A lab report written for PHY 3001: General Physics II. Nominated by Professor Ramzi Khuri:
“In eleven years of teaching physics at Baruch, I have had the pleasure of reading several superbly written laboratory reports. Even amongst this distinguished group, Elizabeth Fanciullo’s laboratory reports are the finest I have ever read. All of her reports represent beautiful syntheses of careful experimentation, critical thinking and clear yet outstanding exposition. As a collection, they would easily surpass any laboratory manual I’ve ever seen in both instructional value and aesthetic appeal. My favorite of her reports was the one on the Magnetic Field of the Earth, in which she describes her measurement of the horizontal component of the Earth’s magnetic field in New York City.”
Name: Elizabeth Fanciullo
Lab Partners: Janna Petrovitch, Chris Missak
Title: Experiment #4 – Magnetic Field of the Earth (performed 02/27/09)
Objective of Experiment:
The objective of Experiment #4, Magnetic Field of the Earth, was to measure the horizontal component of the magnetic field of the Earth by creating a second magnetic field at the center of a loop of wire, which carried a current, then compare our measurement with the accepted value for the horizontal component of the Earth’s magnetic field at New York City: 2 ∙ 10-5 Tesla.
Underlying Physics Theory Tested:
Though not always visibly recognizable, magnetism is a phenomenon that influences all matter, including Earth. Bar magnets illustrate the fundamental magnetic properties most visibly and simply: two magnets will either attract or repel each other, depending on which ends of the magnets are closest together. Furthermore, while the north pole of one magnet attracts the south pole of another (“opposites attract”), two north poles or two south poles will repel each other (“likes repel”).
According to James S. Walker’s book, Physics (2nd ed.), the “direction of the magnetic field, B, at a given location is the direction in which the north pole of a compass points when placed at that location.” In general, magnetic field lines exit from the north pole of a magnet and enter at the south pole, and always form closed loops; they never start or stop anywhere (Walker). The Earth’s magnetic field is similar to a bar magnet. The north pole of a compass needle (often the part painted red) points toward the north magnetic pole of the Earth. But, since opposites attract, what we think of as the Earth’s geographical north pole is actually the south pole of the Earth’s magnetic field. Likewise, the Earth’s geographical south pole is actually the north pole of the Earth’s magnetic field.
Earth’s magnetic field has both a horizontal and vertical component. However, in our experiment we only wanted to obtain the horizontal component, which we called BE. To do so, we set up a system that consisted of a loop of wire, which carried an electric current created by a battery. The current loop behaves much like a bar magnet, in that one side of the loop acts like the north magnetic pole and the other side acts like the south magnetic pole. As a result, when we placed the compass at the center of the loop, we made sure to rotate the loop so that its plane was parallel to the horizontal component of the Earth’s magnetic field. In other words, we made sure the north pole of the compass pointed not only at 0° (in the horizontal direction), but also pointed directly in line with the current loop. When we turned on the current, it flowed through the loop and produced a second magnetic field, which we called BI. (Experiments have revealed that electric currents always produce magnetic fields.) The “right hand rule” of physics to determine the direction of the magnetic field (point the thumb in the direction of the current, then curl fingers around the wire to reveal the direction of the field) showed the magnetic field flowed perpendicular to the current in the loop. Because the magnetic field flowed perpendicular to the loop, it also flowed perpendicular to Earth’s north direction (because the horizontal component of Earth’s magnetic field was parallel to the plane of the loop). The new magnetic field, BI, forced the compass to deflect from North and rotate by an angle, θ, which essentially created a magnetic field triangle, where the line connecting BE and BI represented the total magnetic field, BTOTAL. BTOTAL equaled BE + BI and, as shown in the triangle below, tan θ equaled BI / BE.
Since we wanted to determine the magnetic field of the Earth, we solved for BE, which gave us the equation: BE = BI / tan θ.
In order to calculate BI, we used the formula which gave the magnitude of the magnetic field at the center of the current loop: BI = Nμ0I / 2R. N equaled the number of loops, which, in our case, was a consistent 15. μ0 was the constant, 4π ∙ 10-7, I was the current reading, and R was the radius of the current loop, which we measured as 0.1 meters.
By adjusting the rheostat (which increased or decreased resistance and, thereby, increased or decreased current) on the circuit box, we obtained various currents flowing through the wire and, therefore, various angles at which the compass deflected from North. We used the angles and current readings to calculate our experimental values for the horizontal component of the magnetic field of the Earth.
Procedure of Experiment:
In order to begin Experiment #4, my partners and I gathered the materials we needed—a circuit box, current loop, battery, compass, multimeter, connecting wires, and probes—and set up our system to look like the following:
As discussed in the previous section, we then adjusted our compass in the center of the current loop, making sure the north pole of the compass pointed at 0° in the horizontal direction and was directly in line with the current loop. By accomplishing this task, we knew the plane of the loop of wire was parallel to the horizontal component of the Earth’s magnetic field.
Next, we turned on the multimeter and set it to 200 mA (milliAmps). In order to make the compass deflect from North and rotate by an angle θ, we needed to increase or decrease the resistance and, thereby, increase or decrease the current flowing through the loop (which produced the second magnetic field). So, we simply pushed down and turned the rheostat on the circuit box until we noticed the compass needle move. Since we knew each mark on the compass represented 5°, we continued to turn the rheostat until the compass needle was exactly in line with one of the 5° incremental marks. We simultaneously observed the multimeter and, when the compass needle reached a readable angle, we recorded both the angle and the current given by the multimeter at that point. After recording our first observation, we made three more observations by turning the rheostat until the compass settled at three more readable angles. We then read and recorded the currents at those angles. By completing all our observations, we could calculate our experimental values for the horizontal component of the Earth’s magnetic field. For each observation, we first calculated the second magnetic field produced, BI, using the formula mentioned in the previous section: BI = Nμ0I / 2R. Since we set the multimeter to milliAmps, we made sure to multiply our current reading, I, by 10-3. By determining BI, we could then calculate the magnetic field of the Earth, BE, also using the formula mentioned in the previous section, where θ was the angle at which the compass deflected from North: BE = BI / tan θ. Once we completed calculating the magnetic field of the Earth for all four trials, we calculated our average, deviations, average deviation and percent average deviation. Finally, we used our average to calculate our percent error and compare our experimental value for the Earth’s magnetic field to the accepted value (at New York City), which was 2 ∙ 10-5 Tesla.
Experimental Data and Calculations:
The fact that magnetism affects all matter meant that, in the laboratory, a multitude of magnetic fields existed. As a result, these nearby magnetic sources and magnetic fields may have slightly interfered with our experiment. These interferences were most likely the primary reason we had relatively small discrepancies in our experimental results.
Additionally, flawed measurement may have contributed to our percent error. It is possible the multimeter may not have been exactly accurate when it read the current, especially given the fact that, on several occasions, we had to reset it because it would not work properly. Likewise, we had some trouble with the rheostat on the circuit box; it took multiple tries before we could get the compass needle to move. Initially, we thought the battery was the culprit. However, when we tried a different battery, it made no difference. At that point, we came to the conclusion that the rheostat was our problem.
Finally, though it appeared the compass’s needle pointed at 0° North and we aligned the compass precisely parallel with the current loop, perhaps we were somewhat off. If we were, this, too, would have affected our results. That said, this potential source of error seemed the most unlikely.
Completing this experiment helped us gain a better understanding of the concept of magnetism, especially the magnetism that exists on Earth. By turning on a current in the wire, we created a second magnetic field at the center of a current loop, which allowed us to measure the horizontal component of the magnetic field of the Earth at New York City. After adjusting the rheostat and observing by how many degrees the compass needle deflected from North, we could calculate our experimental value for Earth’s magnetic field. We completed four separate observations, which gave us an average magnetic field of 1.82 x 10-5 Tesla. The accepted value was 2 x 10-5 Tesla. In the end, our percent error was a fairly small 9%. Analyzing potential sources of error led us to the conclusion that nearby magnetic sources and magnetic fields present in the laboratory most likely caused disruptions and, therefore, the low percent error in our experiment.
Walker, James S. Physics. 2nd ed. New York: Prentice Hall, 2004.
Elizabeth Fanciullo received her Bachelor of Arts degree in Broadcast Journalism from the University of Kentucky in 2005. She reported and produced television news for two-and-a-half years in Kentucky and Indiana, before deciding to pursue a new career. In 2008, Elizabeth and her husband moved to New York City, where she attended Baruch College as a post-baccalaureate student, in order to satisfy the science pre-requisites for dental school. Elizabeth is currently a first-year dental student at the University of Medicine and Dentistry of New Jersey in Newark, New Jersey.