Electricity

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Electricity Magnetism

• Seb Oliver
• Lecture 7 Electric Potential

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Summary Lecture 6

• Electric Flux
• Gausss Law
• Examples of using Gausss Law
• Isolated charge
• Charged shell
• Line of charge
• Uniform sphere

• Properties of Conductors
• E is zero within the conductor
• Any net charge, Q, is distributed on surface
  (surface charge density ?Q/A)
• E immediately outside is ? to surface
• ? is greatest where the radius of curvature is
  smaller

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Electric Potential
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Todays Topics

• Work Energy
• Electric Potential Energy
• Electric Potential
• Electric Equi-potential Lines
• Potential Superposition

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Work Energy
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Work

• You do work when you push an object up a hill
• The longer the hill the more work you do more
  distance
• The steeper the hill the more work you do more
  force

The work W done on an object by an agent exerting
a constant force is the product of the component
of the force in the direction of the displacement
and the magnitude of the displacement
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Work done by gravity
d
m
mg
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Work done by gravity
d
m
mg
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Energy is capacity to do work

• Gravitational Potential Energy
• Kinetic Energy
• Energy can be converted into other forms of
  energy
• When we do work on any object we transfer energy
  to it
• When an object does work it looses energy
• Energy cannot be created or destroyed

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Quiz

• A person lifts a heavy box of mass m a vertical
  distance h
• They then move a distance d, carrying the box
• How much work is done?
• A) mghd
• B) mgh mgd
• C) mgh
• D) mgd
• X) Dont know

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Quiz

• A body of mass m is moving in an orbit of radius
  r with velocity v.
• What is the work done by a centripetal force (F
  mv2/r) for each orbit
• A F 2?r
• B 0
• C mv2

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Conversion of Gravitational Potential Energy to
Kinetic Energy
Work done on object
Using Work Energy makes the problem much easier!
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Electric Potential Energy
d
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Electric Potential Energy
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Electric Potential Energy

• Work done (by electric field) on charged particle
  is QEd
• Particle has gained Kinetic Energy (QEd)
• Particle must therefore have lost Potential
  Energy ?U-QEd

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Electric Potential
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Electric Potential Difference
The electric potential energy depends on the
charge present
We can define and electric potential V which does
not depend on charge by using a test charge
Change in potential is change in potential energy
for a test charge divided by the unit charge
Remember that for uniform field
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E. Potential Potential Energy vsElectric Field
Coulomb Force
Electric Field is Coulomb Force divided by test
charge
D Potential is D Energy divided by test charge
D Energy is D Potential multiplied by test charge
Coulomb Force is thus Electric Field multiplied
by charge
If we know the potential field this allows us to
calculate changes in potential energy for any
charge introduced
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Electric Potential, units
SI Units of Electric Potential
Units are J/C
Alternatively called Volts (V)
We have seen
Thus E also has units of V/m
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Potential Difference in a Uniform field
C
d
A
B
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Potential Energy on a general path in non-uniform
field
Advanced
B
Divide the path up into small parts over which E
is constant
E
F?
A
F
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Electric Potential of a single charge
A
Advanced
E
B
if V0 at rA?
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Electric Potential of a single charge
A
Remember that
It can be shown that
E
B
if V 0 at rA?
This looks a bit like the formulae for the
potential in a Uniform Field
Potential energy Arbitrary shape
Potential difference Arbitrary shape
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Equi-potential Lines
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Electric Potential is a scalar field
Electric Potential is a scalar field
it is defined everywhere
it doesnt depend on a charge being there
but it does not have any direction
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Equi-potential Lines
Equi-potential Lines
Like elevation, potential can be displayed as
contours
Equi-potential Lines ? Field
Like elevation potential requires a zero point,
potential V0 at r?
Like slope elevation we can obtain the Electric
Field from the potential field
The Electric Field is the slope of the Electric
potential
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Potential from many charges
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Potential from more than one charge
Principle of superposition
Total Potential is sum of all individual
potentials
Each potential is
Thus Total potential is
Which can be written
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Potential Energy in 3 charges
Energy when we bring in Q2
Now bring in Q3
So finally we find
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Summary Lecture 7

• Work Energy
• Electric Potential Energy
• Electric Potential
• Potential in a uniform field
• Potential from a point charge
• Electric Equi-potential Lines
• Potential Superposition