Electric Potential

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Electric Potential
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CONSERVATIVE FORCES
A conservative force gives back work that has
been done against it
Gravitational and electrostatic forces are
conservative Friction is NOT a conservative force
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CONSERVATIVE FORCES
A conservative force gives back work that has
been done against it
When we lift a mass m from ground to a height
h, the potential energy of the mass increases by
mgh. If we release the mass, it falls, picking
up kinetic energy (or speed). As the mass falls,
the potential energy is being converted into
kinetic energy. By the time it reaches the
ground, the mass has acquired a kinetic energy ½
mv2 mgh, and its potential energy is
zero. The gravitational force gave back the
work that we did when we lifted the mass.
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CONSERVATIVE FORCES
A conservative force gives back work that has
been done against it
The gravitational force is a conservative
force. The electric force is a conservative
force as well. We will be able to define a
potential energy associated with the electric
force. A charge will have potential energy when
in an electric field. Work done on the charge
(by an external agent, or by the field) will
result in changes in the potential energy of the
charge.
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CONSERVATIVE FORCES
A conservative force gives back work that has
been done against it
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POTENTIAL ENERGY
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POTENTIAL ENERGY
Potential energy is a relative quantity, that
means, it is always the difference between two
values, or it is measured with respect to
a reference point (usually infinity).
We will always refer to, or imply, the change in
potential energy (potential energy difference)
between two points.
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POTENTIAL ENERGY IN A CONSTANT FIELD E
The potential energy difference between A and
B equals the negative of the work done by the
field as the charge q is moved from A to B
?UAB UB UA -WAB -FE L q E L
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POTENTIAL ENERGY IN A CONSTANT FIELD E
E
Potential energy difference between A and B
?UAB UB UA - ? q E.dl
But E constant, and E.dl -1 E dl, then
?UAB - ? q E.dl ? q E dl q E ? dl q E L
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POTENTIAL ENERGY IN A CONSTANT FIELD E
The potential energy difference between A and
B equals the negative of the work done by the
field as the charge q is moved from A to B
?UAB q E L when the q charge is moved against
the field
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• At which point (A or B) is the potential energy
  larger,
• For a positive charge q ?
• For a negative charge q ?

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L
B
A


x
D
An electric field E a/x2 points towards
x. Calculate the potential energy difference
?UAB UB UA for a charge q
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ELECTRIC POTENTIAL DIFFERENCE
The potential energy ?U depends on the charge
being moved. In order to remove this dependence,
we introduce the concept of electric potential ?V
?VAB VB VA Electric potential difference
between the points A and B
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ELECTRICAL POTENTIAL DIFFERENCE
The potential energy ?U depends on the charge
being moved. In order to remove this dependence,
we introduce the concept of electrical potential
?V
?VAB ?UAB / q
Electrical Potential Potential Energy per Unit
Charge
?VAB Electrical potential difference between
the points A and B
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ELECTRIC POTENTIAL IN A CONSTANT FIELD E
The electric potential difference between A and B
equals the negative of the work per unit charge,
done by the field, as the charge q is moved from
A to B
?VAB VB VA -WAB /q qE L/q E L
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ELECTRICAL POTENTIAL IN A CONSTANT FIELD E
?VAB ?UAB / q
The electrical potential difference between A and
B equals the work per unit charge necessary, for
an external agent, to move a charge q from A to
B
?VAB VB VA -WAB /q - ? E.dl
But E constant, and E.dl -1 E dl, then
?VAB - ? E.dl ? E dl E ? dl E L
?UAB q E L
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ELECTRIC POTENTIAL IN A CONSTANT FIELD E ?VAB
POTENTIAL ENERGY IN A CONSTANT FIELD E ?UAB
?VAB ?UAB / q
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UNITS
Potential Energy ?U Joule ? N m (energy
work force x distance) Electric Potential ?V
Joule/Coulomb ? Volt (potential
energy/charge) Electric Field E N/C ?
V/m (electric field force/charge
potential/distance)
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Cases in Which the Electric Field E is not
Aligned with dL
E
A

?

B
Since F q E is conservative, the field E is
conservative. Then, the electrical potential
difference does not depend on the integration
path. One possibility is to integrate along the
straight line AB. This is convenient in this case
because the field E is constant, and the angle ?
between E and dL is constant.
B
E . dl E dl cos ? ? ?VAB - E cos ? ? dl
- E L cos ?
A
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Cases in Which the Electric Field E is not
Aligned with dL
E
X
A
C


?
?
L

B
Another possibility is to choose a path that goes
from A to C, and then from C to B
?VAB ?VAC ?VCB ?VAC E X
?VCB 0 (E ? dL)
Thus, ?VAB E X but X L cos ? - L
cos ?
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Rank the points A, B, and C in order
of decreasing potential energy, for a charge q
is placed at the point.
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Equipotential Surfaces (lines)
Since the field E is constant
Then, at a distance X from plate A
All the points along the dashed line, at X, are
at the same potential. The dashed line is an
equipotential line
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Equipotential Surfaces (lines)
X
It takes no work to move a charge at right
angles to an electric field E ? dL ? ? EdL
0 ? ?V 0 If a surface (line) is
perpendicular to the electric field, all the
points in the surface (line) are at the same
potential. Such surface (line) is called
EQUIPOTENTIAL
EQUIPOTENTIAL ? ELECTRIC FIELD