Physics+2025+Lab+8

Phys 2025 Lab 8 - Magnetic Fields Your Name: Time of Day Class Starts: Day of Week: Date: Your partner’s names: In this lab, you will learn about where magnetic fields come from, how they are shaped, and why magnets behave the way they do. Shapes of The Magnetic Field Magnetic fields are generated by currents and moving charges. The magnetic field generated by an infinitesimally short segment of current carrying wire is described by the Biot-Savart Law: d ~ B = μ 0 I 4 ⇡ r 2 dL ⇣ ˆ r ⇥ ˆ I ⌘ where μ 0 = 4 ⇡ ⇥ 10 - 7 T m/A is called the permeability of free space, dL is the length of the wire segment, and r is the distance from the wire. The magnetic field curls around the wire segment in circles, (as shown below), and diminishes in strength with increasing distance according to an inverse-square law. The magnetic field of a longer wire can be found by adding up (or integrating) the magnetic field contribution from each segment of the wire. For example, the magnetic field of a straight, infinitely long wire is given by ~ B straight = μ 0 I 2 ⇡ r ⇣ ˆ r ⇥ ˆ I ⌘ which has the same shape as the magnetic field of a wire segment, but with a magnetic field strength that decreases as 1 /r instead. 1

The magnetic field of a loop is donut-shaped, with the magnetic field contributions from each wire segment adding construc- tively at the center, (as shown below). A solenoid is a coil of wire made of many wire loops whose combined magnetic field is much stronger than that of a single loop. A magnetic dipole is the magnetic field of a wire loop of infinitesimally small radius. The magnetic field due to the spin of an electron is represented as a magnetic dipole. In most materials, the electron spins are oriented randomly, so the individual magnetic fields cancel out. However, in a permanent magnet the electron spins are all aligned in the same direction, and the individual magnetic fields combine constructively to create a powerful magnetic field. The magnetic field of a permanent magnet looks roughly like that of a solenoid. The magnetic fields for a solenoid, a magnetic dipole, and a permanent magnet are shown below. Since the magnetic fields of a loop, a solenoid, a magnetic dipole, and a permanent magnet are all roughly the same shape, we will sometimes treat all magnets as though they are wire loops in the discussions that follow. 2

Observe the behavior of the magnet. Try changing the orientation of the boat and see what happens. Play around with the compass until you are convinced that it works as expected. In your own words, describe the behavior of the magnet as the answer to Question 1.A Return the neodymium magnet to the instructor when you are finished. Why Do Magnets Attract/Repel? Consider two loop magnets placed one on top of the other. Then the magnetic field from the first magnet will bend slightly outward as it encounters the wire loop of the second magnet. If the magnets are magnetically aligned, then the magnetic force felt by the second magnet will be mostly directed out- ward, but also slightly directed towards the first magnet, resulting in a net attraction. If the magnets are magnetically anti-aligned, then the magnetic force felt by the second magnet will be mostly directed inward, but also slightly directed away from the first magnet, resulting in a net repulsion. Now consider two loop magnets placed side-to-side. Then the magnetic field from the first magnet points straight down as it encounters the wire loop of the second magnet, but gets weaker with increasing distance. If the magnets are magnetically aligned, then the magnetic force felt by the closer side of the second magnet will be di- rected away from the first magnet, and the magnetic force felt by the far side of the second magnet will be directed towards the first magnet. However, the magnetic field is stronger closer to the first magnet, so the result is a net repulsion. If the magnets are magnetically anti-aligned, then the magnetic force felt by the closer side of the second magnet will be directed towards the first magnet, and the magnetic force felt by the far side of the second magnet will be directed away from the first magnet. However, the magnetic field is stronger closer to the first magnet, so the result is a net attraction. 4

Experiment 2: Magnetic Attraction/Repulsion In this experiment, you will verify the magnetic attraction/repulsion rules. For this experiment, you will need • 2 Ceramic Disk Magnets (labeled) • 1 Refrigerator Magnet (Halbach) Push the 2 ceramic magnets together, so that their north poles are facing each other. Record whether the magnets attract or repel in Table 2.A . Repeat for every combination of north and south poles. Place the 2 ceramic magnets flat on the table, so that their north poles are facing up. Push the magnets together and record whether they attract or repel in Table 2.B . Repeat for every combination of north and south poles. Refrigerator Magnets When you place a magnet next to the steel/iron surface of a refrigerator, the electrons in the iron align with the field of the magnet, and the metal becomes temporarily magnetized. The permanent magnet is then attracted to the magnetized surface, and the magnet sticks. It may surprise you that many refrigerator magnets do not have a single north and south pole, but are in fact composed of multiple magnets with di ↵ erent orientations combined together in a clever arrangement called a Halbach array . The magnetic fields combine in such a way that the magnetic field is strong on one side and weak on the other, which is why one side of a fridge magnet seems “magnetic” while the other does not. Bring the north pole of one of the ceramic magnets close to the “magnetic” side of the refrigerator magnet. Do the magnets stick? Record whether the magnets attract , weakly attract , or don’t attract in Table 2.C . Repeat for every combination of north/south poles and “magnetic”/“non-magnetic” sides. 5

Check o ↵ your circuit with the instructor . In Logger Pro or Graphical Analysis, set the y-axis of your graph to “Magnetic Field” and the x-axis to “Current”. Set the data collection time to 60 seconds. Begin data collection, then slowly turn the current knob on the power supply until you reach 1.5 Amps. Stop data collection, then turn the current knob all the way back down to 0 Amps. Warning: Do NOT leave cur- rent flowing in the circuit for longer than necessary . The magnetic field at the center of a solenoid, (as derived from the Biot-Savart Law), is given by B = ✓ μ 0 N p L 2 + D 2 ◆ I where L is the length of the solenoid, D is the diameter of the solenoid, and N is the number of loops in the solenoid. (Intuitively, increasing the number of loops amplifies the magnetic field strength, while increasing the length or the di- ameter spreads the wire out further away from the center, diminishing the magnetic field strength.) The relationship between magnetic field strength and current is linear, with the slope being equal to the expression in parenthesis. Perform a linear best fit and record the slope of your magnetic field vs current graph as the answer to Question 3.A Now, use your ruler to estimate the length ( Question 3.B ) and diameter ( Question 3.C ) of the solenoid 7

Using your measurements from Questions 3.A, 3.B, and 3.C, solve for the number of loops N ( Question 3.D ). Does your answer seem reasonable? Move the magnetic field sensor out of the way, then turn the current back up to 1.5 Amps. Place the ceramic magnet inside the solenoid, then lift up the solenoid tube and hold it vertically above the table. Describe what happens as the answer to Question 3.E . When you are done playing with the magnet, turn the current back down to 0, and remove the magnet. Place the steel bolt inside the solenoid, point-first, so that the head of the bolt rests at the center of solenoid. Bring the paper clip close to the steel bolt. Is the paper clip attracted to the steel bolt when the current is o ↵ ? ( Question 3.F ) Turn the current back up to 1.5 Amps, and bring the paper clip close to the steel bolt. Is the paper clip attracted to the steel bolt when the current is on? ( Question 3.G ). The magnetic field from the solenoid causes the electrons in the steel bolt to align, temporarily magnetizing the steel bolt. Turn the current back down to 0, and let the next lab group start using the Arksen. 8

Answer Sheet Experiment 1 A) Describe the behavior of the magnet. Experiment 2 A) Determine whether the following poles attract or repel when placed face-to-face. Face-To-Face North South North South B) Determine whether the following poles attract or repel when placed side-by-side. Side-By-Side North South North South C) Determine whether the following attract or repel when placed face-to-face. Halbach Magnet North South “Magnetic” “Non-Magnetic” Experiment 3 A) slope = Δ B Δ I = ⇣ μ 0 N p L 2 + D 2 ⌘ = mT/A B) L = cm C) D = cm D) N = E) Describe what happened when you placed the ceramic magnet in the solenoid. F) Is the paper clip attracted to the steel bolt when the current is turned o ↵ ? I) Is the paper clip attracted to the steel bolt when the current is turned on? 10 The alside of the magnet points toward the geographical post . R = repel E It A = attract R E A R Not really repelling A A R R 2 6 . 171 ⊥ ne en 3 =18 18 The magnet was in the middle of the solenoid No yes

Experiment 4 A) What is the highest frequency you can hear? Hz B) What is the lowest frequency you can hear? Hz 11 14 I