Transcript 24-2 Electric Potential

Lecture PowerPoints
Physics for Scientists and
Engineers, 3rd edition
Fishbane
Gasiorowicz
Thornton
© 2005 Pearson Prentice Hall
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Chapter 24
Electric Potential
Main Points of Chapter 24
• Definition of electric potential
• Calculation of electric potential of various
charge distributions
• Equipotential surfaces, conductors, and the
relationship between electric potential and
electric field
• How a conductor’s shape affects the electric
field
• Examples
24-1 Electric Potential Energy
The potential energy of a
point charge can be found
from the Coulomb force:
(24-5)
24-2 Electric Potential
Electric potential = electric
potential energy per unit
charge; no dependence on
test charge
For a point charge:
(24-6)
(24-7)
24-2 Electric Potential
• Electric potential difference is also work
needed per unit charge to move test charge
through electric field
• Therefore, electric potential can be found by
integrating the field along the path taken:
(24-9)
24-2 Electric Potential
The Electric Potential of Charge Distributions
For a set of point charges:
For a continuous
distribution of charge:
24-2 Electric Potential
Units of Electric Potential
Definition of the volt (energy
per unit charge):
(24-13)
Units of electric field – can write volts/meter
as well as newtons/coulomb
(24-14)
24-2 Electric Potential
The Electron-Volt
• An electron-volt is the energy an electron gains
when it is accelerated though a potential
difference of one volt.
• Electron-volts are useful in atomic, nuclear, and
particle physics.
24-3 Equipotentials
• An equipotential surface connects points that
are all at the same potential.
• The electric field is everywhere perpendicular to
the equipotential surface.
• The surface of a conductor is an equipotential.
24-3 Equipotentials
Electric equipotential surfaces are analogous
to contour lines on a topographic map (lines of
constant elevation)
24-4 Determining Fields from
Potentials
• To find the potential from the field: integrate along the path
• To find the field from the potential: take directional
derivatives
(24-9)
(24-29)
24-5 The Potentials of Charge Distributions
If the electric field is known:
(24-9)
For one point charge:
(24-7)
For many point charges:
(24-11)
For a continuous charge
distribution:
(24-12)
24-6 Potentials and Fields Near Conductors
• Surface of a conductor is an equipotential
• Electric field is perpendicular to surface
24-6 Potentials and Fields Near Conductors
The Role of Sharp Points on Conducting Surfaces
• Surface is equipotential
• Therefore, sharper points mean
stronger fields
• Field strength is inversely
proportional to radius of curvature
(24-37)
24-7 Electric Potentials in Technology
• Van de Graaff Accelerator
• Produces highly energetic
charged particles
24-7 Electric Potentials in Technology
• Field-Ion Microscope
• Images of individual atoms
24-7 Electric Potentials in Technology
• Xerography
• Relatively cheap way to make copies
of anything that will fit on the glass
24-7 Electric Potentials in Technology
• Scanning Tunneling Microscope
• Can image individual atoms
• Can also move single atoms to make
desired configuration
Summary of Chapter 24
Electric potential:
(24-6)
(24-9)
Relationship of field and
potential:
(24-29)
• Electric field is perpendicular to equipotential surface
• Surface of a conductor is an equipotential; field stronger
where strongly curved