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Chapter 20
Electric Potential and
Electric Potential Energy
Units of Chapter 20
• Electric Potential Energy and the
Electric Potential
• Energy Conservation
• The Electric Potential of Point Charges
• Equipotential Surfaces and the Electric
Field
• Capacitors and Dielectrics
• Electrical Energy Storage
20-1 Electric Potential Energy and the
Electric Potential
The electric force is conservative; therefore,
there must be a potential energy associated
with it.
It takes work to move an electric charge
perpendicular to an electric field:
As usual, the change in potential energy is
the negative of the work:
20-1 Electric Potential Energy and the
Electric Potential
Just as it was useful to define the electric field,
it is useful to define the electric potential (NOT
potential energy):
The electron volt is a unit of energy:
20-1 Electric Potential Energy and the
Electric Potential
The electric field is related to how fast the
potential is changing:
20-2 Energy Conservation
In general, for a mass moving from A to B due
to a conservative force,
For the electric force,
so that
20-2 Energy Conservation
Since the force on a negative charge is
opposite to the field direction,
Positive charges accelerate in the direction of
decreasing electric potential;
Negative charges accelerate in the direction of
increasing electric potential.
In both cases, the charge moves to a region of
lower potential energy.
20-3 The Electric Potential of Point Charges
The difference in potential energy between
points A and B is
20-3 The Electric Potential of Point Charges
Therefore, the electric potential of a
point charge is:
shown here for a positive and
negative charge, respectively
20-3 The Electric Potential of Point Charges
The electric potential of a group of point charges
is the algebraic sum of the potentials of each
charge.
20-4 Equipotential Surfaces and the
Electric Field
On a contour map, the curves mark constant
elevation; the steepest slope is perpendicular to
the curves. The closer together the curves, the
steeper the slope.
20-4 Equipotential Surfaces and the
Electric Field
Electric potential and
the electric field have
the same relationship
– there are lines (or, in
three dimensions,
surfaces) of constant
potential. The electric
field is perpendicular
to these equipotential
lines, and strongest
where the lines are
closest together.
20-4 Equipotential Surfaces and the
Electric Field
For two point charges:
20-4 Equipotential Surfaces and the
Electric Field
An ideal conductor is an equipotential surface.
Therefore, if two conductors are at the same
potential, the one that is more curved will have a
larger electric field around it. This is also true for
different parts of the same conductor.
20-4 Equipotential Surfaces and the
Electric Field
There are electric fields inside the human
body; the body is not a perfect conductor, so
there are also potential differences.
An electrocardiograph
plots the heart’s
electrical activity:
20-4 Equipotential Surfaces and the
Electric Field
An electroencephalograph measures the
electrical activity of the brain:
20-5 Capacitors and Dielectrics
A capacitor is two conducting plates separated
by a finite distance:
20-5 Capacitors and Dielectrics
The capacitance relates the charge to the
potential difference:
20-5 Capacitors and Dielectrics
A simple type of capacitor is the parallel-plate
capacitor. It consists of two plates of area A
separated by a distance d.
By calculating the electric
field created by the charges
±Q, we find that the
capacitance of a parallelplate capacitor is:
20-5 Capacitors and Dielectrics
The general properties of a parallel-plate
capacitor – that the capacitance increases as
the plates become larger and decreases as the
separation increases – are common to all
capacitors.
20-5 Capacitors and Dielectrics
A dielectric is an insulator; when placed between
the plates of a capacitor it gives a lower potential
difference with the same charge, due to the
polarization of the material. This increases the
capacitance.
20-5 Capacitors and Dielectrics
The polarization of the dielectric results in a
lower electric field within it; the new field is
given by dividing the original field by the
dielectric constant κ:
Therefore, the capacitance becomes:
20-5 Capacitors and Dielectrics
The dielectric
constant is a
property of the
material; here are
some examples:
20-5 Capacitors and Dielectrics
If the electric field in a dielectric becomes too
large, it can tear the electrons off the atoms,
thereby enabling the material to conduct. This is
called dielectric
breakdown; the
field at which this
happens is called
the dielectric
strength.
20-6 Electrical Energy Storage
By considering how much energy it takes to
move an increment of charge, ΔQ, from one plate
to the other, we can find the total energy stored
in the capacitor:
20-6 Electrical Energy Storage
The energy stored in a capacitor can be put to a
number of uses: a camera flash; a cardiac
defibrillator; and others. In addition, capacitors
form an essential part of most electrical devices
used today.
If we divide the stored energy by the volume of
the capacitor, we find the energy per unit
volume; this result is valid for any electric field:
Summary of Chapter 20
• Electric force is conservative, and has a
potential energy associated with it
• Change in electric potential energy:
• Change in electric potential:
• Relation between electric field and electric
potential:
• Total energy (electric potential energy plus
kinetic energy) is conserved
Summary of Chapter 20
• Positive charges accelerate in the direction of
increasing potential
• Negative charges accelerate in the direction of
decreasing potential
• Electric potential of a point charge:
• Electric potential energy of two point charges:
• Total electric potential and total electric
potential energy are sums of those due to
individual charges
Summary of Chapter 20
• Equipotential surfaces are those on which the
electric potential is constant.
• The electric field is perpendicular to the
equipotential surfaces.
• Ideal conductors are equipotential surfaces.
• A capacitor is a device that stores electric
charge.
• Capacitance:
Summary of Chapter 20
• Capacitance of a parallel-plate capacitor:
• A dielectric is an insulator that increases a
capacitor’s capacitance.
• A dielectric is characterized by its dielectric
constant.
• A sufficiently large electric field can cause a
dielectric to break down.
Summary of Chapter 20
• A capacitor also stores electric energy.
• Electric energy stored in a capacitor:
• Energy density in an electric field: