Physics 241 Lab – Matt Leone
Week 3: Electric Field Maps
(Thursday - Revised)
Leone@physics.arizona.edu (email preferred), PAS 376, o. 520-621-6819
Office Hours: M & W 11:00-11:50, or by appointment.
Consultation Room (PAS 372): F 12:00-12:50
General Comments:
• Be sure not to borrow text from the lab manual (or any other source) in writing your report.
This is considered plagiarism.
• Read over the grading of your first lab report carefully. Talk to me after lab or at office hours
about issues you have about the grading. Try to understand what I took points off for so you
can get better scores next time.
• If you have your grade changed a bunch, it means you were graded early in the stack. Then I
changed my mind later about how to award points, and went back to fix yours. Its my way of
being fair even though it looks messy.
• Be sure to describe concepts accurately in theory section.
• A good online resource for I sometimes use is located at:
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/efiecon.html#c1
Lab Report Grading – A key to my grading style:
• “ok” – Not great, but not really wrong. Short for “ok, I’ll let that go.”
• “(blank)” – A little better than ok gets no comment at all.
• “NP” – No Penalty. There is a problem, but it is not your fault. Usually when you are trying to
use advanced knowledge you don’t know accurately enough yet.
• “(checkmark)” – I like it, but its not so good that I’d write “good”.
• “good” – What you did, that was good.
• “(dot)” – I looked at it, felt like commenting, but couldn’t think of anything to say. Often when
I am going through a section and getting a general idea of your understanding. Its me trying to
keep track. Really, just ignore it.
• “more” – you need to write more!
• “?” – I am baffled by what I see (and probably unhappy about it).
Lab 3 – Summary:
In this lab you will be finding the electric fields created by various distributions of charge on a
2-dimensional sheet of conductive paper. You will find the field by
1. Measuring the electric potential (voltage) to map the energy landscape (per unit charge).
2. Using math to calculate the electric field strength and direction at some places of the
conductive paper.
You learning objectives are:
• To understand the conceptual connection between electric potential and electric field.
• To understand the mathematical connection between electric potential and electric field.
• To learn how to approximate a derivative with finite-sized measurements.
Lab 3 – DEMO:
1. Hook up parallel plate conductive paper with 10 Volts of potential difference.
2. Map many points of 7 Volts to be able to sketch the line of 7 Volts equipotential.
!
Lab 3 – Matt’s theory discussion on board
1. ENERGY LANDSCAPE: U(x,y) mountain analogy. The U(x,y) mountain is created by a
positive charge on the top with Styrofoam examples. Steepness of mountain gives direction and
strength of force on a small positive test charge down the U(x,y) mountain.
2. ENERGY LANDSCAPE PER UNIT CHARGE: V(x,y) mountain analogy. The V(x,y)
mountain is created by a positive charge on the top with Styrofoam examples. Steepness of
mountain gives direction and strength of Electric Field down the V(x,y) mountain.
3. Math relating “steepness” concept to “negative slope/derivative” math operation.
o 1-D potential, V(x).
o 2-D potential, V(x,y) (Cartesian coordinates then polar coordinates for central potential)
4. Math relating F and U using slope compared to E and V … it’s the same math!
5. How to approximate a derivative in the lab.
6. Example problem of sketching electric field lines using equipotentials.
7. Example of how to find the x AND y component of the electric field at a point, E x (x o , y o ) and
E y (x o , y o ) .
8. Example problem of plotting graph of V(x,y) along
a line of symmetry.
r
9. Example problem of calculating and plotting E along line of symmetry
! using your graph of
V(x,y) along the same line of symmetry.
Lab 3 – Suggestions for Procedure !
1. Use DIPOLE conductive paper. Plot at least 5 equipotential lines (dashed/labeled) on a sheet
of special graph paper (copied and in the lab room). MAKE COPY FOR PARTNER.
2. Sketch at least 8 electric field lines (solid).
3. Make a qualitative statement of your best guess where the electric field is strongest and
weakest. Explain your reasoning. (Put this in the results of your report.)
4. Choose a point of low symmetry along one of your electric field lines. Measure each
component of the electric field at that point to verify your field line is in the correct direction.
Find the magnitude of the electric field. At that point of your graph, draw the electric field
component you found using two vectors.
At this point you should see something like:
5. On regular graph paper, graph V(x,y) along a line of symmetry.
6. On another sheet of regular graph paper, use the derivative approximation to calculate and
graph E(x,y) between pairs of V(x,y) points.
7. Redo steps 1-6 for the PARALLEL PLATE CAPACITOR paper.
8. Use the CRT paper and use voltage measurements in the x and y-directions to find the electric
field vector at three interesting points.
9. CLEAN UP LAB STATION.
Lab 3 – Report Guidelines
This week’s lab has you performing relatively simple tasks in order to understand some VERY
important concepts. For this reason, your THEORY section will be the most important of the report.
In this lab, results will mean graphs, calculated values and qualitative statements. (Ellipsis means you
should not need help here on what to write about).
1. Title - …
2. Goals - …
3. Theory –
a. Concepts: Describe the how the concept of electric potential is related to topographical
maps, and how the steepness of the topography ties this analogy to the electric field. I
will be looking for explicit discussion of E-field directionality as well as what the lines
of equipotential represent in this analogy.
b. Math: Discuss how to relate E and V mathematically. Describe in words the meaning
of the equations. Discuss how to relate F and U mathematically. Compare the math of
E&V to F&U.
4. Procedure - …
5. Results
Describe your results, but leave interpretation until the conclusion.
Your results are
• The 2 attached sketches you made of lines of constant V and lines of constant E for
each charge arrangement. (steps 1-2)
• Some typed qualitative statements about these sketches (like where E is strongest
and weakest, etc.) EXPLAIN YOUR REASONING. (step 3)
• The calculated electric field components at a single point (type the results as well as
have it drawn on graph). (step 4)
• The 2 graphs you made of V along the lines of symmetry. (step 5)
• The 2 graphs you made of E along the lines of symmetry. (step 6)
• The electric field at three interesting points of the CRT paper. (step 8)
6. Problems – answer these in lab! If you can’t get them done in time, get free help in the
tutor room: PAS 376.
a. Polarization attraction. Based on some issues in your last report, please find the force
on the upper charge from the two polarized charges beneath. Now use this result to
explain why a polarizeable peanut is attracted to a charged plate.
(NEXT PAGE)
b. Below is a sketch of some equipotential lines (dashed) and some field lines (solid). The
points where these intersect are labeled. If an electron is released from rest at point e,
which intersection will it reach some time later? Explain your reasoning. Now find the
velocity of that electron when it reaches that point.
Hint: Work from energy perspective: "K = #"U = #(q"V ) = #(#e"V ) where
1
e=1.6x10-19 Coulombs. And K = mv 2 .
2
c. Answer questions 1-7 (Qi – Qvii) and analysis question 1 (Ai) of the lab manual pages
!
20-21.
7. Conclusion – Interpret your results!based on things you discussed in your theory section.
8. Attachments