VPython Assignment

The assignment consisted on creating the potential on a circle centered around three charges.

I used a for loop to complete the assignment. The for loop i used starts from 0 to 44, which makes the loop run 45 times, so 45 spheres will be printed out. The 44 number was a random number I used after my tries, because it creates a perfect circle with the same space between each sphere. The rate() instruction displays each sphere at a certain frequency. This instruction is required because the assignment ask for an animation of the program, or else, it  would just display all the spheres at the same time. I used rate(3), so each sphere is supposed to appear after 1/3 seconds. The rest of the code, was based on what we did in class. However, for the location of each sphere, I used the cos and sin functions for x and y respectively in order to simulate a circle. This was also used on the label of each potential because without it, the label will block some some previous spheres.

This is the final output.

This is the animation.

Lab 14: Potential of Continuous Charge Distribution

First thing we did was to calculate the electric potential from a continuos charge distribution at a distance x from a point P. We used V = kq/r, The electric potential at the top is V = kq/x, since P is at x distance apart from the ring. For the middle is V = kq/sqrt(x^2+2a^2), we used the pythagorean theorem to find r, and finally for the bottom is V = kq/sqrt(x^2+4a^2).

After some derivations, we did an example of electric potential due to a finite length line-charge. First, we compute the results in excel using the formula V = k.lambda/sqrt(x^2+y^2). The obtained result was V = 2.47x10^6, by dividing the rod into 20 pieces.

Then, we did by hand the same procedure, dividing the rod into 20 pieces. Through some algebra, we got the equation above. Then we just used the given values and our electric potential was the same as first calculated in excel.

Professor Mason showed us 2D and 3D visual representation of equipotentials and electric field lines. In the 3D applet, we saw how the electric field lines from one sphere gets and repelled away and moves into the other sphere.

For the electric potential lab, we used a multimeter to calculate the potential difference on the conductive paper from one metallic mark to x distance from it by setting the power supply at 15V. First we calculated each potential at different separations going to the left, then we calculated the potentials to the right.

This is a table of values gathered during the experiment.

Lab 13: Electric Potential Energy

We started the day by setting up different electric circuits. The task consisted on making the bulbs dimmest or brightest as possible. For the dimmest case, we found that the batteries must be in parallel and the bulbs must be in series because the voltage of the batteries stays the same, and must be distributed through each bulb.

For the brightest case, the batteries need to be in series, and the wire connected to both bulb holder in a parallel arrangement.

Representation of both cases

We then conducted an experiment, where professor Mason heated up water through current across the heater at constant volts. 

This graph shows how the temperature of the water increases over time at constant voltage.

The experiment was repeated by doubling the voltage.

Using the equation V = IR, we said that if the voltage is doubled, then the current will also double. Then that means the power increases by a factor of 4, using the relation, P = IV, assuming that the resistor is negligible, then we have, 2P = 2I.2V.

We did an exercise that consisted in calculating the work it takes for a vehicle from point A to reach to point C. Regardless of the path it takes, the amount of work is the same. By using the formula
W = Fdcos(theta), we can say that the horizontal paths requires zero work since the angle is 90 degrees. And the vertical path is just force x distance. So the amount of work calculated was -2J. We then applied the same reasoning to the work done in an electric field. We noticed that the parallel path with respect to the electric field is greatest while the perpendicular path is zero.

This picture shows the derivation of Voltage as a function of electric field and distance.

Then we integrated the previous formula with infinite distance, we can say that the voltage is just the dot product between coulomb constant and the charge of electron over some distance r.

Then we did an exercise applying the formula V = kq/r  for some charges placed at random locations.

Finally with the previous exercise, we simulated the same problem, but using Vpython, we drew 3 charges and 3 spheres, and calculated the potential difference between them at each location.

Lab 12: Current, Voltage and Ohm's Law

We started the day by lightning up a bulb through a wire touching either the positive or negative end of a battery and at the same time touching the base of the light bulb. The bulb lights because the wire transfers the electrical current from the battery onto the filament of the bulb, which gets so hot that it glows and give off light.

 In this picture we drew conditions when a bulb will light and when it won't. 

 We used two batteries, and the result of it was that the bulb's light got brighter because there is more energy provided from the power supply which is then used by the bulb.

 Professor Mason introduced the electroscope. He first rubs a rod with animal fur, and then places it on the top of the electroscope. The charged rod transfers the charge into the electroscope which gives the plates the same charge, causing them to repel each other.

 We then work with an ammeter to measure the current flow from the battery to the bulb and then to the ammeter. Later, we measure the current flow through the battery onto the ammeter and then into the bulb. We noticed that the current is the same in both cases, meaning the current in a circuit is always constant, because only energy is used up through the process.

 This is a example problem in finding the drift velocity of electrons through a 12-gauge copper wire.

 Professor Mason introduced use voltage, current and power, and their respectively units.

We then conducted an experiment using a nichrome wire, is a wire used in toasters. This experiment demonstrates Ohm's law by looking at the relationship between the applied voltage across a resistor and the current through the resistor.

 By looking at both graphs we can say that they are relatively proportional due to their linear relationship between each other.

 Finally, we looked into factors that affect the resistance of wires. First, it depends on the resistivity of the material, which is proportional to the resistance, it is proportional to the length, however is it inversely proportional the area.

Lab 11: Gauss' Law

We started the day drawing the electric fields of two positive charges with a negative charge. The electric field of a positive charge points outwards while the electric field of a negative charge points inwards. From the enclosed amount of lines entering and exiting the charges we determined that the net flux is proportional to the net charge.

Professor Mason conducted an experiment using the Vandergraff generator and a gated cylinder. Where a negative charge was sent to the cylinder, we assume that the outer foils will move away since all the charges inside the gated cylinder is zero while the charges outside are negative, so that will repel the outer foils.

Professor Mason asked where should one go when is thundering while the individual is inside the car. We said that the person should just remain in the car, because the metal in the car acts as a shield from any external electric field, which prevents the lightning from traveling within the car, and conducts it down to the ground.

We discuss that if we double the radius of a sphere that will affect its circumference by the same amount, also it will affect the area by a factor of 2, and the volume by a factor of 4. In addition, if we halved the radius, the circumference, area, and volume should have the same corresponding proportionality.

Professor Mason started putting things inside the microwave. The first experiment was a steel wool, after being heated up, it made a giant ball of sparks.

When microwaving a fork, it produces sparks on the tips.

Microwaving a CD, causes the aluminum coating on the CD to act as an antenna for radiation, which produces a firework-like display of sparks.

Microwaving a light bulb causes it to light up instead of producing sparks. Also it changes color because the gases inside the bulb reacted to the microwaves, producing a spectrum of colors.

The following picture shows the procedure made to calculate the electric field of a cylinder

Finally we found the gravity of Earth through some substitutions.