PHY 212 LAB Magnetic Field As a Function of Current Apparatus DC Power Supply two D batteries one round bulb and socket a long wire 10-Ω resistor set of alligator clilps coil Scotch tape function generator and coax-to-alligator-clip cable cup speaker headphone cable with split wires ipod or iphone two sets of 4 neodymium magnets a compass Goal In this lab, your goals are: 1. to determine the N and S poles of a magnetic dipole 2. to determine the N and S poles of an electromagnet (i.e. current-carrying coil) 3. to investigate how a speaker works, with a coil, cup, and magnet 4. to learn how to use a compass to measure magnetic field 5. to measure the magnetic field as a function of current in a long, straight wire 6. to measure the magnetic field as a function of distance for a long, straight wire PhET: Magnet and Compass. Determine the N and S poles of a magnetic dipole. Observation: A compass needle points in the direction of the net magnetic field (due to other sources) at the location of the compass needle. Explanation: If the compass needle points in a different direction than the magnetic field at its location, then there is a torque on the compass needle that causes the needle to rotate until the N end of the compass needle points in the direction of the net magnetic field. If there is sufficient frictional forces (i.e. damping), the needle will eventually stop oscillating and will be in static equilibrium, aligned with the magnetic field. Thus, a compass needle is an indicator of the direction of magnetic field. 1. Run the PhET simulation: Magnet and Compass. 2. The magnetic field is created by a dipole magnet. There are tiny compass arrows shown throughout space that show you the direction of magnetic field at various points in space around the dipole magnet. The brightness of each needle is used to indicate how strong the magnetic field is at that location. 3. Move the compass around the magnet. 1
Did you notice that the compass needle oscillates after you stop moving the compass? Why does the compass needle eventually stop oscillating and come to rest, in static equilibrium? Feel free to investigate a real compass to figure out the answer. 4. After investigating the direction of magnetic field around the dipole magnet, sketch the magnetic field at the locations on the picture below. Figure 1: Dipole magnet. Write a general rule: The magnetic field due to a dipole magnet at a point along the axis of the magnet points the N pole and the S pole. At a point along the perpendicular bisector of the magnet, the magnetic field points At a point on the equator of Earth, the compass needle points toward geographic N. Sketch Earth as a circle and draw the compass needle at the equator at the left side of the circle. At this point, what direction is the magnetic field? 2
You can model Earth as a dipole magnet that is nearly aligned with its axis. Sketch a dipole magnet through Earth such that the magnet s axis is aligned with Earth s axis. Label the N and S poles of the magnet. 5. In the PhET simulation, check the box that says Show planet Earth. Compare it to the sketch that you drew. Resolve any differences. 6. The compass that you place on a desktop only measures the component of magnetic field that is parallel to Earth s surface. However, the actual magnetic field due to Earth at a point on its surface points downward. For example, look at the direction of the magnetic field near the N geographic pole. The angle that a needle would put toward Earth is called the dip angle and is measured with a compass needle that can rotate in the vertical plane. PhET: Magnets and Electromagnets. Determine the N and S poles of a currentcarrying coil. 1. Run the PhET simulation: Magnetics and Electromagnets. 2. Click the tab for Electromagnet. 3. Change the number of loops to 1. You ll notice charge moving through the wire. Do the spheres represent electrons or positive charge (i.e. conventional current)? 4. Uncheck the box Show Electrons. 5. Wrap your fingers around the loop in the direction of conventional current and note the direction of your thumb. How does the direction your thumb compare to the direction of the magnetic field indicated by the compass needles along the axis of the loop? This use of the right-hand rule is used to figure out the direction of magnetic field along the axis of a current-carrying loop. 6. Move the compass around. 3
Sketch a side view of the loop below and sketch the direction of conventional current at the top and bottom. If you model the loop as a dipole magnet, which side (on the left or on the right) is the N pole? Label the N and S poles of your loop. Force of a magnetic dipole on another magnetic dipole You ve observed in your everyday life that magnets attract or repel. Let s investigate. 1. Obtain a set of four neodymium magnets. We ll treat this is a single magnetic dipole. 2. Use your compass to determine the N and S poles of your magnet. Place a large piece of Scotch tape on the N side of your magnet. (Note: I want no tape residue left on the magnets, so use a big piece that can easily be pulled off. Do NOT write on the magnets.) 3. Obtain a second set of four neodymium magnets to use as a magnetic dipole. Determine the N and S poles of this dipole and indicate the N end with a piece of tape. 4. Now, observe which poles attract and which poles repel for your magnets. Record your observations below. Same poles. Opposite poles. 5. Connect a power supply, large wire coil, and an ammeter in series. Set the power supply at 1 V. Measure the current flowing through the coil. Increase the voltage until a current of 1 A flows through the coil. Note that a current limiter on the power supply will limit high currents. You have to turn up the limiter to allow a 1 A current. 6. The coil is called an electromagnet and acts as a magnetic dipole. Use your compass to determine the N side and S side of the electromagnet. Use a piece of Scotch tape to indicate the N pole of the electromagnet. Use your right-hand rule to determine which direction current is flowing in your coil based on what you know to be the direction of the magnetic field along the axis of the coil. Record the direction of the current by sketching a picture of the coil and indicating whether the current flows clockwise or counterclockwise around the coil if you are facing the coil. 4
7. Observe whether the set of four neodymium magnets (a magnetic dipole) will be attracted or repelled by the coil, in accordance with the same rules you observed above for two interacting magnetic dipoles. Record your observations below. 8. Switch the leads on the coil in order to reverse the current. Observe the interaction of your coil with the magnetic dipole. Describe how changing the direction of the current affected the poles of the electromagnet and the direction of the magnetic field created by the electromagnet. 9. Connect a function generator. to the coil. Press the square wave button on the function generator. Press the 10 button to set the frequency meter to the 10 scale. Adjust the frequency until it is about 5 Hz. 10. Hold the magnetic dipole (set of four neodymium magnets) at the center of the coil. Record your observations. 11. Adjust the frequency as you are holding the magnets. 12. To help you visualize what the function generator is doing, run the PhET simulation: Magnetics and Electromagnets. Click the Electromagnet tab and click the AC current source. Describe the motion of the charge in the wire and describe how this affects the magnetic field along the axis of the loop. It helps if you place the large compass along the axis of the loop. 5
Now, explain in detail using words and diagrams why it is that you feel an alternating force, which alternates between pushing and pulling on the magnets. Show the direction of the current in the coil if it attracts the magnet. Show a separate picture for the current in the coil if it repels the magnet. Exploring a speaker A speaker has a wire coil that is connected to the output of an amplifier. The sound produces an alternating current in the wire that oscillates in both magnitude and direction (that is, it alternates" and is thus not constant). As a result, it creates an alternating magnetic field along the axis of the coil that oscillates (or alternates) in strength and direction. 1. Hold a magnetic dipole close to the wire coil. Record your observations of what you feel. When the coil and magnetic dipole attract, what direction is the current in the coil? When the coil and magnetic dipole repel, what direction is the current in the coil? Sketch two separate pictures. What are the essential parts of any speaker, including earbuds or headphones or the speaker in your cell phone, for example? Describe how a speaker works. Measuring magnetic field as a function of current in a long, straight wire A compass points in the direction of the net magnetic field at the location of the compass. Moving electrons flowing through a wire create a magnetic field everywhere in space. A compass placed under a wire is affected by magnetic fields from two sources: (1) the Earth, and (2) the current in the wire. 6
Figure 2: 1. Move all wires and batteries far from the compass so that the compass points toward geographic North. Assemble a circuit consisting of one battery, a long copper wire, and a 10 Ω resistor in series. Leave one alligator clip disconnected 2. Align the long wire carefully with the compass needle, then connect the circuit. Don t move the compass! Carefully measure the compass deflection (to the nearest 2 ) when current is flowing through the circuit. θ = Sketch a picture of the net magnetic field at the location of the compass, the magnetic field of Earth at the location of the compass, and the magnetic field at the location of the compass that is due to the current flowing through the wire. The component of the Earth s magnetic field in the plane of the compass is approximately 2 10 5 T at this location. Use trigonometry and your sketch of the right-triangle above to calculate the magnetic field at the location of the compass due to the current in the wire. In the following steps of the experiment, you will find the relationship between the magnetic field produced by a the current in a wire and the magnitude of the current. 7
What is the theoretical equation for the magnetic field at a distance r from a long, straight wire due to the current in the wire? 3. Set the compass on the edge of the table so that it points N. Use a piece of Scotch tape, folded and stuck to the bottom of the compass to keep it fixed to the table and aligned with N. 4. Connect a voltage source (i.e. power supply), a 10 Ω resistor, a long wire, and a current meter (i.e. ammeter) in series. 5. Adjust the voltage of the voltage source until the current reads 0.1 A. 6. Lay the wire on top of the compass, along the N-S axis. Measure the following data: I = θ = Using the deflection of the compass from N, calculate the magnetic field due to the wire: B wire = 7. Adjust the voltage to until I = 0.2 A and again measure current and magnetic field. Repeat until you fill out the data table below. Table 1: Magnetic field as a function of current for a long, straight wire I (A) θ ( ) B wire (T) 0.1 0.2 0.3 0.4 0.5 8. Graph B vs. I in Logger Pro, and fit the appropriate function to the data. 8
Record the curve fit and the proportionality constant. 9. Use a ruler to measure as closely as possible the distance between the center of the compass needle and the wire. r = m. Using your curve fit parameter and the distance r, calculate the constant µ0 4π. Compare your measured value of µ0 4π to the theoretical value of 1 10 7 T m/a. Magnetic field as a function of distance from the wire Now, we will measure how the magnetic field at a location from a wire varies as a function of the distance from the wire r. You have already learned how to measure magnetic field by measuring the deflection of a compass needle, and you will use this same technique to measure magnetic field. 1. Place the compass on the edge of the table and align it with geographic N. 2. Obtain a ruler and hold it perpendicular to the table. 3. Using the same circuit as before (battery, a long wire, ammeter, and 10 Ω resistor), hold the wire along the N-S axis at a distance above the compass that causes a deflection of 10. Measure the distance of the wire from the table and calculate/record its distance from the center of the compass needle. Do this for other deflections, and record your results below. r (m) θ ( ) B wire (T) 5 10 15 20 25 30 4. Using Logger Pro, graph B vs. r. Assume a power relationship so that B 1/r and fit a curve to your data. 9
5. Record your curve fit and the proportionality constant. 10