Workshop: Using Visualization in Teaching Introductory E

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Workshop Using Visualization in Teaching
Introductory EMAAPT National Summer Meeting,
Edmonton, Alberta, Canada.Organizers John
Belcher, Peter Dourmashkin, Carolann Koleci,
Sahana Murthy
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MIT Class Electric Potential
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Potential Energyand Potential
Start with Gravity
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Gravity Force and Work
Gravitational force on m due to M
Work done by gravity moving m from A to B
PATH INTEGRAL
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Work Done by Earths Gravity

• Work done by gravity moving m from A to B

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PRS QuestionSign of Wg
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PRS Sign of Wg
Thinking about the sign and meaning of this
Moving from rA to rB

1. Wg is positive we do work
2. Wg is positive gravity does work
3. Wg is negative we do work
4. Wg is negative gravity does work
5. I dont know

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PRS Answer Sign of Wg
Answer 3. Wg is negative we do work

• Wg is the work that gravity does. This is the
  opposite of the work that we must do in order to
  move an object in a gravitational field.
• We are pushing against gravity ? we do positive
  work

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Work Near Earths Surface
G roughly constant

• Work done by gravity moving m from A to B

Wg depends only on endpoints not on path taken
Conservative Force
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Potential Energy (Joules)

• U0 constant depending on reference point
• Only potential difference DU has physical
  significance

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Gravitational Potential(Joules/kilogram)

• Define gravitational potential difference

That is, two particle interaction ? single
particle effect
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PRS QuestionMasses in Potentials
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PRS Masses in Potentials
Consider 3 equal masses sitting in different
gravitational potentials A) Constant, zero
potential B) Constant, non-zero
potential C) Linear potential (V ? x) but sitting
at V 0
Which statement is true?

1. None of the masses accelerate
2. Only B accelerates
3. Only C accelerates
4. All masses accelerate, B has largest acceleration
5. All masses accelerate, C has largest acceleration
6. I dont know

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PRS Answer Masses in Potentials
Answer 3. Only C (linear potential) accelerates

• When you think about potential, think height.
  For example, near the Earth
• U mgh so V gh
• Constant potential (think constant height) does
  not cause acceleration!
• The value of the potential (height) is
  irrelevant.
• Only the slope matters

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Move to Electrostatics
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Gravity - Electrostatics
Mass M Charge q ()
Both forces are conservative, so
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Potential Potential Energy
Units Joules/Coulomb Volts
Change in potential energy in moving the charged
object (charge q) from A to B
Joules
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Potential External Work
Change in potential energy in moving the charged
object (charge q) from A to B
Joules
The external work is
If the kinetic energy of the charged object does
not change,
then the external work equals the change in
potential energy
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How Big is a Volt?
Know These!

• AA, C, D Batteries 1.5 V
• Car Battery 12 V
• US Outlet 120 V (AC)
• Residential Power Line
• Our Van de Graaf
• Big Tesla Coil

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Potential Summary Thus Far

• Charges CREATE Potential Landscapes

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Potential Landscape
Positive Charge
Negative Charge
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Potential Summary Thus Far

• Charges CREATE Potential Landscapes

Charges FEEL Potential Landscapes
We work with DU (DV) because only changes matter
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2 PRS QuestionsPotential Potential Energy
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PRS Positive Charge
Place a positive charge in an electric field. It
will accelerate from

1. higher to lower electric potential lower to
   higher potential energy
2. higher to lower electric potential higher to
   lower potential energy
3. lower to higher electric potential lower to
   higher potential energy
4. lower to higher electric potential higher to
   lower potential energy

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PRS Answer Positive Charge
Answer 2. acc. from higher to lower electric
potential higher to lower potential energy

• Objects always move (accelerate) to reduce
  their potential energy. Positive charges do this
  by accelerating towards a lower potential

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PRS Negative Charge
Place a negative charge in an electric field. It
will accelerate from

1. higher to lower electric potential lower to
   higher potential energy
2. higher to lower electric potential higher to
   lower potential energy
3. lower to higher electric potential lower to
   higher potential energy
4. lower to higher electric potential higher to
   lower potential energy

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PRS Answer Negative Charge
Answer 4. Neg. acc. from lower to higher
electric potential higher to lower potential
energy

• Objects always move (accelerate) to reduce
  their potential energy. Negative charges do this
  by accelerating towards a higher potential

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Potential Landscape
Positive Charge
Negative Charge
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Creating PotentialsCalculating from E,Two
Examples
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Potential in a Uniform Field
Just like gravity, moving in field direction
reduces potential
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Potential Created by Pt Charge
Take V 0 at r 8
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PRS QuestionPoint Charge Potential
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PRS Two Point Charges
The work done in moving a positive test charge
from infinity to the point P midway between two
charges of magnitude q and q

1. is positive.
2. is negative.
3. is zero.
4. can not be determined not enough info is given.
5. I dont know

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PRS Answer Two Point Charges
3. Work from ? to P is zero

• The potential at ? is zero.
• The potential at P is zero because equal and
  opposite potentials are superimposed from the two
  point charges (remember V is a scalar, not a
  vector)

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Potential Landscape
Positive Charge
Negative Charge
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Group Problem Superposition
Consider the 3 point charges at left. What total
electric potential do they create at point P
(assuming V? 0)
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Deriving E from V
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Deriving E from V
A (x,y,z), B(xDx,y,z)
Ex Rate of change in V with y and z held
constant
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Deriving E from V
If we do all coordinates
Gradient (del) operator
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PRS QuestionsE from V
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PRS E from V
Consider the point charges you looked at earlier
You calculated V(P). From that can you derive
E(P)?

1. Yes, its kQ/a2 (up)
2. Yes, its kQ/a2 (down)
3. Yes in theory, but I dont know how to take a
   gradient
4. No, you cant get E(P) from V(P)
5. I dont know

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PRS Answer E from V
4. No, you cant get E(P) from V(P)

• The electric field is the gradient (spatial
  derivative) of the potential. Knowing the
  potential at a single point tells you nothing
  about its derivative.
• People commonly make the mistake of trying to do
  this. Dont!

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PRS E from V
The graph above shows a potential V as a function
of x. The magnitude of the electric field for x
gt 0 is

1. larger than that for x lt 0
2. smaller than that for x lt 0
3. equal to that for x lt 0
4. I dont know

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PRS Answer E from V
Answer 2. The magnitude of the electric field
for x gt 0 is smaller than that for x lt 0

• The slope is smaller for x gt 0 than x lt 0
• Translation The hill is steeper on the left
  than on the right.

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PRS E from V
The above shows potential V(x). Which is true?

1. Ex gt 0 is gt 0 and Ex lt 0 is gt 0
2. Ex gt 0 is gt 0 and Ex lt 0 is lt 0
3. Ex gt 0 is lt 0 and Ex lt 0 is lt 0
4. Ex gt 0 is lt 0 and Ex lt 0 is gt 0
5. I dont know

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PRS Answer E from V
Answer 2. Ex gt 0 is gt 0 and Ex lt 0 is lt 0

• E is the negative slope of the potential,
  negative on the left, positive on the right
• Translation Downhill is to the left on the
  left and to the right on the right.

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Group Problem E from V
A potential V(x,y,z) is plotted above. It does
not depend on x or y. What is the electric field
everywhere? Are there charges anywhere? What
sign?
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DemonstrationMaking Measuring Potential(Lab
Preview)
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Configuration Energy
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Configuration Energy
How much energy to put two charges as pictured?

1. First charge is free
2. Second charge sees first

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Configuration Energy
How much energy to put three charges as pictured?

1. Know how to do first two
2. Bring in third

Total configuration energy
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Group Problem Build It
1) How much energy did it take to assemble the
charges at left? 2) How much energy would it
take to add a 4th charge 3Q at P?
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Equipotentials
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Topographic Maps
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Equipotential Curves
All points on equipotential curve are at same
potential. Each curve represented by V(x,y)
constant
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Direction of Electric Field E
E is perpendicular to all equipotentials
Constant E field
Point Charge
Electric dipole
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Properties of Equipotentials

• E field lines point from high to low potential
• E field lines perpendicular to equipotentials
• Have no component along equipotential
• No work to move along equipotential

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Summary E Field and Potential Creating
A point charge q creates a field and potential
around it
Use superposition for systems of charges
They are related
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E Field and Potential Effects
If you put a charged particle, (charge q), in a
field
To move a charged particle, (charge q), in a
field and the particle does not change its
kinetic energy then
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Experiment 1 Equipotentials

• Download LabView file (save to desktop) and run
  it
• Log in to server and add each student to your
  group (enter your MIT ID)
• Each group will do two of the four figures (your
  choice). We will break about half way through
  for some PRS

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PRS QuestionsMidpoint Check
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PRS Lab Midpoint Equipotential
The circle is at 5 V relative to the plate.
Which of the below is the most accurate
equipotential map?

1. 1
2. 2
3. 3
4. 4
5. 5
6. 6

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PRS Answer Equipotential
Answer
The electric field is stronger between the plate
and circle than on either outer side, so the
equipotential lines must be spaced most closely
in between the two conductors.
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PRS Lab Midpoint Field Lines

1. 1
2. 2
3. 3
4. 4
5. 5
6. 6

The circle is at 5 V relative to the plate.
Which of the below is the most accurate electric
field line map?
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PRS Answer Field Lines
Answer
Field lines must be perpendicular to
equipotential surfaces, including the conductors
themselves.
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Experiment 1 Equipotentials

• Continue with the experiment
• If you finish early make sure that you talk about
  the extra questions posed at the end of the lab.
  Labs will be asked about on the exams (see, for
  example, the final exam from Fall 2005)

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PRS QuestionsLab Summary
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PRS Lab Summary Potentials
Holding the red plate at 5 V relative to the
ground of the blue plate, what is true about the
electric potential at the following locations

1. V(A) gt V(B) gt V(C) gt V(D)
2. V(A) gt V(B) V(C) gt V(D)
3. V(A) V(B) gt V(C) V(D)
4. V(D) gt V(C) V(B) gt V(A)
5. V(B) gt V(C) gt V(D) V(A)
6. V(A) gt V(D) V(C) gt V(B)

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PRS Answer Potentials
Holding the red plate at 5 V relative to the
ground of the blue plate Answer 2. V(A) gt V(B)
V(C) gt V(D)

• The potential at A is nearly 5 V.
• The potential at B C 2.5 V (they are both
  halfway).
• The potential at D is about 0 V.

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PRS Lab Summary E Field
Holding the red plate at 5 V relative to the
ground of the blue plate, what is true about the
electric field at the following locations

1. E(A) gt E(B) gt E(C) gt E(D)
2. E(A) gt E(B) E(C) gt E(D)
3. E(A) E(B) gt E(C) E(D)
4. E(D) gt E(C) E(B) gt E(A)
5. E(B) gt E(C) gt E(D) E(A)
6. E(A) gt E(D) E(C) gt E(B)

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PRS Answer E Fields
Holding the red plate at 5 V relative to the
ground of the blue plate Answer 5. E(B) gt E(C)
gt E(D) E(A)

• The potential changes most rapidly (and hence E
  is largest) at B. It also changes at C, but not
  as fast. The potential is very uniform outside,
  so the E field out there is nearly zero.

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PRS Lab Summary Charge
Holding the red plate at 5 V relative to the
ground of the blue plate, what is true about the
amount of charge near the following points

1. Q(A) Q(C) gt Q(B) Q(D)
2. Q(A) gt Q(B) Q(C) gt Q(D)
3. Q(A) Q(B) gt Q(C) Q(D)
4. Q(D) Q(C) gt Q(B) Q(A)
5. Q(B) Q(D) gt Q(A) Q(C)
6. Q(A) gt Q(D) Q(C) gt Q(B)

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PRS Answer Charge
Holding the red plate at 5 V relative to the
ground of the blue plate Answer 3. Q(A)
Q(B) gt Q(C) Q(D)

• Charges go where the field is highest (higher
  field ? more field lines ? more charges to source
  sink). Field at A B is the same, so Q is as
  well. Higher than at C D.

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PRS Kelvin Water Dropper
A drop of water falls through the right can. If
the can has positive charge on it, the separated
water drop will have

1. no net charge
2. a positive charge
3. a negative charge
4. I dont know

Can
Water Drop
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PRS Answer Kelvin Water Dropper
Answer 3. The drop has a negative charge

• The positive charge on the can repels positive
  charge to the top of the drop and attracts
  negative charge to the bottom of the drop just
  before it separates. After the drop separates
  its charge is therefore negative.

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