PHYS2016_Lab5_MagneticFields-AMANDA

Lab Notes PHYS 2016 Lab 5: Magnetic Field After opening this google doc and before proceeding: File - Make a copy, then share the copy with team-mates with editing rights Everyone needs to be logged in to their UMN Google accounts. Activity I: Smartphone Sensor Exploration - It records magnetic field in microTeslas - When the X plot reads close to zero, the y plot is about 4 microTesla. When the Y plot reads about zero, the X plot is about 20microTesla. All of my group members' phones are relatively close(within a few numerical values). - For these plots, the magnitude of the magnetic field when x was about 0 was 37.52microTesla. When the y was about zero, the magnitude was about 70.36 microTesla. - When I move my phone so the Y axis lines up pointing north, it reads to that the x is 0.56μT, my Y 28.37μT, my z at -35.90μT, and my absolute(magnitude) was at 45.76μT.

- When I rotate my phone so the y-axis is pointing west, it reads so that x is 5.93μT, y is -0.17μT, and z is -41.96μT, and my absolute(magnitude) is 42.38μT . - These two measurements make sense because when the y axis is pointing north, the x component was about zero. And when the y axis was pointing west, the y component was about zero. When comparing these two measurements, I make sense of it all based on the absolute measurement, as they are both about 42-45μT. It makes sense the absolute magnetic fields of both measurements are about the same value. - It surprises me that Earth's magnetic field is such a small number. I would have expected that the strength would be a lot greater. It could be noted that the values were all taken at relatively the same spot(on the table, with the phone laying flat). I would expect that if you went somewhere with greater magnetic field strength, like near rose quartz mines, the magnetic field would increase as I do know that certain minerals affect the field. Activity II: Basic observations of a wire’s B-field A- Predictions

(a) sin(θ) = B W / B E (b) tan(θ) = B W / B E (c) tan(θ) = B E / B W (d) sin(θ) = B E / B W B- Observations - We connected the power supply to the ammeter and resistor which was also connected to a thin metal wire. This wire sat in a wooden frame with the compass sitting a few centimeters below. This frame sat on the X on the table to avoid any extra outside influences. A current was ran through the wire, and the deflection observation was recorded SITUATION DEFLECTION(movement) DEFLECTION(Degrees) A North-East movement ~10 degrees B North-west movement ~60 degrees C North-East movement ~60 degrees D North-South movement(counterclockwise) ~180 degrees Activity III: Magnetic field as a function of distance - By using the equation from question 5 above tanθ=B W /B E . Θ would the measurement taken from the compass as the deflection degree. B E is a constant number as is the earth’s magnetic field strength and will always be the same at the given location. - The magnetic field sensor was located by the volume bottoms on an iPhone 12. It was found by placing the phone on the X(on the table) with the y axis pointing north. We then moved the fridge magnet around the phone until we saw a change in movement, which happened around the volume buttons. - X(horizontal) component of B E field= 0.15μT DISTANCE(m) ANGLE Deflection B W (Calculated) μT 0.027 70 degrees North to East(clockwise) 0.412 0.058 65 degrees North to East(clockwise) 0.322 0.075 55 degrees North to East(clockwise) 0.214 0.097 50 degrees North to East(clockwise) 0.179 0.116 45 degrees North to East(clockwise) 0.150

0.146 41 degrees North to East(clockwise) 0.130 0.207 35 degrees North to East(clockwise) 0.105 0.237 30 degrees North to East(clockwise) 0.087 - Distance was taken by measuring from the compass to the wire in cm and converting to m for more reliable future analysis. - Current moving from south to north when the compass needle is where it should(lined up with the wire). The current running through the wire is at 4amps. It could be noted that the magnetic field was going clockwise through the current if looking from above the compass, which was still lined up on the wire with the needle pointing north. We covered almost all of the distances allowed in the wooden frame, skipping one that was really close to the other hole, hence why there is a jump of degrees between 65 degrees and 55 degrees. We also made sure to use the top hole to really test the magnetic field when the wire is the furthest away from the compass. - After the third measurement taken, I inferred that the angle would keep moving down by about 5 degrees each time, as well as that the deflection would always be clockwise(North to East) each time because of the way the current was flowing through the wire. - B w was calculated by taking the tan(deflection amount) and multiplying it by the magnetic field of the earth which was found to be 0.15μT at the same point where the compass was placed throughout testing. This measurement was calculated at each measurement in the table above. Activity IV: Graphing and Analysis (individual effort) Figure 1. This is the first graph I made which represents the distance(in meters) on the x-axis plotted against the Magnetic field of the Wire(B w ) which was taken in microTelsa(μT). This

Figure 3. The last graph I made is the log-log plot of the data I collected. It includes the natural log of distance(taken in meters) vs the natural log of the magnetic field(taken in microTesla). It can be easily noted that the plot follows a completely linear model, ln(distance(m))=mx+b. The correlation coefficient is also at exactly 1.000, meaning that this graph is by far the best fit. The experiment was performed by placing the wooden frame with the compass in the middle on the blue X which was taped on our table. The needle of the compass was facing north, and the wire was in alignment with the north-facing needle. The wire was moved at different distances away from the compass and the distance away and the degree of deflection was recorded in the data table above as 4.0amps of current was run through the wire. We figured out that because the current was running from South to North(in relation to the compass facing north and in alignment with the wire) that the wire’s magnetic field was moving west to east(clockwise) around the wire. This was determined based on the right-hand rule(thumb pointing to where the current is flowing and fingers curl in direction of the magnetic field. We made sure to make the measurements as equally distanced apart as we could, however, some holes in the wood frame were skipped to make sure a good range of distances was covered. My conclusion is that the last graph(figure 3) is by far the best plot to represent the data. It is the plot of ln(distance(m)) vs ln(magnetic field(B w )(μT)), representing a log-log graph. It shows a linear relationship, ln(Distance(m))=mx+b, and has a correlation coefficient of 1.000. The perfect correlation coefficient shows us that all of the plot points are on the line of best fit, which is what is desired. The other two plots(figure 1 and figure 2) are both good plots; however, the lines do not represent the data as best they could. Overall, based on the data taken and the plots that as the distance increases, aka as the wire moved farther away from the compass, the magnetic field becomes weaker. This

relationship is most easily seen in the data table above or in figure 1, which shows the relationship between distance and the magnetic field. One big thing that I noticed throughout taking data points was that it was difficult to read the exact degree of change in the compass. As soon as the wire was filled with current the needle on the compass moved in a clockwise direction(North to East); however, it was difficult to gauge whether the needle was pointing at exactly 40 degrees(for example) or if it could have been pointing to 42 degrees(again, for example). This error should be noted within the experiment and improved if the experiment were to take place again.