Electric Potential

1
Electric Potential

• Physics 102
• Professor Lee Carkner
• Lecture 12

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PAL 11 Electric Field

• Ratio of lines touching 3q to lines touching -1q
  must be 3 to 1
• Extra lines from 3q go to infinity
• Positive test charge repelled

3
PAL 11 Electric Field

• To find electric field at a point between the
  charges
• q for the charges is e 1.6X10-19 C,
• 3q (3)(1.6X10-19)
• 1q (1)(1.6X10-19)
• Measure r (convert to m)
• Since both fields point the same way (to the
  right), add them up

4
Electrical Force and Energy

• Like any other force, the electrical force can do
  work
• If a force does work, the potential energy must
  decrease
• Let us represent PE as U
• Decrease in PE (DU) equal to the work
• Energy is conserved

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Potential

• DU -W -qEd
• Electric Potential (V)
• Potential given in volts (joules/coulomb)
• 1V 1 J/C

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Potential Difference

• DV Vf - Vi DU/q
• The potential differences between two points is
  the difference in electrical potential energy
  between the two points per unit charge
• For any given point with potential V
• Potential is the potential energy per unit charge
• Compare to E F/q and F qE

7
Potential Confusion

• Potential energy depends on the test charge,
  potential does not
• The symbol for potential is the same as its unit
• e.g.

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Signs

• As a positive charge moves along the electric
  field, the particle gains kinetic energy and the
  field loses potential and potential energy
• The potential energy lost by the field goes into
  work
• DU W 0 or -DU W
• An electric field will naturally move a particle
  along the field lines, doing positive work and
  resulting in a decrease in potential and
  potential energy

9

• Down
• field does work
• Up
• you do work
• field does negative work

E
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Potential Energy and Potential

• Positive charges want to move along E field,
  negative against it
• The natural movement will decrease potential
  energy
• Positive charges move naturally from high to low
  potential
• Negative charges move naturally from low to high
  potential

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Work

• Work done by the system is positive if it
  decreases the potential energy
• Work done by the system is negative if it
  increases the potential energy
• The negative work done by the system is the
  positive work done on the system

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Todays PAL

• Consider 4 situations charge moves with E
  field, charge moves against E field, - charge
  moves with E field, - charge moves against E
  field
• For each situation
• What is the sign of the change in potential
  energy?
• What is the sign of the potential difference
  (final-initial)?
• What is the sign of the work done by the system?
• Does this happen naturally?

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Work and Potential

• Positive work done by the electric force reduces
  potential energy (W -DU)
• W -q(Vf-Vi)
• If there is no potential difference there is no
  work done by the electric force

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Potential and Energy

• As a particle moves from an initial to a final
  position, energy is conserved
• Since U Vq
• Kf Ki qVi -q Vf
• Thus if you go from high to low potential
  (downhill) the particle speeds up

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Conductors

• All points on the surface must be at the same
  potential
• Since there is no field inside the conductor, the
  electric potential is constant inside the
  conductor

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Equipotentials

• Equipotentials lines are drawn perpendicular to
  the electric field
• The equipotentials for a single point charge are
  a series of concentric circles
• This would mean the same point had two values for
  V

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Point Charges and Potential

• Consider a point charge q, what is the potential
  for the area around it?
• At infinity the potential is zero
• It can be shown that
• For a single point charge

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Potential Energy and Two Charges

• U k q1 q2 / r
• Example two positive charges brought close
  together have an increase in potential energy

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Finding Potential

• Potential is a scalar (not a vector) and so can
  be found by summing the magnitudes of the
  potentials from each charge
• Total V V1 V2 V3

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Next Time

• Read Ch 17.7-17.9
• Homework, Ch 17 P 10, 16, 35, 46