Electric Potentials

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Electric Potentials
Points to take away

• ELECTRICAL POTENTIAL ENERGY is related to the
  work done on a charge.
• The ELECTRICAL POTENTIAL DIFFERENCE is distinct
  from energy and is also called voltage.
• The ELECTRICAL POTENTIAL depends on a zero-point
  definition.

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Work Refresher

• Work tells us how energy changes
• W ?E
• Work also links force and displacement
• W F d cosT
• W F d when
• W -F d when
• Remember that work can be done ONLY by the
  component of the force that lies along the
  direction of the displacement

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Work Electricity

• We will discuss electrical work in the specific
  case of parallel plates 1) F and d are parallel
  and 2) F is constant
• W F d q0 E d
• Using the work-energy theorem, we can relate the
  work to the electrical potential energy
  difference
• W ?U Ufinal Uinitial q0 E d

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Example

• How much does the potential energy of a proton
  change if it is moved from the negative to the
  positive plate?
• If the proton is then released, how fast is it
  going just before it hits the neg. plate?

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Potential Difference

• Just like we defined the electric field as the
  force per unit charge, we define the potential
  difference (voltage) as the potential energy
  difference per unit charge
• ?V ?U/q0
• This may seem like a minor (and insignificant)
  change, but it allows us to calculate potential
  energy changes for any amount of charge

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2 Person Discussion

• Write down the potential difference when the
  proton is moved from the neg. to pos. plates in
  terms of E and d.
• If E2000 N/C and the plates are 1 cm apart, what
  is the voltage?

d
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Potential Difference

• Many things in electricity are done by convention
  (e.g., which charges are positive, which are
  negative)
• We will always treat positively charged objects
  as being at higher (more positive) electrical
  potential than negatives.
• Sometimes it is convenient to set the potential
  equal to zero at the negatively charged object,
  but this is not necessary.

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Potential Difference

• This convention means that
• positive charges move towards regions of low
  (more negative) potential
• negative charges move towards regions of high
  (more positive) potential
• What is the potential difference when the
  electric field is not uniform?
• The basic nonuniform field is due to point
  charges.

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Whole Class Discussion

• The parallel plates below have a uniform electric
  field of 30 N/C between them.
• Rank from highest (most positive) to lowest (most
  negative) the electrical potential differences
  between the sets of points listed.

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Why Bother?

• We use voltages and potentials because they are
  simpler than fields and forces.
• Energies and potentials are just magnitudes,
  there are no directions to worry about.
• It is easy to get the total energy of a
  collection of point charges using these concepts
  each charge interacts with all other charges,
  just add up energies for each interaction

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Next

• Section 16.2 Potentials and Fields
• Defining equipotentials
• Equipotentials and fields
• DONT FORGET TO DO YOUR PRE-CLASS QUIZ!