-Electric Potential Energy -Electric Potential

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-Electric Potential Energy -Electric Potential

• AP Physics C
• Mrs. Coyle

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Gravitational Potential Energy
A
Higher Potential Energy
DUA-gtB UB-UA - Wfield
Lower Potential Energy
B
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Consider a positive test charge in the following
electric field.

A
Higher Potential Energy
DUA-gtB UB-UA - Wfield
Lower Potential Energy
B
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Electric Potential Energy

• When a point charge qo is in an electric field E
• The force from the field is FqoE
• The work that the force of the electric field
  does to move the charge from point A to B (in the
  direction of the field) is WFd
• As the charge is moved by the electric force it
  loses potential energy but gains kinetic energy.

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Change in Electric Potential Energy

• Change in Electric Potential Energy
• (Final PE- Initial PE)
• DUA-gtB UB-UA - Wfield
• The (-) sign (- Wfield ) indicates the loss of
  potential energy when the charge moves in the
  direction of the field.

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The Electric Force is Conservative

• The force, F qoE, caused by the electric field
  and experience by the charge is conservative.
  That is
• The work done by the conservative force does not
  depend on the path taken.
• A trip back to the original position would have a
  change in energy of zero.

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• Consider an infinitesimal displacement vector ,
  ds, that is oriented tangent to a path through
  space.

ds
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• The work done by the electric field is
• W F.ds qoE.ds
• As this work is done by the field, the potential
  energy of the charge-field system is changed by
  ?U -qoE.ds
• For a finite displacement of the charge from A to
  B,

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• Change in potential energy of the system.

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Electric Potential Energy

• Which point is at a higher electric potential
  energy location? Consider a positive test charge.

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If qo is negative, then ?U is positive when the
charge is moved in the direction of the electric
field by an external force.

• Consider the analogy of a bow and arrow. If you
  pull back the arrow from the bow, the arrow will
  gain potential energy.
• In order for a negative charge to move in the
  direction of the field, an external agent must do
  positive work on the charge.

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• Electric Potential Difference (Voltage )
• work per unit charge required to move a charge
• between two positions in an electric field.
• DV W/q , qo is a positive test charge
• Scalar
• Unit 1 Volt 1 J / C
• It takes one joule of work to move a 1-coulomb
  charge through a potential difference of 1 volt

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Electric Potential

• The potential energy per unit charge, U/qo, is
  the electric potential
• The potential is independent of the value of qo
• The potential has a value at every point in an
  electric field
• The electric potential is

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Electric Potential

• The potential is a scalar quantity
• As a charged particle moves in an electric field,
  it will experience a change in potential

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Using Conservation of Energy

• Using conservation of energy, if the voltage
  difference is known, the potential energy
  difference can be calculated for a given charge.
• If all the potential energy is converted to
  kinetic energy, then final speed can be
  calculated.

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Electron-Volts

• A unit of energy
• One electron-volt is defined as the energy a
  charge-field system gains or loses when a charge
  of magnitude e (an electron or a proton) is moved
  through a potential difference of 1 volt
• 1 eV 1.60 x 10-19 J
• Remember that e1.60 x 10-19 C

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Summary of Charged Particle Released from Rest in
a Uniform Field

• A positive charge released from rest moves in the
  direction of the electric field.
• The change in potential is negative.
• The change in potential energy is negative.
• The force and acceleration are in the direction
  of the field.

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Potential in a Uniform Electric Field

• ?V-Ed
• E -?V/dThe negative sign indicates that the
  electric potential at point B is lower than at
  point A
• Another unit for electric field is 1 V/m 1 N/C
• We can interpret the electric field as the change
  of the electric potential with position.

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Electric Potential

• Which point is at a higher electric potential?

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Note

• Electric Field lines point to the lower potential

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Note

• Electric potential is independent of any test
  charges that may be placed in the field.
• Electric potential is a characteristic of the
  field.

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Equipotentials

• Point B is at a lower potential than point A
• Points B and C are at the same potential
• Equipotential surface is a surface consisting of
  a continuous distribution of points having the
  same electric potential

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Equipotentials and Field Lines

• Equipotential surfaces are always perpendicular
  to field lines.

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Equipotential Lines

• Simulation of Field with Equipotential Lines
• http//glencoe.mcgraw-hill.com/sites/0078458137/st
  udent_view0/chapter21/electric_fields_applet.html