Lab Notes: Electric Fields and Point Charges


This lab is very straightforward.

But there many notes that students should be read in preparation.

The notes below are intended mainly for the Phy262L students who have to do extended reports for this lab.

But Phy112 students can profit from the notes too even though they don't have to do some things like the error analysis and the log-log plot.

  1. Marked preparation readings for Phy262L students.

    The readings below must be read completely BEFORE the lab period to get the prepartion mark. There are NO part marks for having read parts of the readings.

    Yes, it is a lot of preparation readings. But the actual lab manipulations are quite short. You should have plenty of time in the first week to get a good set of data, create the 3 required figures, do the error analysis, and divide up the report writing tasks among the group members. There is only one lab report per group. In the second week of the extended lab, there will be lots of time to retake any data if needed, complete the lab report, proofread the lab report, and hand it in by the following Monday, February 14, 5pm (either to me, under my door, or by email attachment).

    Remember this lab is 15 % of the course grade in itself. So it's a big deal in itself. It's also a big deal in learning error analysis and report writing skills---which is the main raison d'Ítre for the lab.

    1. Requirements for Extended Lab Write-Ups in the lab manual.
    2. Field Mills, Electric Fields, and Point Charges in the lab manual.
    3. Supplementary Syllabus Items Phy 262L which are now as close to finalized as they ever will get.
    4. The lab notes Electric Fields and Point Charges which you should be reading write now.
    5. Wikipedia article electromagnetic shielding.
    6. Wikipedia article Faraday cage.
    7. Wikipedia article triboelectrification.
    8. Online article About Electric Field Mill Operation.

  2. Part 1 of the lab is qualitative and is concerned with electric shielding. Read Wikipedia articles on electromagnetic shielding and the Faraday cage as preparation.

    These articles help you to understand how a field mill works. Then read all 3 pages of About Electric Field Mill Operation.

    You must do 2 shielding measurements. The manual just says one.

    First, try a neutral ungrounded metal plate. The metal plate with the plastic holder can be used for this. Holding the metal plate with your hand grounds it.

    Second, use an ungrounded metal plate. Holding the plate with your hand grounds it.

    Explain the different results in your lab report.

  3. Our field mills are excellent modern devices.

    But they are designed for course laboratories, not professional work, and so are intentionally simplified devices and don't have a lot of options.

    One peculiarity is that the read-out is in kilovolts even though field mills measure electric field, not electric potential.

    Recall:

    
                           Delta V = - integral (vec E)*(dvec s)
    
                                where (vec E) is the electric field
                                and
                                (dvec s) is a differential displacement vector.
    
             
    What the read-out means is that if the measured electric field is constant and extends 100 mm and points in the direction of the extension, then the read-out electric potential would be the change in electric potential over that 100 mm.

    So to convert the read-out to electric field, one uses the formula:

                             V_read-out
                     E = ----------------   ,
                             100 mmm
             
    but this just gives E in MKS units of kV/mm. To convert to V/m (which are the MKS units of electric field), one uses the formula
                             V_read-out
                     E = ----------------  * con1  * con2 =  V_read-out * con   .
                             100 mmm
             
    Find conversion factors (AKA factors of unity) con1, con2, and con. DO IT NOW.

    ANSWER.

    Where is the electric field actually being measured? Well the manufacturer has declined to specify, but about 0.3 +/- 0.1 cm below the rotating shutter of the field mill seems to be the location of the sensor plate. So that is the location of the measured electric field---as far as I can tell.

    Electric field is a vector field. So what is the direction of the electric field measured?

    The read-out is positive for a downward field (i.e., a field pointing straight down along the axis of the rotating shutter).

    The read-out is negaiive for a upward field (i.e., a field pointing straight up along the axis of the rotating shutter).

    What if the electric field is not aligned with the axis of the rotating shutter? Some partial measurement of the electric field that would be present at the sensor plate in the absense of the field mill is being done, but it's not clear exactly how to interpret that partial measurement---the manufacturer leaves us guessing.

    So for quantitative measurements, it is best to make sure the electric field is aligned with the axis of the rotating shutter.

    In this experiment, the graphite-covered ball is aligned with that axis for all quantitative measurements.

    Just to give you comparison values for electric field, the natural electrical field of the Earth is about 150 V/m near the surface and points downward and the electrical breakdown field of air is about 3*10**6 V/m.

    The former value is pretty small and perhaps negligible compared to the error in the electric field in our experiment. When the latter value is reached, one can get an electrical discharge which can happen a from static electricity or when a circuit broken or in the form of lightning. The electrical breakdown field of air will not be reached in the measurments.

  4. The theory tested in the quantitative part of this experiment is formula for electric field of a spherically symmetric charge distribution (which is also the formula for charge distribution of any shape that is localized and remote from the point of measurement). This formula can be derived from Coulomb's law. The formula itself is
     
                                   kq 
                       (vec E) = ------- (hat r)   ,
                                  r**2
    
                      
                            where k=c**2*mu_0/(4*pi) exactly  (Wkipedia:  Coulomb's law)
    
                                   approximately 8.987 551 787 * 10**9 N m**2/C**2
    
                                   approximately 9 * 10**9 N m**2/C**2
    
                                   approximately 10**10 N m**2/C**2, 
    
                             q is charge in coulombs,
                             r is distance from the center of the distribution to the point of evaluation,
                             (hat r) is a unit vector point from the center of the distribution to the point of evaluation.
    
              
    In this experiment, we are only interested in the magnitude of the electric field, and so will be studying the formula
                                   kq 
                             E = -------   .
                                  r**2
              
    In our case, the spherically symmetric charge distribution is charge on the graphite covering of a ball.

    Graphite is a conductor and any charge put on the graphite will spread into a spherically symmetric distribution---which we know by symmetry and mutual repulsion of like charge---unless the system is perturbed from spherical symmetry by an external electric field.

    There are two procedures of charging the ball.

    1. The first way is to rub wool on a stryofoam which charges both by triboelectrification. Charge is then transferred to the to the ball by wiping ball on the styrofoam.

      What is sign of the charge on the ball?

      Well click on the triboelectric effect and determine what charge the styrofoam gets and that is the ball's charge. DO IT NOW.

      ANSWER.

    2. The second way starts the same way, but we don't wipe the styrofoam on the ball.

      We just hold the styrofoam near the ball and ground the ball by touching it with our hand while the hand also touches a good ground like the top of the field mill.

      You remove your hand before removing the styrofoam.

      What kind of charging is this?

      What is the charge on the ball in this case?

      < blink>ANSWER.

    I prefer the second procedure since it doesn't rub graphite of the ball.

    So use the second procedure, despite what the manual says.

  5. Measurements of the electric field.

    The electric field is measured using the field mill---only take the absolute value---the sign does NOT matter to the analysis of the formula.

    If you charge the ball they I asked for, it should have positive charge and give a positive reading on the field mill.

    Convert the electric field read-outs to MKS units using the conversion formula derived above.

    The distance measurements can be written down in centimeters, but for plotting convert to meters---or otherwise there is a heck of confusion in interpreting the plots.

    The distance measurements are from the CENTER of the charge distribution to the location of the sensor plate of the field mill which is 0.3 +/- 0.1 cm below the top of the field mill---as far as I can tell.

    You should use distances (in centimeters): 3, 4, and thereafter in 2 centimeter increments as far as you can go which is about 30 centimeters. NOTE I ask you to go closer than the lab manual recommends.

    You need to estimate an error (formally an uncertainty) for the distances.

    The distance error is due to both the error in the sensor plate location and the ball center location.

    I'd guess it is of order 0.3 cm---but you must decide from your own judgment about how well you are determining distance.

    You must also estimate an error in the electric field measurements.

    The first thing to do is to check if there is a background electric field when all charged objects are remote from the field mill.

    There may be a significant one or not.

    The actual background field should be of order natural electrical field of the Earth (i.e., about 150 V/m).

    You should try to field down to this level before charging the ball, but with the ball just above the field mill.