Dipole Moments and Flux

The net force that the electric field produces on these charges is zero. However, the direction of these forces creates a torque about the midpoint of the distance between these two objects. The moment of this dipole is the product of the distance between these two charges and their charge. 

The work performed on the dipole by the torque is the negative of the change in potential energy of the dipole. At 90 degrees, there is zero potential energy and the dipole is in a stable position.

This is our prediction of what a given code written in python will produce.

These field lines help to describe the features of an electric field. The higher the maginude of the the charges, or the closer the charges are, the more dense the shading will be. Also, the lines flow away from positive charges, and toward negative charges. The 3 dimensional shapes at the bottom depict flux. Electric fields flow out a surface containing a
positive charge, and produce a positive flux. Electric fields flow out of a surface of containing a negative charge and produce a negative flux.

Flux is zero when the area vector is directed perpendicularly to an electric filed. Here the only two sides witnessing flux are the sides shaded green. The net flux through a closed surface is zero.

Electric Fields

Electric fields are dependant on the magnitude of the charge producing the field, the distance of the charge from a test charge, and they can produce forces on other electrically charged objects.

An electric field vector can be calculated by multiplying the direction of the position vector by the limit of the magnitude of the electric field as test charge goes to zero.

The steps listed are an algorithm for a computer program to calculate an electric field.

Our assumption of what the given code will produce

The total electric field at point 1 is 8*10^10 N/C.

In order to calculate the total electric field at point 2, we had to find the x and y components of each of the fields produced by the two charges, and add them together. Here is the field caused charge 2.

Here is the field caused by charge one. As you can see, the vector E, total was calculated by adding each of the two components.

Integration of a charge uniformally distributed across a line to find the total electric field.

3D Computer Modeling

The first challenge in the lab, creating a 3D image of three spheres with arrows.

In the code behind the image are two lines in red. These lines ad a '#' symbol inserted before any of the red letters. This any character placed after the symbol on the same line will not play a role in the program.

By naming variables, referencing them later in the code allows you to re-use whatever information you have stored for that variable.

Placing the left most sphere twice as far from the y-axis lower the magnitude of the slope of each vector.

Here are the codes for vectors.py and vectors2.py

Electric Charges

Oppositely charged particles are attracted to each other, while particles of the same charge feel a repulsion between each other.

As a charged tape nears the skin of someones arm, the force of attraction strengthens. Some strips of tape repel each other, while others attract each other. This observation led to the conclusion of there being more than one type of charge.

Calculations for the forces of gravity in both the x and y directions of a pendulum.

The magnitude of the force attracting or repelling two charged particles is inversely proportional the distance between them.

Our data representing the repulsion between to metal balls of the same charge. The smaller graph, as we can see from the inverse relationship, is a representation of Electric force as a function of the distance of separation.

By newtons third law, the electric force on charged particle 1 due to charged particle 2, by newton's third law, is equal and opposite to the force on particle 2 due to particle 1. Knowing this, and Coulomb's Law (F = kQq/(r*r)), the forces present in an electrically charged system can be defined.

These are the answers to the conclusion section of the lab demonstrating the variations in the electric force due to separation distances. 

As a result of the charges that flow through the belts connecting the silver top with the bottom, the paper feels a repulsion

The ratio between an electric force and the force of gravity on an object results in an amazingly large unitless number. Therefore, the the force of gravity is considered negligible in problems concerning subatomic particles.

Entropy

These are the Temperature vs. Entropy Diagrams for adiabatic, isothermal, isobaric, and isochoric processes. The are under the curve of a T vs. S diagram is the energy of the process.

A miniature Stirling Engine that uses external temperature differences to operate.

The coefficient of performance (cop) is a ratio of what is desired, to the amount of energy or work required to achieve what is desired.

The effectiveness of an engine is a ratio of the actual efficiency to the theoretical efficiency of a carnot engine operating between the same two temperatures.

Using the total change in entropy, and understanding that the change in entropy of the system the "engine" is zero, we can find the final temperature of a mixture of hot and cold water in the same cup. Contrary to our assumption that mixing two equal masses of water, one at boiling and at freezing temperatures, will result in a final temperature of 50 degrees Celsius, we see that the final temperature will actually be 46 degrees Celsius. This is due to a loss of energy as the two water come to equilibrium.

For a carnot engine, the cop can be determined if given the two temperatures the engine will be operating in between. From here, the energy of the hot and cold resevoirs can also be determined.

This here is the calculation of the amount of time needed to freeze 4.20 kg of water at 18 degrees Celsius.

Professor Mason begins an experiment to demonstrate the combustible properties of various gases.

When the bubble is filled with helium, the bubble will float, and even combust if introduced to a large quantity of heat.

The entropy of a system cannot be calculated. However, a change in entropy in reference to a specific state can be measured and is defined as the energy entering or exiting the system over the temperature. These three methods can disrupt the entropy of our classroom.

Carnot and Otto Engines

It is possible to create a transfer of energy due to a difference in temperature. We saw this when a device used to transfer energy has one end place in cold water, and the other in warm water. The device has a disk that spins in whichever direction the heat flows.

Change in internal energy is equal to the addition of heat and work performed. Since heat equals the product between the number of moles, the molar heat capacity at constant pressure, and the change in temperature, and the work perform equals the product between the number of moles present, the ideal gas constant, and the change in temperature, these values can be substituted into the first law of thermodynamics, and a relationship between the ideal gas constant and the molar heat capacity at constant pressure is formed. 

Since the ideal gas constant equals the difference between the molar heat capacity at constant pressure and the molar heat capacity at constant volume, R can be substituted for. This forms a relationship between the product of the change in temperature and the number of moles present, and the  change of the product of pressure and volume over the difference in molar heat capacities and constant pressure and volume respectively.

For an adiabatic process, we determined that the sum of the change in pressure divided by the initial pressure, and the change in volume over the initial volume multiplied by gamma results to zero. Because gamma is always greater than one, the ratio of the change in pressure to initial pressure must be greater than the ratio of the change in volume to initial volume.

Through some algebra we arrive at this conclusions which states that for an adiabatic process, the product between the temperature and the volume raised to one less than gamma is constant.

This is the derivation for work in an adiabatic process.

When given the initial and final pressure and volume for an adiabatic process, finding the work done is easy.

From A to B, and C to D, the system undergoes an isothermal process From B to C, and from D to A, the system undergoes an adiabatic process. This is known as the carnot cycle.

This table list the changes in internal energy, as well as the work perform and heat associated with each process. We found that the efficiency of the above carnot cycle is 36%. This is the highest possible efficiency for an engine operating between 200 K and 300 K.

This machine demonstrates the process that an otto engine undergoes. It operates on a four stroke engine cycle. There is in intake stroke, a compression stroke, a power stroke, and an exhaust stroke. Air and fuel enters the cylinder on the intake stroke, and compressed in the compression stroke. The air fuel mixture is then ignited, violently forcing the piston down, then then piston pushes all the excess heat out of the cylinder, and the cycle repeats.

In a diatomic molecule, there are an extra 2 degrees of freedom. One is associated to the rotation perpendicular to the molecules axis, and the other perpendicular to each other.

Increasing the pressure as the piston compresses the gas, providing larger cylinders, and increasing the rate at which the cams operating the piston rotates can all increase the power output of an engine.