8/31/2011
Question I
Chapter 16
Electric Energy
and
Capacitance
Three equal positive charges are placed on the
x-axis, one at the origin, one at x = 2 m, and
the third at x = 4 m. Of the following points,
which has the greatest magnitude electric field?
a. x = 1 m
b. x = 3 m
c. x = 5 m
e. The electric field has the same magnitude at
all three positions.
Ea = -1/9,
Question II
Summary
If the distance between two equal point
charges is tripled, and the charges are
doubled, the mutual force between them
will be changed by what factor?
a. 9.0
b. 3.0
c. 4.33
d. 4/9
e. 4
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
Eb = 1/9, Ec = 1.15 in units of kQ
Potential and Potential difference
Potential due to point charges
Energy conservation
Work and Potential Energy
There is a uniform
field between the
two plates
As the charge moves
from A to B, work is
done on it
W = Fd=q Ex (xf – xi)
∆PE = - W
= - q Ex ∆x
Only for a uniform
field
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Potential Difference
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
Potential Difference, cont.
∆V = VB – VA = ∆PE / q
Potential difference is not the same as
potential energy
Another way to relate the energy and
the potential difference: ∆PE = q ∆V
Both electric potential energy and
potential difference are scalar quantities
Units of potential difference
V = J/C
A special case occurs when there is a
uniform electric field
∆V = VB – VA= -Ex ∆x
Potential Energy Compared
to Potential
Electric potential is characteristic of the
field only
Independent of any test charge that may be
placed in the field
Due to an interaction between the field and
the charge placed in the field
Energy and Charge
Movements, cont
Energy and Charge
Movements
Electric potential energy is
characteristic of the charge-field system
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
Gives more information about units: N/C = V/m
A positive charge gains electrical
potential energy when it is moved in a
direction opposite the electric field
If a charge is released in the electric
field, it experiences a force and
accelerates, gaining kinetic energy
As it gains kinetic energy, it loses an equal
amount of electrical potential energy
A negative charge loses electrical
potential energy when it moves in the
direction opposite the electric field
Summary of Positive Charge
Movements and Energy
When a positive charge is placed in
an electric field
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
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Electric Potential of a Point
Charge
Summary of Negative Charge
Movements and Energy
When a negative charge is placed in an
electric field
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 increases
Its kinetic energy increases
Work has to be done on the charge for it to
move from point A to point B
V = ke
The electric field
is proportional to
1/r2
The electric
potential is
proportional to
1/r
A potential exists at some point in
space whether or not there is a test
charge at that point
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
Potential is
plotted on the
vertical axis
In arbitrary units
Two charges have
equal magnitudes
and opposite
charges
Example of
superposition
The algebraic sum is used because
potentials are scalar quantities
Electrical Potential Energy
of Two Charges
Dipole Example
q
r
Electric Potential of
Multiple Point Charges
Electric Field and Electric
Potential Depend on Distance
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
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
PE = q2 V1 = k e
q1q2
r
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Notes About Electric Potential
Energy of Two Charges
If the charges have the same sign, PE is
positive
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
Draw a diagram of all charges
Note the point of interest
Calculate the distance from each charge
to the point of interest
Use the basic equation V = keq/r
Include the sign
The potential is positive if the charge is
positive and negative if the charge is
negative
16.13
Electric potential at NE corner
Use the superposition principle
when you have multiple charges
The force would be attractive
Work must be done to hold back the unlike
charges from accelerating as they are
brought close together
Problem Solving with Electric
Potential, cont
Problem Solving with Electric
Potential (Point Charges)
Take the algebraic sum
Remember that potential is a
scalar quantity
So no components to worry about
Problem 16.23 α particles charge 2e and mass 4 mp
and moving at 2 x 107 m/s. How
close do they get to a gold nucleus
(79e).
Summary
Potential and Potential difference
Potential due to point charges
Energy conservation
Charged conductors
Equipotential surfaces
Topography of energy landscapes
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