Lab #10_ Measurements Of Magnetic Fields

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Dec 6, 2023

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Lab #10: Measurements Of Magnetic Fields Lawrence Erispe, Ryan Fung, Date: October 26, 2023 Abstract: In this lab, we are estimating the strength of Earth’s magnetic field by using a Hall probe magnetometer and comparing the estimated value of Earth’s magnetic field to other magnetic fields. For the other part of this lab, we will be attempting to verify the Biot-Savart law by measuring the magnetic field of a single Helmholtz coil and a double Helmholtz coil. Experimental setup and measurements: The goal of the first experiment is to verify the Biot-Savart law by measuring the magnetic field at the center of the Helmholtz coil using only one coil. For this experiment we need black and red BNC, Hall sensor, Helmholz coil, LabPro data acquisition and Logger Pro software, and Pasco DC power supply. We followed the diagram below for the set up of this experiment ensuring the white dot on the Hall sensor is parallel to the coil. We then flip the switch on the Helmholtz coils labeled “one coil”. We then turned on the Pasco DC power supply and set it to 3.0 amps. Before we could start logging data, we had to “zero out” the probe. We did this by removing the probe, standing back and figuring out different orientations where the probe was giving us the lowest possible value. Once we found that, we “zeroed out” the probe via the Logger Pro software. Then placing the probe back, making sure it is parallel to the coil, we began taking data. Here for this experiment, we were to set the probe at varying distances. We started at z = 0.0 m and increased the distance by 0.01 m until we reached z = 0.19 m. Using the equation B = ( I μ 0 NR 2 )/2(R 2 +Z 2 ) 3/2 we use our data points and log them on Logger Pro. We perform a curve fit to get the vale for μ 0 . Similarly for the second part of the lab, we have to verify the Biot-Savart law by measuring the magnetic field, now using two coils. Instead of varying the distance, we are now varying the current. Starting off at I = 0.0A, we increase the current in 0.25A increments until we reach I = 4.0A. Now we are using the equation B= ( I μ 0 N)/(5/4) 3/2 R and just like the previous experiment, we log our data points and perform a curve fit to get the value for μ 0 . For the last part of the lab, we estimated the strength of the Earth’s magnetic field using the Hall probe. We oriented the Hall probe in such a way that the white dot pointed towards the north. We estimated the strength of the Earth’s magnetic field to be 0.011 mT. The earth’s magnetic field is weaker than a typical refrigerator magnet and MRI machine, but a lot stronger than the magnetic field generated by currents in the human brain.

Experimental Data: Distance vs. Magnetic Field Strength For A Single Coil Distance Z (m) *Assumption: No uncertainty* Magnetic Field Strength (mT) ± 0.001 mT Magnetic Field Strength (T) ± 0.000001 T 0.0 1.735 0.001735 0.01 1.710 0.001710 0.02 1.663 0.001663 0.03 1.604 0.001604 0.04 1.524 0.001524 0.05 1.440 0.001440 0.06 1.345 0.001345 0.07 1.244 0.001244

0.08 1.150 0.001150 0.09 1.055 0.001055 0.10 0.970 0.000970 0.11 0.886 0.000886 0.12 0.806 0.000806 0.13 0.736 0.000736 0.14 0.669 0.000669 0.15 0.609 0.000609 0.16 0.554 0.000554 0.17 0.504 0.000504 0.18 0.459 0.000459 0.19 0.422 0.000422

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