Electric Fields: flux, torque

Lab Day 10: 3/26/15 Electric Fields, torque, and Flux

Purpose:The purpose of today's experiments were to analyze the idea of torque and flux when applied to electric fields. 

Electric Dipole, Torque

The electric dipole moment is the product of the magnitude of the charges and the separation between two charges and is directed from the negative charge to the positive charge. The net force on the dipole is zero. We can apply torque on this concept in our electric field. , the torque is defined as the R vector cross the F vector and  there with torque on both charges there is a clockwise rotation. To find the torque in terms of q,E,theta, and A, the force is Eq, while the dipole vector would be 2Aq. By substituting these terms, we come up with the torque as the dipole vector cross the electric field vector.

Work, Potential Energy(enclosed)

The work is shown in relationship to torque where we derived the equation of work in terms of a rotation. Using the expression found for torque, we were able to find the work done in rotating the dipole due to the work energy theorem.

We went further to find the potential energy enclosed which is just the dot product of the electric dipole moment with the electric field. 

3-D modeling of Electric Field vectors and Arrow positions

In this activity, we used the Vpython modeling program to look at the electric field vectors in 3-D where we learned to program the electric field vectors to point in specific axis. The whiteboard above shows the predicted model where the arrows all point toward the positive x-axis. However in reality, the arrows all point toward different positions due to the two point charges as seen in the screenshot view of the model.

The electric field lines are useful in showing a continuous way to show the density of the electric field caused by point charges.In our drawing we have a positive particle and a negative particle and the field lines are drawn going toward the negative particle where we can observe how the more closely packed lines (more dense) represents areas with higher electric field strength.

Flux Model

The nail bed is an example of a flux model. The nails are normal to the wooden surface and we can see that each nail can be observed as electric field vectors. When Prof. mason used a wire, he captures as much vectors as the rectangular wire allows it. It is seen that the maximum flux is obtained when the angle between the area vector and electric field vector is zero. When the wire is tilted, there is less electric field vectors and as it gradually goes to 90 degrees, since there is less electric field vectors, there would be less flux as well. Therefore, we can use the idealized model of 

flux to calculate the flux in relationship to the electric field.

We can identify flux as the number of electric field lines passing through a given surface. The flux going in where the electric field vector and the change in area is parallel allows us to find that flux is equal to the electric field vector dot the area. The model below of a cube shows that flux is present (green surface) when the normal vector is parallel to the electric field vectors, while the flux is zero (red surfaces) when the normal vector is perpendicular to the electric field vector. 

Electric Field!

Lab Day 9: 3/24/15 Electric Fields

Purpose: The purpose of today's experiment was designed to focus on the electric field. The electric field can be derived from coulumbs law. We were able to utilize vpython to analyze the forces and arrows in an electric field looking at a point particle in three dimensions.

Experiment:

We began class by relating the gravitational force with electric field and calculated electric field below using electrical force and electric field equations.

Next, we used trigonometry to define our constants and determine our unit vector quantities of electric field. The electric field can be defined using a given point charge at a particular distance away.

Here are calculations of the net electric field which is just the sum of all the electric field vectors that we derived above. We were able to determine this by identifying the direction of the force and finding the distance between each particle that is causing it to attract/repel.

When a point particle is not designed in a straight line the electric field can be derived using the x and y components as shown in the calculations below. In fact when we take the limit of the electric field, we find that it is zero.

3-D Modeling of Electric Fields

Next, our group made predictions of the program of the electric field that was designed and it consisted of a point particle with three axis cylindrical in shape. 

Predictions of Vpython model program

By using Vpython modeling program, we produced the predicted electric field. Initially the arrows were pointing in the same direction toward the positive x-axis. We converted it, by auto scaling for each of the six vectors inserting as seen in the screenshots below to produce the correct position for the arrow vector.

Superposition Electric Field Vectors

Excel calculations a rod divided by 10 parts.
Find the electric field on the rod.

In this activity, we looked at the electric field calculations along the axis of a rod. We further analyzed a rod with 10 increments which allows us to determine the electric field in x and y components which can be calculated in excel for each of the 10 parts. Using superposition, we can derive vectors in order to find the net electric field in different components. The calculations from the white board allowed us to create multiple variables to find the net electric field in excel. The electric field was found and by using the proportionality of the components we found the x and y electric field vectors.

Excel Calculations of Electric Field Components

Calculations of Electric field

Electric Field due to a differential Charge Symbolic Calculations

In this part, we took the integral of the electric field using the line charge density where dq=(lamda)dx to find the equation that relates to the magnitude of the electric field. 

Introduction to Vpython Program

Homework Assignment: 3-D Modeling in Python

Purpose: 
The purpose of this activity is to learn how to use the 3-D modeling program called Vpython by being able to use the sequencing editor to develop spheres and arrows using vector quantities. This program is used as a tutorial to help master the basic functions of sequencing and create a visual model.

Experiment:
In order to start the program, I started off by typing in the code [from visual import *] and saved the initial file, The initial file was named Vectors1.py which modeled three different spheres with arrows pointing in different directions that were identified from the instructional video.

Challenge Task 1: Vectors1.py
The results gave a 3-D projection with three different colored spheres. The arrows were pointed in random positions that were manipulated through the vector quantity in 3 dimensions (x,y,z).

Next I used the option using # adding comments that was seen to not affect the code listed.

Challenge Task 2: Vectors2.py
In the next task, by assigning names to the spheres, it made it easier to develop the arrows used to connect the spheres in a counterclockwise direction.

Then, one of the spheres was moved twice as far from the y-axis and the three arrows remained connected, By changing the y-axis value and labeling the vector positions, the arrows adjusted to the connected positions.

By adding a new line using the print command, the printed value of the vector position was displayed in the python shell screen.  This allows the value of any sphere (variable) to be identified. 

Conclusion:

In this program, I was able to manipulate the tools using the editor, shell, and visual representations available to create the structures dependent on a vector quantity. By using the Vpython program, the 3-D shapes of spheres connected by arrows were displayed which is important in identifying electrical fields and charges. It visualized the simple basic shapes that would be used a lot in electric fields and forces where the motion of the spheres can be animated.

Electrical Charge and Force

Lab Day 8: Electrical Charges and Forces

In this experiment, we used two sticky tapes and held them next to each other with the non sticky sides together and the two tapes started to repel away from each other.

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We further labeled the bottom side B and the top T. When the top strips were brought together, they were attracting while the bottom strip started to repel. The interaction between the top and bottom strip attracted slightly.

This clip showed the attraction of the top and the repelling of the bottom

Below is the summary of the two sticky tapes and how they attracted and repelled each other dependent on the interaction of charges. 

Since we have observed that there are forces between charged objects seen in the scotch tape interactions, we further analyzed the idea of a charged ball that is hanging where the first ball is slowly going near the hanging ball making it repel. 

The force can be calculated using the length L and the angle that is formed as forces are acting on the ball. Below showed the symbolic representations of the forces acting on the hanging ball where the force of separation was found. 

We used the proposed idea based on our symbolic calculations above to analyze the video to create a Force vs, Separation distance graph. The movie showed a ball that was charged hanging on a string where another ball (also charged) was going toward the hanging ball causing it to repel.

Graph of Force Vs. Separation Distance

Graphical Analysis:

The graph showed that the relationship between force and separation distance was inversely proportional.The best fit was F=A/X^2 where the graph shows that the force is proportional to 1/R^2. Primarily we can observe that the charges or signs can be negative on both of the balls or positive since it was seen to repel. 

The calculated values are shown below where we can see that using Coulumb's law, the percent difference is found to be 11%. There are sources of error found which can be caused by the inaccurate plotting of the points of the ball at each point manually by "eyeballing".

Calculations/conclusions of Electrical Force Law Analysis 

In this setup we have electrical Charges
 from the ball from electricity

We can tell by our calculations that electrical force is definitely greater than gravity which is consistent with our experiment. When we put two plates on top, they went up and away from the ball which was run by electrical forces.

Conclusion:
In conclusion of today's experiments, there are charges caused by electrical forces that cause an object to either attract or repel.  The electrical force is derived from the charge on one particle acting on another particle. When we analyze the ideal of electrical force, we can use Coulumb's law which allows us to measure the electrical force which is found to be greater than gravity.

Entropy and Cycles

Lab Day 7: Entropy and Cycles

Purpose:

In today's class, the purpose was to analyze entropy and different types of engine cycles including reversible and irreversible processes. The different type of cycles in comparison to the carnot cycle include the otto cycle, diesel cycle, stirling cycle, and the brayton cycle. These cycles have different types of conditions which often makes them more or less efficient.

Experiment:

Entropy was measured to be the ratio of Heat energy absorbed over the thermal energy and the process is determined using the states of equilibrium. This is also considered as the amount of disorder where we can see that it is useful in explaining how heat input does not always cause a change in temperature. 

Diesel Engine: there is a 4-step cycle

1.Adiabatic compression
2. Constant pressure
3. Adiabatic expansion
4. Constant Volume

In the first step there is the compression stroke, where there is the adiabatic compression of gas and diesel fuel in the cylinder. The second is the ignition of gas fuel mixture where large compression causes burning to happen when pressure is constant. The third is the expansion stroke where it is adiabatic (no heat transfer). There is an isentropic expansion of gases and there is positive work. The last part is the exhaust in which it returns to the same volume and is the same at the initial and ending of the exhaust and intake stroke.

Otto Cycle: 

 Next there is the 4 stroke cycle engine which is called the Otto Cycle where it was able to carry out four piston strokes in one combustion cycle.The Otto engine is the closest to a real engine of an automobile.

1. The intake stroke consist of the piston moving down where the intake valve opens due to low pressure of air/fuel mixture. 

2. The compression stroke is when Bottom Dead Center is at maximum volume and the piston moves up, the pressure increases and volume decreases. At the end, ignition starts rapidly causing the piston to go downward. 

3. The power stroke is the force that cause the piston to go downward when the valves are closed. There is no energy where internal energy decreases along with temperature. 

4. Exhaust Stroke- at BDC exhuast valve is open which cause the piston to move up and pressure outside cylinder decreases. Gas leaves the cylinder and volume decreases.

Stirling Cycle: 

The Stirling cycle is an example of a Carnot Engine where we have work done due to differences in temperature. 

1. Isothermal compression of working gas

2. Constant Volume where heat is absorbed from energy storing device

3. Isothermal expansion of gases and there is positive work done.

4. Heat transfer from working gas to energy storage at constant pressure. heat stored is same as second step of cycle. 

This is an example of a Stirling engine where ice is put on top and the bottom is a beaker of water that is heated. The blades in fact moved counterclockwise due to the Stirling engine. We did the same experiment but had the temperatures reversed and it was seen to move the other direction. 

As a result, we calculated the efficiency of the cycle using Carnot's efficiency. The efficiency was calculated to be 23%  for our example of a Stirling engine. 

In this reversible engine, we identified that the change in entropy is zero S=0 in which we can calculate the final temperature by setting the system to zero. The final temperature is 46 degrees which is low and reasonable because it shows that some of the heat has become work. The work done in this reversible process is therefore the heat from the hot minus the heat from the cold. If we compare its efficiency to a carnot engine, it is less because thermal efficiency is much less due to the fact that a carnot cycle produces the highest possible efficiency in which temperatures do not change because their reservoirs are infinite. 

The density of bubble is higher and inside the bubble is hot air. As professor mason blows into the tube, the bubble comes up and pops. The second experiment showed how the flame went up when the bubble ignited. Since the bubble is less dense, it floated up and once ignited, it led to a rapid combustion as seen in the demonstration where flame went up. 

Conclusion:

Based on calculations and experiments on the new engines discussed, the different cycles all represent different types of conditions in which the efficiency is different. The entropy of a system is measured as the amount of disorder in a system. In fact as we briefly discussed the cycles in class, the Wankel and Brayton cycles both fell short because in brayton cycle it was suppose to have constant pressure but due to heat combustion it did not. On the other hand, The Wankel engine had flaws because it was suppose to be even more efficient than the otto cycle. We can conclude that the best heat engines can be determined on the basis of comparson to an ideal Carnot engine.