Chapter 20: Electric Potential

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Chapter 20 Electric Potential Potential Energy

• Brent Royuk
• Phys-112Concordia University

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Terminology

• Chapter Title
• Electric Potential and Electric Potential Energy
• Section 20-1
• Electric Potential Energy and the Electric
  Potential
• Electric Potential Voltage
• Note We will start by considering a point
  charge, section 20-3.

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Electric Potential Energy

• Consider two point charges separated by a
  distance r. The energy of this system is
• To derive this, you need to integrate Coulombs
  Law.
• Potential energies are always defined relatively.
  Where is U 0 for this system?
• What is negative energy?
• This is a scalar quantity.
• The Superposition Principle applies.
• We are often interested in changes, rather than
  absolutes.

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Electric Potential

• Definition
• This is called the electric potential (which
  shouldnt be confused with electric potential
  energy), the potential, or the voltage.
• Remember potential is energy per charge.
• Units
• In MKS, energy/charge Joule/Coulomb 1 Volt
• In everyday life, whats relevant about this
  infinity stuff? Nothing, really.
• Potentials tend to be differences. Another
  conventially chosen zero the earth.

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Comparisons

• An Analogy
• Coulomb Force --gt Electric Field (Force per
  charge), as
• Electric Potential Energy --gt Electric Potential
  (Energy per charge)
• How is electric potential energy similar to
  gravitational potential energy?

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Electric Potential

• For a point charge,

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Electric Potential Examples

• A battery-powered lantern is switched on for 5.0
  minutes. During this time, electrons with total
  charge -8.0 x 102 C flow through the lamp 9600 J
  of electric potential energy is converted to
  light and heat. Through what potential
  difference do the electrons move?
• Find the energy given to an electron accelerated
  through a potential difference of 50 V.
• a) The electron volt (eV)
• An electron is brought to a spot that is 12 cm
  from a point charge of 2.5 ?C. As the electron
  is repelled away, to what speed will it finally
  accelerate?
• Find the electric field and potential at the
  center of a square for positive and negative
  charges.
• What do positive and negative voltages mean?
• E-field lines point in the direction of
  decreasing V.

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Electric Potential Examples

• How much work is required to assemble the charge
  configuration below?

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Electric Potential Examples

• Consider the three charges shown in the figure
  below. How much work must be done to move the
  2.7 mC charge to infinity?

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Potential in a Uniform Field

• Lets let an electric field do some work as we
  move a test-charge against the field
• The work done by the field is
• W -qoEd
• Assuming we start at the U 0 point, we get
• U -W qoEd
• Signs? See next slide.
• Using the definition of the potential we get V
  Ed

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Potential in a Uniform Field

• Sign considerations
• Work done by the field is negative, which makes
  the potential energy positive (useful).
• Compare with gravity

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Potential in a Uniform Field
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Potential in a Uniform Field

• Example A uniform field is established by
  connecting the plates of a parallel-plate
  capacitor to a 12-V battery. a) If the plates
  are separated by 0.75 cm, what is the magnitude
  of the electric field in the capacitor? b) A
  charge of 6.24 ?C moves from the positive plate
  to the negative plate. How much does its
  electric potential energy change?

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Equipotential Surfaces

• An equipotential surface has the same potential
  at every point on the surface.
• Equipotential surfaces are perpendicular to
  electric field lines.
• The electric field is the gradient of the
  equipotential surfaces.
• How are equipotential lines oriented to the
  surface of a conductor?

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Equipotential Surfaces
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Equipotential Surfaces

• Comparative examples
• Isobars on a weather map.
• Elevation lines on a topographic map.

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Capacitors

• A plate capacitor
• It takes energy to charge the plates
• Easy at first, then harder
• Q CV
• C is the capacitance
• Bigger C means more charge per volt, bigger
  charge storage device
• 1 farad (F) 1 coulomb/volt
• ?o 8.85 x 10-12 C2/Nm2 (permittivity of free
  space)
• Connect with k
• What area plate separated by a gap of 0.10 mm
  would create a capacitance of 1.0 F?

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Dielectrics

• In real life, capacitor plates are not naked, the
  gap is filled with a dielectric material
• Dielectrics are insulators.
• Keeps plates separated, easier to build.
• Also increases the capacitance
• The dielectric constant
• Isolated capacitor insert dielectric, E is
  reduced by 1/?
• ? the dielectric constant
• C ?Co

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Dielectrics
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Electrical Energy Storage

• Graph V vs. q
• What is the area under the curve?

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Electrical Energy Storage

• A defibrillator is used to deliver 200 J of
  energy to a patients heart by charging a bank of
  capacitors to 750 volts. What is the capacitance
  of the defibrillator?