Lab 4, part one: Electric and magnetic fields

Transcription

1 Astronomy 102 Name: Lab 4, part one: Electric and magnetic fields Learning outcome: Ultimately, to understand how a changing electric field induces a magnetic field, and how a changing magnetic field induces an electric field, and how both are aspects of electromagnetic radiation. Electromagnetic radiation, as we ve seen in previous exercises, is pervasive. Yet until the middle of the 19 th century, physicists widely believed that EM waves could exist in a vacuum. Further, they did not connect EM waves to light, even though some of them suspected that there would be a connection. The magnetic field of a coil of current-carrying wire Equipment needed: a coil of wire, a power supply, the Labquest data loggers with magnetic field strength detectors, a set of small compasses In 1819, Hans Oersted did a demonstration for his graduate students, trying to show that a current in a wire generated a magnetic field; to detect the magnetic field, he held a compass near the wire. At first, his demonstration failed, but then he had the insight to change the orientation of his compass, and the needle turned in response to the current; when he reversed the current flow direction, the needle of the compass turned the other way. Ampère s Law (Maxwell Equation 4) states that an electric current generates a magnetic field, and this exercise will illustrate that point. First, set up the coil and power supply in the middle of the room; if possible, keep the coil upright, but you can lay the coil flat. Don t connect the power supply yet. Array the compasses such that they are scattered inside and outside the coil at differing distances from the coil.. 1. On the next page, sketch the floor plan of the room, indicating where the coil is, and how it is oriented. The instructor will show you which way north is in the room, though the compasses should make that pretty obvious! Turn on the power supply. 2. Show, on your sketch, the orientation of the needles of each compass (use a different color pen or pencil to show the change). Try to make the orientations as accurate as possible, so that you can tell if the needle orientation is only a little affected, or if it is affected a lot. Turn off the power supply.

2 3. Calibrate all of the Labquest dataloggers and the magnetic field strength detectors by making sure they get the same reading for the terrestrial magnetic field strength. Place a detector near every spot where there is a compass. Turn on the power supply, and note, on the sketch, the value of the magnetic field strength. Do the magnetic field strengths correspond well with the amount of deflection on the compass needles? N 4. As best as you can, draw the magnetic field lines on your sketch. Draw arrows pointing towards the north pole on each line; if there are lines only connected to the south pole, draw an arrow going away from the south pole. What pattern does this resemble (think back to Lab 1)? 5. Draw a circle around either pole in your sketch; it should cross a number of magnetic field lines. The flux of the magnetic field is calculated by counting all the field lines that cross the circle that are pointing toward the pole and subtracting the number of field lines pointing away from the pole. What is the flux around the pole you have chosen? If you had chosen to draw the circle in an area far away from either pole, would the flux have been larger or smaller?

3 The ring launcher Equipment needed: ring launcher, a set of different mass and material rings, a field extender, and an electronic balance In 1865, James Clerk Maxwell published an article titled A Dynamical Theory of the Electromagnetic Field in the Philosophical Transactions of the Royal Society of London. In the article, he described a set of equations that unified the until-then separate forces of electricity and magnetism as one force called electromagnetism. Eventually, his equations were distilled into the four Maxwell s Equations of Electromagnetism. Because the phenomena were discovered long before Maxwell s time, the individual equations are known by other scientists names. In particular, Faraday s Law (Maxwell Equation 3) suggests that a changing magnetic field induces an electric field. If there is a conductive material, like a wire, in the field, an electric current will be set up in the material. A good illustration of these principles is found in the ring launcher. The launcher is simply a coil of wire attached to an electrical cord when plugged into the wall socket, the alternating current (AC) of a standard building power supply will generate an alternating direction electric current in the coil, which in turn will generate an alternating direction magnetic field within the coil and an alternating direction electric current and magnetic field in any ring of material placed around the coil. The two magnetic fields (inside the coil and inside the ring of material) will repel and move the ring up. Actually, the generation of force is still not that well explained; check out a recent attempt at explanation by a physics professor: This doesn t mean that we can t at least discover some empirical relationships about the force that propels. 5. Place the coil attached to the bulb circuit on the ring launcher and briefly turn on the launcher. What happened to the bulb? Explain this phenomenon, using the word induction or induced.

4 6. Now carefully launch (or attempt to launch) various rings of different materials and sizes. Record the information in the table below; with the height the ring goes up, you can be approximate. Ring material Ring height (cm) Ring mass (g) Maximum movement height (cm) The rings are all machined to be the same thickness and diameter, so when a ring is double the mass of another ring of the same material, it is twice the height of the other ring. 7. The conductivity of a ring depends on the area though which the current will move for the rings, the area is the inside of the ring. So if one ring is twice the mass of another ring of the same material, what can be said about the ring s area (compared to the other ring s area)? 8. So what is the mathematical relationship between ring height and ring conductivity, roughly?

5 9. Test this theory: copper has about twice the conductivity of aluminum. Look at the data for the aluminum and copper rings of the same height. Which would you predict would have a greater maximum movement height, and why? Was your prediction true? How confident are you about the ring height/conductivity connection in part b? 10. How did the split ring do? Explain the result in terms of Maxwell s Equations. 11. Place the iron core snugly in the middle of the coil, then launch a ring. Record the maximum movement height in centimeters and compare this number to the movement height of the same ring without the iron core. Why does the iron core improve the maximum movement height?

6 The non-existence of magnetic monopoles Gauss s Law for Magnetic Fields (Maxwell Equation 2) states that there can be no magnet with only one pole (a monopole). Another way to state this is the flux from any magnet must equal zero (since it has both a north and a south pole). You ll measure this by using the magnetic field sensor from Lab 1. Needed: magnetic field sensor Labquest data logger three-fingered clamp and a ringstand meter stick (maybe two of these) cylindrical rare-earth magnet Attach the three-fingered clamp to the ringstand about six inches above the base of the stand. Clamp the magnetic field sensor and adjust it so that the sensor is horizontal and the white dot (the sensor itself) is pointing downwards. Connect the sensor to the data logger, and make sure the Earth s magnetic field is being detected. Place the magnet on one of its flat sides on top of a meter stick at a convenient graduation (mark). This will be your zero cm point. Choose a positive and negative direction for distance measurements along the meter stick (that is, one direction away from the magnet should be increasing positive distances; the other direction should be increasing negative distances). Place the meter stick with the magnet onto the ringstand base such that the magnet is positioned under the magnet. Get the largest absolute value of the magnetic field possible, and this will be your start point. Remember, the sensor has a maximum value it can read, so adjust the height of the sensor higher if you max out the sensor. Remember, also, that the Earth s magnetic field is a minimum value; if this is the maximum value you obtain from the magnet when it is under the sensor, adjust the height of the sensor lower. 12. On the next page is a table of measurements of magnetic field strength you will take at various distances, both positive and negative, from the start point. You will adjust the distance by sliding the meter stick along the positive or negative direction until the desired distance is achieved. One way to keep track of how much you have moved is to keep another meter stick next to the one with the magnet, and don t move that one while the magnet meter stick moves; this way, you can figure out the distance. The + infinity and the infinity distances indicate a sufficiently far distance that you are certain you are detecting only the Earth s magnetic field; do record this field strength as well!

7 To calculate the corrected magnetic field strength, simply subtract the Earth s magnetic field strength you recorded at one of the infinite distances from the magnetic field strength at that distance. When you are done with all of the measurements, flip over the magnet and remeasure all the distances in the other set of columns provided. Original orientation of magnet Flipped orientation of magnet Distance (cm) Magnetic field strength (mt) Magnetic field strength (mt) 0 Corrected mag. Field strength (mt) Corrected mag. Field strength (mt) infinity infinity total

8 13. Sum all of the corrected magnetic field strengths in the original orientation of the magnet, and enter that into the total cell on the table. Do the same for the flipped orientation of the magnet. One of these numbers may be negative; that s okay. 14. Sum the two total numbers what do you get? If, instead of millitesla, you think of the magnetic field strength as a measure of flux (the number and orientation of magnetic field lines), argue whether you have a magnetic monopole or a magnetic dipole.