Lab 7: EC-5, Faraday Effect Lab Worksheet Name This sheet is the lab document your TA will use to score your lab. It is to be turned in at the end of lab. To receive full credit you must use complete sentences and explain your reasoning clearly. Last week in lab you looked at the properties of static (time-independent) magnetic fields, produced by permanent magnets and by loops of current. These static fields varied throughout space both in direction and magnitude, but were the same at all times. This week you discover some very unusual properties of time-varying magnetic fields. In particular, a time-varying magnetic field produces an electric field! This means that there is more than one way to make an electric field. You can make an electric field with electric charges, as around a point charge or between charged capacitor plates, but also an electric field accompanies a time-dependent magnetic field. So wherever there is a time-dependent magnetic field, there is also an electric field. This means that you can produce an electric field just by waving a permanent magnet around in the air. Not a very big electric field, but an electric field nonetheless. In this case the electric field is said to be induced by the time-varying magnetic field. This induced electric field exerts a force on charged particles, and so work is required to move a charged particle against this field. Pretty much like the electric fields we ve worked with before, except that there aren t any electric charges around producing this electric field. A. Induced fields in a loop of wire A simple way to measure this induced electric field is to put a piece of wire where you want to measure the electric field. At any point in a conductor where there is an electric field, there is also a current, according to r j = " E r, where r j is the current density, E r is the electric field, and " is the conductivity. This means that there can be an electric field in the wire, and a current in the wire, without a battery anywhere!
Faraday s law: Faraday discovered a quantitative relation between the induced electric field and the time-varying magnetic field. He found that the EMF around a closed loop is equal to the negative of the time rate of change of the flux through a surface bounded by the loop: " = # d$ dt. The EMF around a closed loop represents the work/coulomb required for you to move a positive charge around that closed loop. One other difference between EMF and electric potential difference is that the potential difference between two points depends only on the beginning point and the end point, and not the path between them. The electric potential works great for electric fields and forces generated from charges because those forces are conservative. The work done to move a charged particle from point A to point B against these fields depends only on the location of points A and B. This means that an electric field line like this cannot be generated by fixed electric charges. A1. Give one reason why the electric field line above cannot be generated by fixed electric charges. 2
However these are exactly the kind of field lines that are generated by Faraday s mechanism! Your book calls these non-coulomb electric fields, and the ones that can be generated from static charges it calls Coulomb electric fields. A2. Again think about the looped field line (above). Suppose that it is a circle 10 cm in diameter, and that the electric field has a constant magnitude of 1 V/cm along this path. Calculate the work you must do to very slowly move a 100 µc charge once around this loop against the field so that it ends up at its starting point. (Remember that the electric field is always tangent to the field line). A3. After you finish moving the charge, it is exactly at its starting point, and is not moving any faster than when you started, so the work you have done has not gone into kinetic energy of the particle. How can you tell that the energy has not been stored as potential energy? A4. The forces from the electric fields generated by the Faraday effect are nonconservative, meaning that energy is apparently not conserved it doesn t show up in another form in any part of the system that we are considering. Here is another example: push a heavy crate from rest along the floor in a circle so that it ends up exactly where it started, again at rest. You did work, but the crate has gained no kinetic energy. Where did the work energy go? A5. The amount or work done against non-conservative forces to get from one point to another generally depends on what path you take. In the example of A4, describe a path where you would need to do twice as much work to get back to the starting point. 3
The concept of EMF was created to describe r nonconservative electromagnetic effects. F It is defined as EMF =" path = W path /q = $ non#coulomb d r s. path q It is the work per coulomb done by the non-coulomb (non-conservative) electromagnetic forces to move a positively-charged particle from A to B along a particular path. It is not enough to know the particle started at A and ended at B. You generally have to know along which path the particle went. r B F Compare this to the electric potential difference V = "W /q = " Coulomb d r s AB #. A q This is the work per coulomb done on (or to oppose) the Coulomb electric fields to move a charge from A to B. The path between A and B doesn t matter, only the endpoints. A5. Now you measure the EMF induced in coil of wire by a changing magnetic flux. You will start by using the 800 turn coil on your lab table. Remember that this induced EMF will cause a current to flow in the wire. So connect the 800 turn coil to the Keithley Digital Multimeter (DMM), making sure that the DMM is set to measure current. Take the long bar magnet and push it toward the coil, watching the current on the DMM. Turn the bar magnet around, and do it again. Summarize your results in the table below. The long arrow on the coil indicates that the coil is wound clockwise from the bottom terminal to the top terminal in this orientation. Connect the top terminal to the red terminal of the DMM for this measurement. Red Black Motion Sign of flux Flux increase or decrease? Sign of induced current N pole moving toward coil N pole moving away from coil S pole moving toward coil S pole moving away from coil Magnet centered in coil, move N pole away Magnet centered in coil, move S pole away 4
A6. Now connect the current sensor (small silver box) to channel A of the Pasco system. Open the Lab7Settings1 file from the course web site and record your data while doing the same experiments. Try pulling the magnet very slowly at a constant speed, and then a little more quickly, again at a constant speed. The current sensor only works up to about 28 ma, so keep your currents below that. Explain the timedependence of the current. The current sensor: This box provides the interface with a voltage proportional to the current flowing into the red banana plug connection and out the black. There is very close to zero resistance between the red and black terminals, so it as if they are connected by a wire. The conversion is 1V per 0.01 amp. A7. What EMF around the loop do these currents correspond to? (Hint: remember that your DMM can also measure resistance). A8. You can also make a measurement that gives you the EMF directly. Unplug the coil from the current amplifier, and the current amplifier from the Pasco interface. Plug the coil directly into channel A of the Pasco interface. Take some data running the bar magnet into and out of the coil. How does this compare to your measurement of the current in A6? A9. Do A8 again using the 400 turn coil. How do your measurements compare to the 800 turn coil.? 5
B. Inducing currents in other conducting objects. As discussed in class, a time-dependent flux will produce currents in any conducting object. These are usually called eddy currents. They generate a magnetic field that adds to the original time-dependent flux. According to Lenz law, the direction of the induced current is such that the generated flux opposes the change in the original flux. B1. In the diagram below, draw the direction of the induced current in the ring. N S B2. In the same diagram, draw the direction of the force on the bar magnet exerted by the induced current. B3. Write a few words below about how you determined the current direction and the force direction. B4. How do the current and force direction change if the North and South pole of the magnet are switched? 6
B5. You have a 6 length of 1/8 wall copper tube, and a strong NdFeB disc magnet. Hold the tube vertically above the lab table, and drop the disc magnet down the tube. Start the magnet so that the disc surface is parallel to table. Describe below what happened. B6. The forces on the magnet are the force of gravity, and the force from the induced currents, as you investigated in B2 above. Explain why the magnet falls in the tube at a constant speed. B7. Now drop the magnet down the tube so that the flat disc surface is perpendicular to the lab table. Describe below the motion of the magnet, and explain why it does this. Hint: sketch in the field lines from the magnet. 7
B8. Now you want to make a quantitative measurement of how long it takes the magnet to drift down the tube. Double up two 6 tubes so that the time measurement is more accurate. You can use DataStudio to measure time intervals by just clicking the start and stop buttons. Do the measurement several times and average the results, then calculate the speed. B9. Now drop the magnet down a long section of 1 diameter 1/16 wall copper tube (get this from your TA there is only one of these). Note that the motion is a little different than it was in the 1/8 wall tube. Measure the time for the magnet to drop the length of the tube to get the terminal velocity, and compare it to B8. Calculate what the ratio of these times should be based on properties of the tubes. Explain. B10. Now drop the magnet down the 12 length 7/8 inside diameter, 1/8 wall copper tube (get this from your TA), and time the fall to get the terminal velocity. Explain why this is different from your result of B8. Hint: sketch the flux lines from the disk magnet. 8
C. Quantitative determination of induced fields. Dropping magnets through tubes is a lot of fun, but it is difficult to make quantitative measurements of induced currents. The magnetic field from a permanent magnet is fairly complicated, and it is difficult to make the flux from it change at a known rate. In this section you produce a magnetic field by passing a current through a large coil of wire. It takes a lot of current to make any reasonably sized field, so you use a power amplifier to supply the necessary current to the coil. If the current through the coil does not change in time, then the magnetic field it produces also does not vary in time. To investigate the Faraday effect, we want to make the magnetic field vary in time. This is done by making the current through the coil vary in time. You will use a smaller 2000 turn sense coil to measure the emf induced at various locations around the large coil. C1. The current in the large coil produces a magnetic field at its center as described by the Biot-Savart law db = µ o Idl # r ˆ. How is this field oriented with respect to the axis of the 4" r 2 coil? C2. Using the Biot-Savart law, write an expression for the magnitude of the contribution to the total field from a small current element of length dl at the center of the loop. C3. Add up the contributions of each current element along the entire length of the coiled wire of 200 turns to get an expression for the magnetic field at the center of the loop. This is the relation between current through the loop and the magnetic field at the center of the loop. 9
Here you will use the 2000 turn sense coil to measure induced emfs at various points. Hook everything up as described in section EC-5c of the lab manual, and place the 2000-turn sense coil at the center of the large coil you are driving with the power amplifier. Click on the Lab7Settings2 file to start up the data acquisition system. You should have a real-time display of the voltage sent to the power amplifier, the voltage drop across the coil, and the induced voltage in the 2000-turn sense coil. C4. Use a 10 Hz triangle-wave for the current in the large coil. Describe the time-dependence of the induced emf in the small coil, and explain its relation to the drive voltage using Faraday s law. C5. From your result in C3, calculate the EMF induced in the sense coil when it is at the center of drive coil. (You should use the average radius of the sense coil). How does this compare to your measurement? C6. Take your bar magnet and wave it around near the drive coil while the data acquisition is running. Explain what is happening. 10
C7. Change the frequency of the triangle wave, and describe quantitatively the change in emf of the small coil. C8. Change the drive voltage to a 10 Hz square wave, and describe the results. Explain these in terms of Faraday s law. 11