Electrical Potential Energy

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Electrical Potential Energy Electrical Potential

• Work, Potential Energy and the Electric Force
• Electrical Potential
• Equipotential Surfaces
• Dielectrics, Capacitors, and Energy

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Electrical Potential Energy Electrical Potential

• Work, Potential Energy and the Electric Force
• Electrical Potential
• Equipotential Surfaces
• Dielectrics, Capacitors, and Energy

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Work, Potential Energy, and the Electric Force

• Consider a positive charge q, moving west through
  a displacement S at a constant velocity in a
  region occupied by a uniform eastward electric
  field E.

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Work, Potential Energy, and the Electric Force

• The charge experiences an eastward electric
  force. For it to move at constant velocity, an
  equal westward force is required.

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Work, Potential Energy, and the Electric Force

• Work done by the westward force
• Work done by the electrical force
• Net work D kinetic energy zero

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Work, Potential Energy, and the Electric Force

• The electric force is conservative. Its work
  does not change the energy of the object.
• The westward force is nonconservative. Its work
  changes the total energy

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Work, Potential Energy, and the Electric Force

• The increase, qES, in the energy of the object is
• electrical potential energy (EPE).
• Like any other form of energy, it has SI units of
  joules (J).
• Every conservative force is associated with a
  form of potential energy.

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Work, Potential Energy, and the Electric Force

• The work done by the forces is the same, even if
  we go from the starting to the ending point by a
  meandering path. Work done by a conservative
  force is path-independent.

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Work, Potential Energy, and the Electric Force

• The increase in electrical potential energy (EPE)
  is also unaffected by our choice of path. D EPE
  depends only on E, q, and the endpoint locations.

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Work, Potential Energy, and the Electric Force

• Call the endpoints of our travel A (beginning)
  and B (end).
• Travel from A to B with a test charge q0.
• Divide through by q0

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Work, Potential Energy, and the Electric Force

• Define a new quantity, electrical potential
• and
• SI units of electrical potential

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Electrical Potential Energy Electrical Potential

• Work, Potential Energy and the Electric Force
• Electrical Potential
• Equipotential Surfaces
• Dielectrics, Capacitors, and Energy

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Electrical Potential

• Since weve talked about the electrical potential
  of points A and B, lets look at what that means.
  Consider a positive point charge, Q, and a point
  A that is a distance r from Q

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Electrical Potential

• What is the electrical potential at point A?
• To answer that question, we need to know how much
  work is required to bring a test charge from a
  point infinitely distant from Q, to point A.

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Electrical Potential

• The force required to move the test charge at a
  constant velocity is not constant with the
  distance x from Q
• In fact, the force isnt even linear with x so
  we cant calculate and use an average force.

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Electrical Potential

• Calculating the potential at point A is a
  calculus problem. The work required to move the
  test charge an infinitesimal distance dx is dW

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Electrical Potential

• Integrate to calculate W

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Electrical Potential

• The potential of a point is relative to zero
  potential, which is located infinitely far away.
• When more than one charge is present, the
  potential is the algebraic sum of the potentials
  due to each of the charges, individually.
• Electric potential is not the same thing as
  electrical potential energy.

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Electrical Potential

• Gravitational
  Electrical
• Another way to express the magnitude of the
  electric field as a potential gradient

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Electrical Potential Energy Electrical Potential

• Work, Potential Energy and the Electric Force
• Electrical Potential
• Equipotential Surfaces
• Dielectrics, Capacitors, and Energy

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Equipotential Surfaces

• Equipotential surface a collection of points
  that all have the same electrical potential.

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Equipotential Surfaces

• The electric field vector is everywhere
  perpendicular to equipotential surfaces. Why?

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Equipotential Surfaces

• The electric force does no work on charges moving
  on an equipotential surface. Why?

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Electrical Potential Energy Electrical Potential

• Work, Potential Energy and the Electric Force
• Electrical Potential
• Equipotential Surfaces
• Dielectrics, Capacitors, and Energy

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Dielectrics, Capacitors, and Energy

• Consider a parallel-plate capacitor, with a
  charge q and a plate area A, the plates separated
  by a distance d. The internal electric field
• A constant electric field E, and a distance d
  between the plates, gives the potential
  difference between the plates

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Dielectrics, Capacitors, and Energy

• Solve for the ratio of the charge to the voltage,
  and define a new quantity, capacitance
• SI units coulomb/volt C2/J farad (F)

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Dielectrics, Capacitors, and Energy

• Dielectric material fancy term for an insulating
  material.
• Separation of surface charge causes a reduction
  of the internal electric field by a factor of k,
  the dielectric constant

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Dielectrics, Capacitors, and Energy

• Fill the capacitor with a dielectric
• Its capacitance is increased by a factor of k,
  the dielectric constant.

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Dielectrics, Capacitors, and Energy
Springs Capacitors
Work is required to compress a spring Work is required to charge a capacitor
Work per unit length increases linearly with compression Work per unit charge increases with the amount of charge
Energy Energy