCLUSION:

Conclusion Work

From this experiment we were able to find the relationship between Electrical Force and Separation Distance, in that they are inversely proportional to each other. Additionally, by examining the B on the F=Ar^B, we find that B equals to about -1.998, which is surprisingly close to -2, the experimental value for B, which shows the the relationship is actually an inverse squared proportion.

The percent difference that was calculated within this equation is rounded to be 100%, with any experimental error caused due to imprecise clicking, when it came to tracking each of the balls when it came to analyzing the video. The picture above shows calculations of the charges when they are equal to each other and when q1=1/2 q2

It is to note that we cannot determine the charge of the balls in this experimentation. It is so due to the fact that the balls were repelling each other during the video. As repulsion between two objects occur whenever both objects are either positively or negatively charge, we can state that we cannot determine the nature of the charges of the ball.

The Mathematical Formulation of Coulomb's Law:
We then decided that it was time to get a clear derivation of Coulomb's Law, using what we have learned form 

An incomplete Coulomb's Law - along with
attracting and repelling forces

The picture to the left shows a semi-finished Coulombs Law equation along with the sign and the direction of a charged (either positive or negative) particle

It is to note that if the charges are either both positive or negative, that the direction of the force is then positive (to the right), however the direction of the force is negative (to the left), if the particles have different charges. This is due to the fact that one of the particles are negative, and since the Coulomb's Law shows a multiplication, it means that we are multiplying by a negative number. This means that whenever the Coulomb's Equation yields a negative number, we are dealing with an attractive force.

It is also to note that Force and charge are directly proportional to each other, and as the charges decrease, the Force must decrease as well.

It is to also note that since we have proved that force and distance are inversely squared proportional to each other, as the distance between the particles decrease, the force vastly increase.

We then prove that Coulomb's Law is in fact consistent with Newton's Third Law, showing that the Electric force between two objects have the same magnitude, just different directions.

Using Coulomb's Law for Calculations:

After getting a clear derivation of Coulomb's Law, the next thing we did a class activity, solving problems using what we have learned

Question 1

Answering question 1

We were given two particles, both with given values in charge and location (2x10^-9 with x=3cm and 3x10^-9 with x= 5cm respectively). We were then told that this system was occurring in a one-dimensional environment, the x-axis. We are asked to find the magnitude of force, along with the direction

The answer obtain was about 1.4x10^-4 N in the negative x-direction, meaning that it was moving to the right.

Question 2

Answering question 2 part 1

Question two is separated into two parts. The first portion of the question asked us to find its unit vector in the Cartesian graph, and express it in terms of cosθ and sinθ

Answering question 2 part 2

The second part of the equation then gave us values for the point charges (reusing the ones from question one, moving the second charge to a distance of x=5 cm and y=6 cm), and asking us to find the magnitude of force and the direction. Since this answer is in terms of x and y, we had two answers, one for the value in the x-axis, and one in the y-axis being added together for its magnitude

Demonstration of Electrostatic Discharge

In the last portion of the lab, we got to view a Van de Graaff generation and a Storm Ball to understand Electric Discharge

Van De Graph lifting hair

Van De Graaff spinning a helicopter rotor

We first focused on a Van De Graaff generator and how it works as depicted above

Inside a Van De Graaff

A Van De Graaff is a machine that transfers static eletricity from the ball like-figure to whatever touching it. Within class, we had some fun touching the Van De Graaff, then other people, as it would cause a mild static shock to the unwilling classmates. 

We saw that within a Van De Graaff contained a moving belt and some copper wire, along with a motor at the bottom. The Van De Graaff generated electricity by using the motor to create electricity. The belt then carried excess electrons from the bottom of the motor to the copper wire, which acted as a brush, and picked up the electrons, spreading them to the top of the Van De Graaff system. The belt then goes down to the bottom, picks up more electrons, and repeats the process.

Its to note that in the second video with the spinning rotor, each tip of the motor picks up a charge, and spins accordingly as a result

Next is understanding how a storm ball works

An active storm ball

A storm ball (or plasma ball as otherwise stated) is a spherical oject that emits electricity out throughout the system. If touched, the electricity will follow your finger.

A plasma ball works by having an inert gas, such as helium or neon (which this demonstration most likely has) within the system. Next electricity is pumped through the system, causing the inert gas to be excited, becoming from a gas to a plasma (the glass not only acting as a display, but as a way for the plasma to be contained) having its filaments being sent from the electrode to the inner glass.

The reason why the electricity can follow our hands is due to the fact that our hands are conductive as well, allowing us to react with electrode and plasma system. 

(9/18/14) Entropy and Cycles

In this lab we went more in depth into heat engines, bringing up the idea of entropy, the assortment of the system, and did experiments to get better acquainted with the idea of entropy.

Class Activity: Turning Green into White

Green water turned white

We started the lab by doing two different types of simple experiments. The first experiment involved burning paper, while the second experiment had a green substance (on the left) enter into the clear substance (on the right) and have it turn completely clear. The idea of entropy, or randomness came into place as we understood



Defining Entropy

Our responses to defining ΔS and examples of  changing ΔS

Here we are given a quantitative form of entropy, notated as  ΔS to be ΔS= ΔQ/T, where Q (in Joules) is the heat and T is the temperature (in K)
We were asked to break down the units of entropy as far as we could, which eventually becomes kgm^3/Ks, to get a better understanding of what entropy is in terms of what we learned from previous physics classes
We then were asked to find examples of a change of ΔS, which we noted as the following:
1) Opening a soda can (gas molecules leaves the soda, increasing ΔS)
2) Diffusing of gas
3) Spilling of water (composition of molecules get scattered, increasing ΔS)

The TS graph

A graph of isothermal and isoentropic process in a T vs S graph

We then focused on learning a new style of graphs in correlation to ΔS, the T vs S graph. This graph allows us to see a cycle in relationship to the P vs V graph style that we have learned previously. Furthermore, we have learned how to convert a PV graph to a TS graph if need be.
We also learned two new cycles from this graph, the Stirling Cycle and the Brayton Cycle

A picture of our example Stirling Engine

We learned more about how a Stirling Engine via experimentation. By taking a Stirling engine, along with hot water (hot reservoir, below the engine)  and ice cubes, we observed how the rudder spins, understanding that heat is moving within the system, allow energy to flow.

Stirling Engine Experimentation

Efficiency Calculation

Additionally, we discovered that a Stirling Engine has the same efficiency as a Carnot Engine, from which, we can then find the efficiency of the Stirling Engine in this case.







Understanding Heat Pumps and Refrigerators
A class example came, in which we had to calculate the COP (coefficient of performance) of both a refrigerator and heater

Finding watts and COP

 This example showed us how to calculate  the amount of wattage needed to use a heater and an air conditioning unit, knowing  its COP and the amount of wattage that was placed into the system

It is to note that in both cases of the heater and air conditioning unit, the amount of wattage let out is of an ideal amount, since they both released more wattage than what was originally placed in (2700W)

Finding Efficiency within an air conditioning unit:
An interesting question was raised up about how much efficiency does a standard air conditioning unit has. Prof. Mason stated that no company will ever release that kind of data, for fear of what to come. Therefore, as the future physicist and engineers that we are, we were asked to convert BTU (worthless units, lb/°F) to a unit that we know it as, Joules

Our conversion factor

Finding the conversion between BTU and Joules required a few steps. We needed to convert BTU to g/°C, which is the definition of a calorie. Once we converted the BTU to calories, we can then convert it to Joules, assuming that a calorie is the amount that it takes for one gram of water to change by one °C, in which we obtained the answer to be about 1200J

Finding Watts

It doesn't stop there, however, as we now have a definitive conversion between BTU and Joules, we should now be able to convert the amount of BTU that the companies use, to the amount of wattage it releases.

Furthermore, with a given amount of amps, we can also find the amount of power that the air conditioning unit requires to function


Class Discussion - Efficiency of Heat between two blocks.
The next class exercise that we had was to find the the heat and the efficiency of two blocks with similar structures, yet different temperatures (0°C and 100°C respectively), as they reach to equilibrium. It is to note that since this reaction is told to be in a reversible process, finding the average of the heats will not help much in the cause

Finding Heat and efficiency

As it was thought, since we are talking bout a reversible function, ΔS is required. Although the ΔS of the engine is zero, that doesn't mean that the total system is zero, as we had to calculate the two different blocks, which after some calculations turns out to be 46.1°C, which is close to 50°C, the temperature if we were to take the average.
Furthermore, we can find the efficiency of the system by finding the amount of work, since e=W/Qh, turning out to be about 30%

Class Discussion: Horsepower and Stairs:
Another interesting discussion occurs, asking to find the amount of floors per minute a person can climb, by using the notion of horsepower and the amount of meters per floor there are

Measuring the amount of meters per floor

Our calculation in finding the floors per minutes

It turns out that we require to know the potential energy in order to find the amount of energy used during our flight to climb these stairs. Once we found our energy, we needed to find time. Luckily we have the conversion between horse power and watts in order to easily find time, which turns out to be 0.1075 minutes. We then took the inverse of the time (since we are looking for it in terms of 1 floor per minute) in order to find the amount of floors climbed per minute, which turns out to be just over 9 floors per minute.

Class Discussion: Freezing a Popsicle
Our last discussion of the day turned out to be finding out how much time does it take to freeze a Popsicle, knowing the Qc, the amount of mass, and the change in temperature.

Calculations of finding the the time of a frozen popsicle 

Since its in a freezer, we need to know its COP. Once we found that, and understanding that it is 3/4 of a horsepower, we needed to find the amount of wattage it uses. to find the amount of work. Knowing these two units helps us find our Qc, and essentially our Qh as well.

Since this is in a refrigerator, our Qc will help find the time it will take to freeze the Popsicle, understanding our thermodynamics Q=mcΔT, and since we are freezing, that Q=mLf, we can plip the equation to look for time, which turns out to be almost 14 minutes.
It is to note that it will actually take a longer time than 14 minutes to freeze a popsicle in the real world due to the fact that the refrigerator is never on 100% of the time, which can slow down the process to a few hours