Chapter 25 Electric Potential

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Chapter 25 Electric Potential

• PHYS 2326-10

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Important Concepts

• Electric Work
• Electric Potential Energy
• Electric Potential
• Potential Difference
• Scalar Fields
• Vector Fields
• Gradient
• Potential Gradient

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Electric Work
4

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Important concepts

• Volt Joule/Coulomb
• Electric Field is
• 1Newton / Coulomb 1 Volt / meter
• Work is Force x distance moved and is the change
  in energy Joules

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Important Cases

• There are 2 important cases to know
• Uniform Electric Field
• Point charges

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Point Charges
dr
ds
?
s
r
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Uniform Electric Field

• E is constant and in the same direction as the
  displacement s

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Example 1chap 25 problem 17

• 4 charges q10microC are brought to a rectangle
  60cm x 15 cm. q1..q3 are fixed at the corners
  while qa is brought from far away to the lower
  left corner. Calculate change in electric
  potential energy

q2
q1
.15
qa
.6
q3
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Example 1 point charges

• eqn 25-12 is electric potential for a set of
  point charges.

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Example 2Uniform field between 2 plates

• Chap 25.1 example
• In uniform field, eqn 25.6 applies
• E(Vb-Va)/d
• Given 2 sheets separated by 0.3cm with 12 volt
  battery applying a voltage across them.

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Example 2

• E(?V)/0.003 4.0E3 V/m
• NOTE Consistancy with units is KEY

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Chapter 26 Capacitance

• PHYS 2326-10

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Capacitance and Dielectrics

• We are leaving the pure electrostatic realm
• and entering electric circuits now

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Concepts to Know

• Capacitors
• Capacitance
• Energy Density

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Capacitance

• Capacitance is the ability for an object to hold
  a charge for a given potential energy
• C Q/?V
• C is the capacitance in Farads
• that can hold a charge Q with an increase in
  potential of ?V volts.
• 1 Farad 1 coulomb of charge per Volt
• This is a huge value

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Capacitors

• Youre responsible for knowing
• Parallel Plate Capacitors
• Spherical Capacitors
• Cylindrical Capactors
• Typical values range from a few pico farads to a
  few thousand micro farads

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Spherical Capacitance

• eqn 26.2 provides for sphere of radius a relative
  to infinity to provide
• C a/k 4peo a
• example 26.2 is spherical capacitance for 2
  concentric spheres of radius Ra and Rb
• C 4peo Ra Rb/(Rb-Ra)

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Parallel Plate Capacitor

• most common type of component although most are
  rolled up or contain many plates
• C eo A/d
• Capacitance is proportional to area /inverse
  proportional to separation

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Cylindrical

• Example 26.1 covers the cylindrical capacitance
• C 2peo L / ln(Rb/Ra)
• Where Rb is the inside radius of the outer
  cylinder and Ra is the radius of the inner
  cylinder and L is the length

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Energy Stored in Capacitor

• Work done to charge a capacitor given by eqn
  26.11 which is the integral of the dw required
  for each dq of charge added
• U ½ QV ½ C V2 Q2 /2C
• Eqn 26.13 is the concept of energy density of the
  electric field
• u ½ eo E2

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Dielectrics

• Rather than k, we have used eo the permittivity
  of free space
• When dielectrics enter in we get a multiplying
  effect of the capacitance due to the dielectric
  constant ? (kappa)
• such that C ?Co