Equipotentials

1
Equipotentials
Points to take away

• No electrical work is done on charges that move
  on equipotential surfaces.
• Equipotentials are related to electric fields
  the direction of the field is opposite to the
  direction of the maximum potential difference,
  the magnitude of the field is the voltage divided
  by a change in position
• A common energy unit for protons, electrons, and
  atoms is the electron-Volt.

2
Equipotentials

• The name says it all equipotentials are sets of
  points where the potentials are equal.
• What does it mean when two locations have the
  same potential?
• The voltage between those points is zero,
• ?V W/q0 0
• No electric work is done on a charge that moves
  along equipotentials.

3
Equipotentials

• But what are equipotentials?
• Like electric fields, they are just mathematical
  constructs that often simplify the situation.
• Unlike fields or forces, you only have one number
  to worry about no directions!

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Example

• What are the equipotentials for the parallel
  plates below?
• How much work is done on a positive test charge
  that moves along path I? Path II?

-
II
I
5
Drawing Equipotentials

• When dealing with individual charges, we draw
  equipotential surfaces that surround the charge.
• This tree ring structure comes from the fact
  that the potential values increase as we approach
  the charge.
• Think about looking down on the pointy end of a
  cone.
• If you cut it into slices, the highest slices
  have the smallest radius.

6
Equipotentials Fields

• There is a very close connection between
  equipotentials and field lines.
• Equipotentials MUST be perpendicular to field
  lines otherwise moving along an equipotential
  would involve work.
• Note that this doesnt tell us anything about the
  magnitude of the field or its direction.
• However, if we know the charges involved, it is
  not difficult to find the direction.

7
Equipotentials Fields

• An indication of the magnitude of the field is
  given by the spacing between equipotentials
  close spacing large field, wide spacing
  small field
• Some examples putting equipotentials and fields
  together.
• I urge all of you to play with this simulation to
  get a feel for both fields and equipotentials.

8
Equipotentials Fields

• Aside from drawing, we can also use
  equipotentials to derive the magnitudes and
  directions of constant electric fields
  quantitatively.
• Remember that we found the voltage of the
  parallel plates to be,

?V W/q0 E d E ?x So, E ?V/?x
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Equipotentials Fields

• How about the direction of the field?
• Which of the parallel plates has the higher
  potential?
• I can increase the potential of a test charge by
  moving it towards the positive plate.
• If I can only move a fixed distance which
  direction do I have to go to get the maximum
  potential increase?
• The electric field points OPPOSITE to that
  direction.

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Whole Class Discussion

• You want to suspend an object in midair using
  charged parallel plates. The object has a mass
  of 1 g and a charge of 5 µC.
• What configuration of parallel plates will you
  need? Draw it.
• What electric field magnitude will you need?
• Assuming the plates are 0.5 m apart, what is the
  voltage between the plates?
• Draw label some representative equipotentials.

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Next

• Sections 16.3 16.5 Capacitance
• capacitors
• dielectrics
• combinations of capacitors
• DONT FORGET TO DO YOUR PRE-CLASS QUIZ!