Electric Potential

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Electric Potential
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Gravitational Potential Energy
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Electric Potential Energy
?PEE (qoE)?d Fd W
?PEE qoE(dA dB )
W DET ?PEE

• Does a proton at rest at point A have more or
  less potential energy than it would at point B?

More
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Electric Potential Energy of Point Charges and
Work

• Much like the book is attracted to the earth due
  to gravity, two unlike charges are attracted to
  one another.
• Conversely, like charges repel.
• It takes positive work to move unlike charges
  away from one another and like charges closer
  together.

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Electric Potential Energy

• What would happen if the charged particle q was
  fixed in place and then particle qo was suddenly
  released from rest?
• It would accelerate away from q.
• It would accelerate towards q.
• It would stay where it is.
• How would the potential energy of this
• system change?
• It would increase.
• It would decrease.
• It would remain the same.

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Electric Potential
We know that W Fd qEd. We can define the
amount of work per unit of charge as
This is also called V (voltage) or potential
difference.
(You could conceive of an analogue as work / unit
mass, although I know of no use for it )
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Electric Potential

• SI Units joule/coulomb 1 volt (V)
• The Electric Potential is the energy per unit of
  charge (J/C).
• We may write it as to emphasize
  
• the fact that it is a potential difference and
  that the zero is arbitrary (like gravity)

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Example 1 Electric Potential

• An object with 2.5?C of charge requires
  1.00x10-3 Joules of energy to move it through an
  electric field. What is the potential difference
  through which the charge is moved?

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Characteristics of a Capacitor

E

• Since the electric field is constant, the force
  acting on a charged particle will be the same
  everywhere between the plates.
• Fe qoE

FA FB FC
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Electric Potential and Work in a Capacitor
D
WAB FdB - FdA
A
qo
WAB qoE?d
F qoE
WAB qo
?V
qo
C
If WAB qoE?d, then what is WCD?

• WCD 0 Joules because the force acts
  perpendicular to the direction of motion.
• Do you remember that W Fdcos??

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Electric Potential of a Capacitor An alternative

• From mechanics, W Fd.
• From the previous slide, W qoEd
• From the reference table, ?V W/qo

Two equal and oppositely charged plates
A
B
qo
F qoE
Uniform Electric Field
?V WAB/qo Fd/qo qoEd/qo Ed
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Example 2Parallel Plates

• A spark plug in an automobile engine consists of
  two metal conductors that are separated by a
  distance of 0.50 mm. When an electric spark jumps
  between them, the magnitude of the electric field
  is 4.8 x 107 V/m. What is the magnitude of the
  potential difference V between the conductors?

V Ed
V (4.8 x 107 V/m)(5.0 x 10-4m)
V 24,000V
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Example 3 Parallel Plates

• A proton and an electron are released from rest
  from a similarly charged plate of a capacitor.
  The electric potential is 100,000 V and the
  distance between the two plates is 0.10 mm.
• Which charge will have greater kinetic energy at
  the moment it reaches the opposite plate?
• Determine the amount of work done on each
  particle.
• Determine the speed of each particle at the
  moment it reaches the opposite plate.
• Determine the magnitude of the force acting on
  each particle.
• Determine the magnitude of the acceleration of
  each particle.

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Example 3 Parallel Plates(cont.)
p
e-

• Begin by drawing a picture and listing what is
  known
• V 100,000V
• d 0.10 mm 1.0 x 10-4m
• qe qp 1.6 x 10-19C (ignore the sign. We are
  only interested in magnitude.)

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Example 3 Parallel Plates(1 2)

• For 1, you could answer 2 first to verify.
• The answer is that the kinetic energy of both
  particles will be the same
• Why?
• because of the formula needed in question 2
  applies to both charges, and work energy.
• Hence Wproton Welectron
• qprotonV qelectronV
• Wproton Welectron (1.6x10-19C)(100,000V)
  
• Wproton Welectron 1.6x10-14 J

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Example 3 Parallel Plates(3)

• Apply the work-energy theorem to determine the
  final speed of the electron and proton.
• W ?KE
• Since the initial kinetic energy is equal to 0J
• W KEf
• W ½ mvf2
• Proton
• Electron

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Example 3 Parallel Plates(4)

• Since F qE, it will be the same for both
  particles because their charges are the same and
  the electric field is uniform between two
  parallel plates.
• We also know that W F?d. Since we know the
  distance between the plates and the work done to
  move either charge from one plate to another, we
  can determine the force as follows

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Example 3 Parallel Plates(5)

• Since we have the force acting on each particle,
  we can now calculate the acceleration of each
  particle using Newtons 2nd Law.

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Equipotential Lines

• Equipotential lines denote where the electric
  potential is the same in an electric field.
• The potential is the same anywhere on an
  equipotential surface a distance r from a point
  charge, or d from a plate.
• No work is done to move a charge along an
  equipotential surface. Hence VB VA (The
  electric potential difference does not depend on
  the path taken from A to B).
• Electric field lines and equipotential lines
  cross at right angles and point in the direction
  of decreasing potential.

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Equipotential Lines

• Parallel Plate Capacitor

Electric Field Lines
Decreasing Electric Potential / Voltage
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Equipotential Lines

• Point Charge

Electric Field Lines
Note A charged surface is also an equipotential
surface!
Decreasing Electric Potential / Voltage
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Equipotential Lines (Examples)

• http//www.cco.caltech.edu/phys1/java/phys1/EFiel
  d/EField.html

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Key Ideas

• Electric potential energy is the work required to
  bring a positive unit charge from infinity to a
  point in an electric field.
• Electric potential (V) is the change in energy
  per unit charge as the charge is brought from one
  point to another.
• The electric field between two charged plates is
  constant meaning that the force is constant
  between them as well.
• The electric potential between two points is not
  dependent on the path taken to get there.
  (Similar to gravity and gravitational PE.)
• Electric field lines and lines of equipotential
  intersect at right angles.

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Electric Potential
We know that W Fd qEd. We can define the
amount of work

• SI Units joule/coulomb 1 volt (V)
• The Electric Potential Difference is equal to the
  Work required to move a test charge from infinity
  to a point in an electric field divided by the
  magnitude of the test charge.
• The Electric Potential is the energy per unit of
  charge (J/C).