Where are we What is this place

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Where are we ? (What is this place ??)
In our studies of electricity and magnetism, to
date we have defined electric charge and
Coulomb's force law defined the electric
field and shown the relationship between
charge and field, that is, Gauss' law
learned how to calculate the electric field
and the electrostatic forces associated
with static charge distributions.
Today we will discuss the electric potential
energy and potential difference
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Electric Potential Energy
Newtons law for the gravitational force and
Coulombs law for the electrostatic force are
mathematically identical. Thus, the general
features discussed in Phys207 for the
gravitational force will apply to the
electrostatic force. In particular, we can infer
that the electrostatic force is a conservative
force.
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Matching Game
Friction Work done around a closed path is
zero A radical political group Grav. And
Elec. Work done depends on path taken
Conservative Force
?
Non-Conservative Force
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Conservative Force

• The electric potential energy associated with
  the electric interaction between two or more
  charged particles within a system depends only on
  the spatial configuration and not how they got
  there.
• Thus we can assign an electric potential energy U
  value to the system of charges for a given
  configuration (the value U is independent of the
  arrival paths of each charge to form the same
  configuration).

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Electric Potential Energy
If the configuration of a system changes from an
initial state i to a final state f, the
electrostatic force does work W on the
particles. Recalling that W ? Fdr, where F
is force and dr is infinitesimal
displacement . The change in ?U in the
potential energy of the system is ?U
Uf - Ui -W
f
i
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Electric Potential
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Electric Potential Difference
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Electric Potential
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Path Independent
C
Consider case of constant field
B
E
Direct Path A - B
h
r
?
A
Long way around A-C-B
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Electric Potential
The units of electric potential or electric
potential difference is volts where
The volt/meter is a more conventional unit for
the E-field
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Potential Due to a Point Charge
Determine the electric potential V at r for a
point charge
Lets evaluate Eds along the path taken by the
test charge. The E field direction is radially
outward while ds is radially inward ?
Substituting for Eds we obtained
The E field for point charge is
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Potential Due to a Point Charge
Substituting for E we obtain the following
integral which is easily determined and evaluated
We have the potential due to a Point Charge.
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Potential Difference Due to a Point Charge
Determine the electric potential difference ?V
between r r1 and r r2 near a positive point
charge ??
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Potential Due to a group of Point Charges
The net potential at a point due to a group of
charges can be determined using of the
superposition principle. The potential resulting
from each charge at a given point is calculated
separately and then summed with the signs
included. For n different charges, the potential
is
qi is the value of the ith charge and ri is
distance of the given point from the ith charge.
The sum is an algebraic sum, not vector sum. An
obviously computational advantage over the
E-field whose vector directions and components
must be considered.
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Superposition Method to determine Potential for a
Dipole
Lets apply the superposition method to an
electric dipole to find the potential at an
arbitrary point P as shown in the figure. At P,
the positive point charge at distance r sets up
potential V and the negative charge at distance
r- sets up a potential V- Therefore the net
potental is
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Superposition Method to determine Potential for a
Dipole
We are usually interested only points far from
the dipole, such that rgtgtd, where d is the
distance between the two charges. Under these
conditions, the approximations that follow from
the figure that
Substituting these quantities , we obtain the
following relationship
Pqd, the electric dipole moment
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Equipotential
Adjacent points that have the same electric
potential form an equipotential surface.
General property The Electric field is
always perpendicular to an
Equipotential surface so no work is done on
charged particle that remains on this surface
The figures are E-fields (blue) and
cross-sections of Equipotential surfaces (yellow)
for a point charge and dipole
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Read the rest of Chapter 25Quiz tomorrow