Magnetism Continued

The day began with a little exercise regarding the direction of the force with regards to a current carrying wire going in the up direction. We then talked about the magnetic force in relationship with current and magnetic field. We also drew a graph of what the magnetic field with respect to time would look like.

We then examined how the magnetic field would look like using Logger Pro and we got a resulting graph shown below.

Mason then did an experiment of how a magnetic field could lift up a uniform ring depending on the density of the ring.

We then tired to draw an example of how the field was supposed to look like and how the current as well as the magnetic field were directed. We also drew some more relationships between current and the magnetic field.

Lastly, we were supposed to predict how the emf and magnetic field were supposed to look like given the graph of the magnetic field.

Overall, the main focus of the day was to draw some more conclusions toward the magnetic field of a current and then draw some predictions on how if plays in different scenarios.

Magnetic Fields and Torque

At the start of class we recapped on what the magnetic field of a magnet looked like and Mason also asked us to find different ways to demagnetize a magnet. Professor Mason also added that the reason why the magnet has that type of magnetic field is because of the structure within the magnet. Using that knowledge we chose to change the shape of the magnet because the structure would change and therefore the magnetic field would not exist anymore. Temperature could also alter the magnet's magnetic filed because a change in temperature also changes the structure of the magnet but slowly.

After talking about how a magnet worked, we reviewed a little of the previous magnetic field concept acting on a closed circuit. We examined how the force would work and what it related to. We used our previous definition of torque and using the force we were able to get the torque of a magnetic field which was equal to half the length squared of the current times the magnetic field times the sine of the angle between them. Using that knowledge we were able to solve our problem using the concept we just learned.

Next we were asked to created our own motor using magnets and allowing the motor to run for a long period of time. The picture of the apparatus is shown below.

We tried different scenarios by switching the positive and negative side when powering the magnetic motor. We found that it spins counterclockwise when the positive is on the north side and clockwise when the negative is on the same side.

Lastly, we applied magnetic torque to a sphere and solved a problem and we also tied the idea of current but using a different definition to magnetism and after that Mason showed us an experiment on how compasses behaved when a magnetic field was present.

Overall, we learned more about magnetic fields and the concepts behind torque and we went more in depth regarding magnetism.

Magnetism and Magnetic Fields

The class began with Professor Mason holding a bar and a compass. Then he showed us that when the compass came into close contact with the compass it no longer pointed just north. He then asked us to get a magnet and put it on the board and put the compass around the magnet. Then he asked to draw the direction that the compass arrow pointed. The picture of what we got is shown below.

After finding out that the arrows in fact made a magnetic field which was made by the magnet we were to draw the lines of the magnetic field. The picture of what it looked like is shown below.

We then moved on to the topic regarding magnetic flux. Professor Mason gave us the relationship between magnetic field and area as well as the angle between those two vectors. We were also able to draw the direction of each of the components for Force, Magnetic field and voltage using the right hand rule.

Professor Mason also showed us how the directions of the fields we drew were applied to an actual wire.

Here is a video of how it was supposed to look like.

We later moved on to applying previous definitions in order to find the relationship between force, current, mass, velocity, frequency and current. 

Lastly, we talked about the effect of a magnetic field on a circuit and found that the force was perpendicular to the current and we also observed how a spin on the magnetic filed would affect the current which is shown in the picture below.

Overall, we were introduced to magnetism and how a magnetic field would affect force and voltage and we also linked the concept of magnetism to previous concepts we had previously learned.

The Oscilloscope and Function Generator

The day began with Professor Mason telling us that the day was going to be spent using an oscilloscope and we were going to use it to determine relationships between graphs and sound as well as learning how to use the oscilloscope and function generator. The picture below shows that of the oscilloscope our group used during the day.

Mason also showed us some relationships between the electrons present within the beam of light and how it shifted if a magnet was used. We also reviewed some electrical key concepts and applied them to the oscilloscope.

First we were asked to use the function generator (the machine above the oscilloscope) and change the different function, amplitude and frequency settings while connected to a speaker and hear what different sounds it made.

The question regarding the different sounds they made were answered in the space below. We found that at 96 Hz, the speakers emitted sound like radio static and that a triangle function gives the lowest amount of sound while a square function gives the loudest sound and a sine function gave sound in between those two ranges. We also found that as the frequency increases, the sound gets sharper.

To finish the sound portion, we also found that as amplitude increases, the sounds gets louder. 

We then moved on to some of the oscilloscope controls and played with some of the controls. We found that by changing the intensity, the brightness of the line changed as well. The focus control allowed us to see the line clearly and not too thick nor too thin. Lastly, the time controls changed how fast the light inside was moving depending on the different outputs of the function generator.

Next, we attached a battery to the oscilloscope in order to measure the steady voltage of the battery. We found that as the current flowed, the light moved from one side to the other in a straight line indicating that the voltage was constant. We also saw what adding a tap key to the battery would do and we saw that it changed the scale on the screen every time it was moved from on to off.

Below are just examples of the different outputs made by the function generator.

We also used the power output in order to see whether our voltage reading was correct which it was very close to.

Lastly, we had to use our knowledge of operating the oscilloscope and predict what type of current was being emitted from the mystery box. Our results are shown below.

The main focus of the day was to let us teach ourselves how to operate an oscilloscope and use a function generator and see how different scenarios affected the functionality of the machines.

Capacitors and Capcitance

The day began with a recap on capacitors and capacitance. We began by doing some work on the lab manual predicting how capacitors would behave and constructing a graph representing how the brightness of a bulb would change over time if a charged capacitor was input into a closed circuit as a power source. We predicted that the brightness would decrease at an exponential rate until the capacitor ran out of power. We also found that the voltage would remain the same throughout the close circuit and as a result the charge would also remain the same, which goes back to the basics of current and voltage learned at the beginning. We also recapped on the behavior of capacitors in series and in parallel. We said that when capacitors were in series, the voltage increases because as the capacitance decreases, the charge remains the same and the voltage gets larger and it would work the opposite for capacitors in parallel. Finally, we measured some of the voltage of batteries in order to see whether our predictions made sense since capacitors also work as batteries.

Below is a picture of the set up we had in order to test for the voltage of the closed circuit.

In order to further understand the behavior of capacitors, Mason decided to let us use Logger Pro and graph the behavior of the capacitors as time increases when a capacitor was charging and when it was losing power. The graph below shows the graph of when the capacitor was decreasing in electric potential, or discharging. 

Below is a data table of the points that were used to make the graph above.

Below is a picture of how the set up was made when we were measuring for the electric potential of the capacitor when charging or when discharging.

The graph of the capacitor charging is shown below. As time increases, the electric potential grows exponentially meaning that potential energy is being stored within the capacitor until it reaches the maximum charge it can hold.

The data table of the data points for the graph above are shown below.

After looking at the behavior of the graphs, we can finally use Logger Pro and construct the best fit for the graphs and thus it led to the theory of exponential decay which showed how the voltage decreases over a period of time. All the derivations are shown below.

Then we decided to work with the theory of exponential decay and solve a problem which asked to find many unknown variables within that equation. We also graphed the relationship between voltage, brightness and current with respect to time with respect to the exponential decay.

Overall, we learned more about capacitors but the main focus of the class was showing how capacitors gained or lost charge and relating it to exponential decay and charge buildup

Kirchhoff's Rules and Capacitors

The day began with a quiz about Kirchhoff's rules and we solved the problem as a class. We began by finding the the current between the two loops in the parallel circuit. We then found that the negative current of the bottom lop plus the current of the top loop is equal to the total current around the whole circuit. Using those equations we were able to solve for the voltage through the top and bottom lop as well as the power of the top and bottom loop. The results are shown below.

We then moved on the topic of capacitors. Capacitors are devices that store electrical charge and electrical potential energy. Mason gave us a relationship between voltage, charge and capacitance which was Q=CV. We were also derive that further by using the definition for charge and voltage into the equation C=kEA/d. We also did our own experiment were we created our own capacitor using two sheets of tin foil in between pages of the lab manual. We recorded the capacitance in nF and drew a graph that compared the relationship between distance and capacitance and drew our conclusions that as distance increases, capacitance decreases.

Next we solved our problem using our new definition for capacitance in order to find the area of a given object. Then we began to learn about relationships between capacitance and circuits and how they behave in parallel and in series.

The capacitors behaved oppositely to the way resistors behaved. When capacitors are in series, the inverse of the total capacitance is equal to the total sum of the inverse of all the capacitors and when capacitors are in parallel, the total capacitance is equal to the sum of all the capacitors. Then, we solved a problem very similar to a resistor one we had.

Finally, we applied Kirchhoff's Rule to a closed circuit with capacitors. Using previous methods, we solved for the voltage across the whole circuit as well as the total energy.

Overall, we learned about capacitors and how to use them within a closed circuit and then we applied Kirchhoff's Rules to a closed circuit involving capacitors instead of resistors.

DC Circuits, Resistors and Kirchhoff's Rules

The day began by talking more about closed circuits and Mason gave the class two set-ups of two circuits each with an on and off switch and these paths were a little more complex than the usual ones he gave us. We were supposed to predict which one of the light bulbs was going to be dimmer and which one was going to be brighter. For the first one we predicted that the light bulb in the top was going to be dimmer because it had a longer path to flow through while the upper light bulb was going to be brighter since it had a smaller path. We also had to predict what would happen to the middle light bulb if the switch was off. We said that the flow of energy was not going in a complete circuit if the switch was off and therefore the light bulb was not going to turn on. For the second set up we had a more complex set-up and we were again supposed to predict which one of the light bulbs was going to be dimmer and which one was going to be brighter if the switch was flipped from off to on. We agreed that the upper light bulb had to be brighter because another flow of electricity was going through that bulb and the lower bulb would have the same amount of light because the path would remain the same.

Using our previous knowledge we then made a chart on how the light bulbs were going to act if they were set up in parallel or series and we agreed that putting light bulbs in series result in the light bulbs being dim, where setting them up in parallel results in the opposite whereas setting the batteries in parallel results in dimmer batteries where setting the batteries up in parallel does the opposite. We also moved on to the topic of resistors and we talked about how to calculate the resistance by looking at the color scheme of each of the capacitors. Our results are shown in the table below.

We then used a multimeter in order to get the exact resistance of each of the resistors using a DC circuit. The multimeter is shown below.

The results from each of our finding is in the upper right hand corner of the picture and it shows that resistors in parallel decreases in value whereas resistors in series increase in value. The relationship as a result is total resistance in a series is the sum of all the resistors while the inverse of total resistance is the sum of all the inverses of the resistors.

The relationship explained previously is put into effect into the problem below. It shows a variety of resistors and we were supposed to solve the total resistance found in the whole system. By using these rules, we came to a value of 100 Ohms.

The day ended by talking about Kirchhoff's Rules which talked about how to find the current, voltage and work of the system. The whole process of how to use these rules involved tracing one flow of current through one loop and tracing another flow of current through another loop. Then using the other rules from before knowing that the current is the same in a series and that the sum of the current in each of the loops is the same as the total current in the whole system one can combine all the equations to solve for multiple unknowns.

Overall, we learned about current through a DC circuit as well as resistors and how resistors in a series and parallel add up. Finally, and probably the most important part of the class, involved Kirchhoff's Rules and how they are used to solve for multiple things in a closed circuit.

Potential and Continuous Charge Distribution

After talking about charges and electric fields on point particles, we moved on to continuous charge distributions. We began with a uniform ring and a point particle a distance x away. The radius of the ring was a and the ring had a charge of q. Since the distance x from the particle and the radius of the ring make a right triangle, the hypotenuse of the triangle would be the distance between the point particle and the charged ring. In order to find the potential, the charge needs to be known and by plugging it in we can get a result. We also moved the point particle up and added an angle between and solved for the charge as well.

Then we used the previous relationships for solving the potential in order to get to the same result. Using the equation of the integral of the energy field multiplied by the change in distance we came to the same equation of some constant K times the charge over the distance is equal to the potential as well.

Next we moved on to a uniform bar and a point particle an x and y distance away from it. The distance change of course sine the bar is uniform and the distance, unlike a circle, does not remain constant. In this case, we had to replace the change in q with some constant lambda dimes the change in the x direction (y is not needed since that distance does not remain the same). We solved for the x value using Wolfram Alpha and found the potential using the known values. We also went ahead and drew some electric field directions between two equipotential particles.

The day ended after we used a volt meter in order to map out the voltage in respect to the electric fields made by the two "point particles." The set-up is shown below. We were supposed to map the distance and voltage into a table.

The result table is shown below. It is shown that as the distance increases so does the voltage.

The main focus of the class period was to know how charge affects continuous objects and finding problem solving techniques so that we can solve said problems. We also had a visual understanding of electric fields as well as finding electric potential values between each of the charges.