Transcript Chapter 16

Chapter 16
Electrical Energy
And
Capacitance
Review

Electric Flux  through area A:
 = EA
i.e. E A cos 
 Each
field line represents one unit of flux
 Density
 The
of field lines = #/A = E
term flux comes from analogy with fluids:
 It
is the ‘flow rate of … through an area’
 While the velocity in a stream changes,
the total flow rate has to remain constant
(conservation of water)
General
Physics
Review

Gauss’ Law:
 For
a closed surface A enclosing charge Q,
A = Q/0
ke = 1/40
 Flux begins at (+) and ends at (−) charge
 (+)
is like a water tap, (−) is like the drain
 It
is a prescription of how to draw field lines.
 It can be used to calculate E (symmetry)
 It is a mathematical statement
of Coulomb’s law (at least half of it)
General
Physics
In the “flowing water” analogy,
what represents the electric field?
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Water velocity
Cross-sectional
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Flow rate
Flow rate per area
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Physics
1.
Which best represents
the charge distribution
on a capacitor? 45
+ + + + + + + + + +
(using principles of
electrostatic equilibrium)
− − − − − − − − − −
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++++ + + + + + ++++
33%
33%
33%
−−−− − − − − − −−−−
3.
+ + + + ++++ + + + +
− − − − −−−− − − − −
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Physics
Electrical Energy
Sections 1 – 4
General
Physics
Electric Potential Energy
The electrostatic force is a
conservative force
 It is possible to define an electrical
potential energy function with this force
 Work done by a conservative force is
equal to the negative of the change in
potential energy
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General
Physics
Work and Potential Energy
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There is a uniform field between
the two plates
As the charge moves from A to
B, work is done on it
W  F cos  Dx
W  qE cos  Dx
W  qE x Dx
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The change in potential energy
between points A and B is
ΔPE = -W = -qEx Dx
 Only for a uniform electric field
EX16.1
General
Physics
Potential Difference
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In general, the potential
difference between points A
and B is defined as the
change in the potential energy
(final value minus initial value)
of a charge q moved from A
to B divided by the size of the
charge
 ΔV = VB – VA = ΔPE / q
Potential difference is not the same as potential energy
General
Physics
Potential Difference, cont.
Another way to relate the energy and the
potential difference: ΔPE = q ΔV
 Both electric potential energy and potential
difference are scalar quantities
 Units of potential difference
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1 V = 1 J/C
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A special case occurs when there is a uniform
electric field
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DV = VB – VA= -Ex Dx
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Gives more information about units of E-field: N/C = V/m
General
Physics
Energy and Charge Movements
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A positive charge gains electrical
potential energy when it is moved in a
direction opposite the electric field
When the electric field is directed
downward, point B is at a lower
potential than point A
A positive test charge that moves from
A to B loses electric potential energy
It will gain the same amount of kinetic
energy as it loses in potential energy
General
Physics
Comparison of Positive Charge to
Mass Movements
General
Physics
Summary of Positive Charge
Movements and Energy
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When a positive charge is placed in an electric
field
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It moves in the direction of the field
It moves from a point of higher potential to a point of
lower potential
Its electrical potential energy decreases
Its kinetic energy increases
Obeys conservation of energy relationship:
KEi  PEi  KE f  PE f
EX16.2a / EX16.3
or DKE  DPE
General
Physics
Summary of Negative Charge
Movements and Energy
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When a negative charge is placed in an electric
field
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It moves opposite to the direction of the field
It moves from a point of lower potential to a point of
higher potential
Its electrical potential energy decreases
Its kinetic energy increases
Obeys conservation of energy relationship:
KEi  PEi  KE f  PE f
EX16.2b
or DKE  DPE
General
Physics
Electric Potential of a Point
Charge
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The point of zero electric potential is
taken to be at an infinite distance
from the charge
The potential created by a point
charge q at any distance r from the
charge is
q
V  ke
r
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A potential exists at some point in
space whether or not there is a test
charge at that point
General
Physics
Electric Field and Electric Potential
Depend on Distance
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The electric field is
proportional to 1/r2
q
E  ke 2
r
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The electric potential is
proportional to 1/r
q
V  ke
r
General
Physics
Problem Solving with Electric
Potential (Point Charges)
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Draw a diagram of all charges
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Calculate the distance from each charge to the point of
interest
Use the basic equation V = keq/r
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Include the sign
The potential is positive if the charge is positive and negative if
the charge is negative
Use the superposition principle when you have multiple
charges
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Note the point of interest
Take the algebraic sum
Remember that potential is a scalar quantity
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So no components to worry about
General
Physics
Electric Potential for an Electric
Dipole
q
V  ke
r
MU30T13-14
General
Physics
Electric Potential of Multiple Point
Charges
Superposition principle
applies
 The total electric potential
at some point P due to
several point charges is the
algebraic sum of the
electric potentials due to
the individual charges
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EX16.4
The algebraic sum is used
because potentials are scalar
quantities
General
Physics
Electrical Potential Energy of Two
Charges
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V1 is the electric potential due
to q1 at some point P
The work required to bring q2
from infinity to P without
acceleration is q2V1
This work is equal to the
potential energy of the two
particle system
q1q2
PE  q2 V1  k e
r
General
Physics
Notes About Electric Potential Energy
of Two Charges
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If the charges have the same sign, PE is positive
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Positive work must be done to force the two charges
near one another
The like charges would repel
If the charges have opposite signs, PE is
negative
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The force would be attractive
Work must be done to hold back the unlike charges
from accelerating as they are brought close together
Active Figure: Electric Potential and Potential Energy
EX16.5
General
Physics
Conductors in Equilibrium
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The conductor has an excess of positive
charge
All of the charge resides at the surface
E = 0 inside the conductor
The electric field just outside the
conductor is perpendicular to the surface
The potential is a constant everywhere on
the surface of the conductor
W = -q(VB – VA) = 0, no work is required
to move a charge between two points that
are at the same electric potential
The potential everywhere inside the
conductor is constant and equal to its
value at the surface
General
Physics
The Electron Volt
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The electron volt (eV) is defined as the
energy that an electron gains when
accelerated through a potential difference of
1V
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Electrons in normal atoms have energies of 10’s
of eV
Excited electrons have energies of 1000’s of eV
or keV’s
High energy gamma rays have energies of
millions of eV or MeV’s
1 eV = 1.6 x 10-19 J
General
Physics
An electron and proton are
accelerated through a potential
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difference of 1V, -1V respectively,
have kinetic energies KEe, KEp.
Which statement is true?
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Impossible to tell?
<
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25%
KE
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KEe > Kep
KEe = KEp
KEe < Kep
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25%
Ke
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Physics
Equipotential Surfaces
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An equipotential surface is a surface on
which all points are at the same potential
 No
work is required to move a charge at a
constant speed on an equipotential surface
 The electric field at every point on an
equipotential surface is perpendicular to the
surface
General
Physics
Equipotentials and Electric Fields
Lines – Positive Charge
The equipotentials for a
point charge are a family
of spheres centered on
the point charge
 The field lines are
perpendicular to the
electric potential at all
points
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General
Physics
Equipotentials and Electric Fields
Lines – Dipole
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Equipotential lines are
shown in blue
Electric field lines are
shown in red
The field lines are
perpendicular to the
equipotential lines at
all points
General
Physics