Objective:

Introduction:

Material:

- IoLab
- Ruler with CM marking
- Magnet
- Computer with IoLab software
- 8.5 by 11 in paper and magazines
- Scotch tape
- A non-conducting object such as a pencil

Procedure:

- Place the IoLab and place it next to the paper and stack of magazines
- Make sure the area of the experiment is clear from wire and cables.
- Place the magnet on top of the paper
- Make sure the magnet is just about level with the center of the IoLab or as perpendicular as possible.
- Place the ruler on top of the paper and make sure that the front of the ruler is flush with the post of the IoLab
- Turn on the IoLab device
- Start the IoLab software on the computer
- Run the Magnetometer on the data sets
- Go to the settings on the IoLab software and use the magnetometer calibration option in order for it to offset the stray magnetic field where they become constant.
- Calibrate the IoLab and check that it gets a good reading of the earthβs magnetic field
- Set the magnet in the direction where the large majority of the magnetic field is on the Y direction of the IoLab
- Open the IoLab software and click on record
- Rotate the magnet until the line is the biggest on the Y direction on the IoLab software
- Use a small piece of tape on the magnet to preserve the orientation of the magnet
- Tape the magnet to a non-conducting object such as a pencil in order to be able to move the magnet along relative to the magnetic field sensor.
- Click the reset button on the IoLab software and begin taking some data
- Place the magnet far away from the device and record for five seconds to create the baseline data
- Place the magnet 10cm away from the device and start moving the device in 0.5cm increments. For each 0.5cm take 5 seconds of data (10cm-2cm).
- Create an excel spreadsheet using all the positions from the experiment

Data:

postion [cm] | Err-Pos [cm] | Bx [uT] | By [uT] | Bz [uT] | Er-x[uT] | Er-y [uT] | Er-z [uT] | Bnet [uT] | “=ln(x)” | ln(C0) Offest correction | x offset correction | ||

15.00 | 59.13 | -86.68 | -43.66 | 7.80E-01 | 0.63 | 1.50 | 3.438843936 | 2.734E+00 | 82.5 | NA | 0.4 | cm | |

15.50 | 61.39 | -81.31 | -44.85 | 7.50E-01 | 0.64 | 1.50 | 3.361070505 | 2.766E+00 | |||||

16.00 | 63.19 | -75.93 | -47.74 | 9.20E-01 | 0.70 | 1.50 | 3.303808808 | 2.797E+00 | |||||

16.50 | 64.27 | -70.56 | -45.70 | 7.70E-01 | 0.71 | 1.50 | 3.149266933 | 2.827E+00 | |||||

17.00 | 65.12 | -64.47 | -45.35 | 9.00E-01 | 0.68 | 1.40 | 2.982682103 | 2.856E+00 | |||||

17.50 | 66.85 | -60.06 | -45.13 | 7.60E-01 | 0.65 | 1.40 | 2.894091853 | 2.885E+00 | |||||

18.00 | 67.20 | -56.66 | -46.37 | 8.60E-01 | 0.65 | 1.40 | 2.826224463 | 2.912E+00 | |||||

18.50 | 67.09 | -52.66 | -46.29 | 7.80E-01 | 0.69 | 1.40 | 2.676736783 | 2.939E+00 | |||||

19.00 | 68.69 | -49.72 | -46.20 | 8.40E-01 | 0.70 | 1.30 | 2.643950876 | 2.965E+00 | |||||

19.50 | 69.54 | -46.64 | -46.16 | 7.80E-01 | 0.68 | 1.40 | 2.573419269 | 2.991E+00 | |||||

20.00 | 70.80 | -44.59 | -46.42 | 8.50E-01 | 0.66 | 1.40 | 2.579526986 | 3.016E+00 | |||||

20.50 | 71.09 | -41.57 | -46.68 | 8.60E-01 | 0.65 | 1.50 | 2.498188832 | 3.040E+00 | |||||

21.00 | 71.07 | -39.29 | -46.32 | 8.70E-01 | 0.66 | 1.40 | 2.397095082 | 3.063E+00 | |||||

21.50 | 71.36 | -37.16 | -46.58 | 8.00E-01 | 0.62 | 1.40 | 2.347859747 | 3.086E+00 | |||||

22.00 | 71.68 | -34.90 | -46.32 | 8.20E-01 | 0.71 | 1.40 | 2.272919404 | 3.109E+00 | |||||

22.50 | 71.90 | -33.17 | -46.06 | 7.70E-01 | 0.57 | 1.40 | 2.208995442 | 3.131E+00 | |||||

23.00 | 72.45 | -31.09 | -46.03 | 8.10E-01 | 0.77 | 1.40 | 2.173522852 | 3.153E+00 | |||||

23.50 | 73.15 | -28.46 | -46.04 | 0.88 | 0.74 | 1.40 | 2.140422273 | 3.174E+00 | |||||

24.00 | 73.08 | -25.78 | -46.31 | 0.85 | 0.75 | 1.40 | 2.050920477 | 3.195E+00 | |||||

Analysis

- Using the methods described in the video estimate the error in the value of n.

To get the error of n you should use the linest function in the excel sheet. You should insert all the net magnetic field values and ln(x) values inside the linest function and then you have to type βtrueβ two time in the linest function. Then you can get the error of n.

- Please provide a detailed mathematical discussion regarding why we used the net magnetic field and not just the magnetic field along the Y-axis?

The magnetic field is shaped like concentric circles, so the magnetic field affects not only the ydirection but also the x and z-direction. So, to get the net magnetic field we have use this

equation B net = βπ΅π₯^{2 }+ π΅π¦^{2 }+ π΅π§^{2}.

- What is the key number that allows one to determine the best value of n?

π
^{2} value of the graph determines the best value of n. If π
^{2} value is close to 1 then it shows that n value is close to the theoretical value. In our graph, π
^{2} value is 0.9862 and this value is close to 1 so it means n value of graph is close to theoretical value.

- Discuss why we changed the value of n to find the error. Could we quantify the process of finding the error in n? Please describe in detail why or why not

The reason why we changed the value of n to find the error is because theoretical value of n must be -3. According to the equation π΅ = ^{πΆ}^{0}_{3}, n value must be -3, so if we change the value of n, we

π can find the error.

- What is the significance of the Y-intercept from your best fit equation?

According to the equation ln(B)=-3ln(r)+lnπΆ_{0}, Y-intercept represent magnetic fields. So, we can get the magnetic field value through the y-intercept.

- Create a number line that compares the expected value for n and the experimental value.

- Create a percent error to compare the expected value of n and the experimental value.

πβπππππ‘ππππ π£πππ’πβπΈπ₯ππππππππ‘ππ π£πππ’π |β3.000β(β3.001)|

%error=Γ100=( )Γ100=0.033%

πβπππππ‘ππππ π£πππ’π 3.000

- List 4 reasons in order of significance that contributed to error in this experiment.

- Y-direction of iolab has to be placed perpendicular to the earthβs magnetic field but position of the iolab is not exact and that causes error.
- If a magnetic device such as a cell phone affects the magnetic field, then the magnetic device causes the error.
- If the iolab device is not calibrated, then it causes error.
- Ruler has error so that cause the error in the experiment.

Graph

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