Ch21_HallowellC

toc = = = = = = = = = =

=Magnetism=

Pre-lab Questions: Magnet Lab
1.The objective is stated in the title. What is your hypothesis? (Attempt to answer the question, to the best of your knowledge.)

The farther the distance from the source of the magnetic field will cause the strength of the magnetic field to be less.

2. What is the rationale for your hypothesis? (Provide detailed reasoning here. This may take the form of a list of what you already know about the topics, with a summary at the end.)

I know from real-life applications that the farther you get away from a magnet, the less you will feel the attraction or repel. In addition, I also know from the equation, that the strength of the magnetic field and the distance from the source have an inverse cube relationship. This means that when the distance increases, the magnetic field decreases.

3. How do you think you might test this hypothesis? (What might you measure and how?)

I will test this hypothesis by moving a magnet farther and farther away from a sensor that will give me the results of the magnetic field. I will also record these specific distances as well.

4. Read the entire procedure through. 5. Design __data table(s)__ in order to record your observations __and__ calculations. Do this in Excel a post this draft on your wiki.

Lab: What is the relationship between magnetic field strength and distance from the source?
By: Chris Hallowell 11/30/11

The goal of this experiment is to determine the relationship between magnetic field strength and the distance between the source and the sensor. I believe that as I move the source further away from the sensor, the strength of the magnetic field will decrease. I know from real-life applications that the farther you get away from a magnet, the less you will feel the attraction or repel. In addition, I also know from the equation, that the strength of the magnetic field and the distance from the source have an inverse cube relationship. This means that when the distance increases, the magnetic field decreases.
 * PURPOSE/HYPOTHESIS**:

The materials used in this lab were as follows: Magnetic Field Sensor, Data Studio and Science Workshop Interface, index card, Meterstick, neodymium magnet.
 * MATERIALS**:


 * PROCEDURE**:

1. Tape the measuring tape or meter stick to the table, and tape the Magnetic Field Sensor to a convenient location. The sensor should be perpendicular to the stick, with the white spot inside the rod facing along the meter stick in the direction of increasing distance. Carefully measure the location of the sensor on the meter stick. This will be your origin for all distance measurements.

2. As a convenient way to measure to the center of the magnet, and to ease handling of the small magnets, allow the two magnets to attract one another through an index card, about 0.5-cm from either edge near the corner. The magnets should stay in place on the card. The card itself will serve to mark the center of the magnet pair.

3. Connect the Magnetic Field Sensor to Channel A of the interface. Set the switch on the sensor to //1x//.

4. Open Data Studio and choose “Create Activity”. Click on “Setup” and add a Magnetic Force Sensor to the icon of the interface. For a display, click on “314 Digits”, which will show the magnetic field strength in Gauss.

5. Zero the sensor when the magnets are far away from the sensor in order to remove the effect of the Earth’s magnetic field and any local magnetism. The sensor will be zeroed only for this location, so instead of moving the sensor in later steps, you will move the magnets.

a. Move the magnets far away from the sensor. b. When the reading in the meter window is stable, click “Tare” on the sensor.

6. Now you are ready to collect magnetic field data as a function of distance.

a. Click “Start”to begin data collection. b. Place the card with the magnets against the meter stick, 2.0 cm from the Magnetic Field Sensor, so the card is perpendicular to the meter stick. Measure from the card to the center of the Magnetic Field Sensor. c. The current magnetic field measurement is shown in the meter window. If necessary, reverse the magnets so the reading is positive, and reposition the card 2.0 cm from the sensor. d. Carefully measure the distance of the card to the sensor. e. Record your data in a table.

7. Continue taking readings every 0.5 cm until you get no more change in Magnetic Field Strength.


 * PHOTO OF SET-UP:**


 * DATA:**
 * The values of the data table have 3 significant figures.


 * GRAPH:**

Percent Error for Exponent
 * CALCULATIONS**:

Magnetic Moment Calculation


 * ANALYSIS/DISCUSSION QUESTIONS:**

1. On Excel, create a graph of magnetic field //vs.// the distance from the magnet. Produce a best fit line using a “Power” function. (Shown above) 2. Compare your data to the ideal inverse-cube model:

a) What value do you get for the constant, //A//, or [( // m // 0 2 // m // ) / (4 p )]? How well does this agree with the value that the rest of the class measured? The value I got for the constant A was .0000002, which was the coefficient of the x-variable. From what I can see, this value was pretty similar to what the rest of the class measured.

b) What exponent do you get for d? How well does this agree with the ideal expression? I got the value of -2.534 for d. This expression agrees pretty well with the ideal expression. Ideally, I would have gotten -3 due to the fact that the distance and the magnetic field have an inverse cube relationship. The percent error between the experimental and theoretical values was 15.53% so it could have been a little closer to -3.

c) From the above comparison, does your magnet show the magnetic field pattern of a dipole? For the most part, my graph was very close to being inversely cubic so I believe my magnet did show the magnetic field pattern of a dipole.

3. Use your value of // A // to determine the magnetic moment // m // of your magnet. The value for the magnetic moment was 1. The calculation is shown above.

4. The units of // m // may suggest a relationship of a magnetic moment to an electrical current. In fact, a current flowing in a closed loop is a magnetic dipole. A current //I// flowing around a loop of area p // r // 2 has a magnetic moment // m // = //I// p // r // 2. If a single current loop had the same radius as your permanent magnet, what current would be required to create the same magnetic field?

5. Discuss the precision of your data, referencing the correlation coefficient to support your conclusion. Overall, due to the value of my correlation coefficient, which was .94094, I feel that my data was pretty precise. A few of the points were a bit off the line, but for the most part, my data was pretty accurate.

Overall, I can conclude that my hypothesis was correct. In the first part of my hypothesis, I stated that as the magnets moved farther away from the sensor, the magnetic field strength would go down. This can be seen in my data table, which showed the magnetic field values going down as the distance increased. In the second part of my hypothesis, I stated that the graph would show an inverse cube relationship. This part of my hypothesis was only partly correct. Despite the fact that the shape of the graph resembled an inverse cube relationship, the actual value of my exponent was a bit low at -2.534 rather than -3. In the end, the percent error of this value 15.53% so the lab was pretty accurate.
 * CONCLUSION:**

As stated above, there was some error in my lab. After reviewing my procedure, I can conclude that there were two main sources of error. The first source came from the fact that the sensor in which I used to measure the values of the magnetic field was a bit skewed. Originally, I was not able to zero the sensor, therefore after I obtained a value, I had to subtract the original value in order to get my net value. In addition, the values that the sensor showed fluctuated very often. It was almost impossible to get the exact value due to the screen flashing many different values. This definitely caused some error. The second source of error was the possible skewed measurements of distance. Although I tried to be perfectly exact, it was very possible that I might have been off slightly in my placing of the magnets when I was obtaining the data. This probably would not have caused a lot of error but it still was possibly an issue.

I feel that this is an important concept to understand because we are trying to prove the equation that explains the basic magnets that we see all the time in the real-world. The magnets that were used in this experiment were the same kind of magnets that we used to play with when we were kids. I feel that it was very interesting to make this connection between AP physics and my childhood.

Motor Activity
By Chris Hallowell 11/30/11

media type="file" key="Movie on 2011-11-29 at 14.56.mov" width="300" height="300"
 * VIDEO OF MODEL MOTOR:**


 * DISCUSSION QUESTIONS:**

1. How does a galvanometer work? A galvanometer is used to detect and measure electric current. It has a pivoting coil of wire that is always in a magnetic field. The coil is attached to a thin pointer that traverses a calibrated scale and shows the measurement. When a direct current flows through the coil, it generates a magnetic field, which works against the magnet that was already there. This causes the coil to pivot, which as a result causes the pointer to point to a value that indicates the electric current.

2. Define motor and generator. A motor is a machine, especially one powered by electricity or internal combustion, that supplies motive power for a vehicle or for some other device with moving parts. A generator is a device that converts mechanical energy into electrical energy.

3. A motor is a device, which converts electrical energy into mechanical energy (motion). Explain how your motor does so. The electrical energy from the circuit, which is being pushed by the battery, flows through the coil which is part of the motor. When this electrical energy passes through the coil, a magnetic force is produced which spins the coil. This spinning of the coil is the mechanical energy, which was converted from the original electric energy.

4. Why does the one rotor support have only ½ of its insulation sanded off? If both sides of the rotor support were sanded down, then the coil would never spin because the magnet would keep pushing it back and forth. When we sand 1/2 of a rotor, this causes the current to be cut off due to the fact that the conductor path has been cut off. This allows the magnets to take no effect and as a result, gravity and momentum take over and allow the coil to spin. When it makes it turn, the circuit is once again connected and the process begins again.

5. How could the motor you built in be converted to a generator? Describe carefully what would have to be changed and what the result would be. A generator is the opposite of a motor in the sense that it converts mechanical energy into electrical energy. As a result, I could spin the coil with my hand. This would be the mechanical energy. This spinning would result in the circuit being connected. Once the circuit is connected, electrical energy is then being produced.

Pre-lab Questions: Magnetic Force Lab

 * 1) The objective is stated as a question. What is your hypothesis? (Attempt to answer the question, to the best of your knowledge.) Include the rationale for your hypothesis (Provide detailed reasoning here. This may take the form of a list of what you already know about the topics, with a summary at the end.) How do you think you might test this hypothesis? (What might you measure and how?)

The magnetic force will be directly proportional to all the other values in the lab. As the other values increase, the magnetic force will increase as well. This will occur because of the equation, F=B(I)(//l//)(sin ** θ) **. This equation shows that when the magnetic field (B), current (I), length of the conductor (l), or angle between the field and current (theta) is increased at all and the others are left constant, the magnetic force will increase. In order to test this hypothesis, we will need to change each variable independently while keeping the others constant. We will need to do that for every variable in order to find the relationships. We will test this using many materials found in our physics room.


 * 1) Read the entire procedure through.
 * 2) Design __data table(s)__ in order to record your observations __and__ calculations. Do this in Excel (preferable), and post a copy on your wiki.

Answer the following questions:

1. How is the direction of the magnetic force oriented with respect to the directions of magnetic field and current which produced it? If the directions of the magnetic field and current are along the x and y axes, then the magnetic force will be on the z-component. This means that if the x and y components are on a piece of paper, the magnetic force on the z-component would either be going in or coming out of the paper.

2. How do changes in the angle between the current and the magnetic field affect the force acting between them? The larger the angle means a greater magnetic force between them. This is seen in the equation above. As the angle increases, the magnetic force increases as well.

3. What angle between the current and the magnetic field produces the greatest force? A 90 degree angle

4. What angle between the current and the magnetic field produces the least force? A 0 degree or 180 degree angle

5. How is the magnitude of the force of magnetism related to the magnitude of the length of the wire carrying the current? As the magnitude of the length of the wire carrying the current increases, the magnitude of the force of magnetism will increase as well.

6. A graph of force vs. current has a trendline with an equation of y = 0.00559x. What is the theoretical magnetic field strength of the magnet used in this experiment if the loop is 4.2-cm long? Show your work. .00559=F/current .00559=(B)(.042)(sin(90)) B=.133 T

7. Find the magnetic force on the conducting loop described above, when the current is 0.352-A. .00559=F/current .00559=F/.352 F= .001967 N