Electric Potential Energy

1
Electric Potential Energy

• A charge q in an electric field behaves similarly
  to a mass m in a gravitational field.
• The electric force F qE is conservative.

Change in potential energy from position a to b
?U is independent of the path from position a to
b
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Electric Potential
The electric field is related to how fast the
potential is changing
For a constant electric field
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Electric Potential and Potential Difference
Electric Potential
Electric potential difference ?V between a and b
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Electric Potential and Potential Energy
Difference in potential energy
Difference in electric potential

• Electric potential V has units of Joules/Coulomb
  which is defined as a Volt
• 1 Volt 1 Joule/Coulomb
• One Joule is the work done in moving one Coulomb
  of charge through a potential difference of one
  Volt.
• Electric field has units of Newtons/Coulomb or
  Volts/meter
• 1N/C 1 J/(mC) 1 V/m

5
Analogy between Electric and Gravitational Fields
m
q
E
G
d
m
q
?U q?V - qEd
?U - mgd
The charge and mass lose potential energy and
gain kinetic energy when they move in the
direction of the field.
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Kinetic Energy of a Charge Accelerated by an
Electric Field

• The kinetic energy acquired by an electron or a
  proton accelerated through a potential difference
  of 1000 Volts
• Uba qVba (1.60 x 10-19 C)(1000 V)
• 1.60 x 10-13 J 1000 eV (electron
  volts)
• 1 keV (kilo electron volt)
• One electron-volt (1 eV) is the kinetic energy
  gained by an elemental charge (electron or
  proton) when it is accelerated through a
  potential difference of one Volt.
• 1 eV 1.6 x 10-19 J

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Electric Potential Energy The Electron Volt

• Suppose a point charge q is moved between two
  points a and b in space, where the electric
  potentials due to other charges are Va and Vb.
• The change in potential energy is
• ?U Ub Ua q(Vb Va) qVba
• Unit Electron Volt (eV) 1 eV 1.6 x 10-19 J
• e.g. a proton accelerated through a potential
  difference of 200 kV acquires a kinetic energy of
  
• 200 keV (losing 200 keV of electric potential
  energy).

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Electric Potential due to Point Charge
Electric Field
Using Calculus, it can be shown
Convention V0 at infinite r
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Electric Potential due to a Point Charge
Electric potential at a distance r from a
positive charge Q
Electric potential at a distance r from a
negative charge Q
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Equipotential Surfaces

• Equipotential surfaces are surfaces of constant
  electric potential (just as lines of constant
  elevation on a topological map are lines of
  constant gravitational potential).
• Equipotential surfaces are always perpendicular
  to the direction of the electric field. (just as
  the fall line is perpendicular to the contour
  lines on a topological map).

Charged Parallel Plates Two Equal
and Opposite Charges