Download Electric potential energy

Physics 272
September 9
Fall 2014
http://www.phys.hawaii.edu/~philipvd/pvd_14_fall_272_uhm.html
Prof. Philip von Doetinchem
[email protected]
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Summary
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Electric dipole in an external field
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Potential energy of an electric dipole
=0: pot. energy minimal, stable equilibrium, dipole parallel to field
=/2: pot. energy 0, dipole perpendicular to field
= pot. energy maximum, dipole antiparallel to field
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Electric-field torque does work on dipole → change in potential energy
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Dipoles try to minimize potential energy
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An uncharged object with a dipole moment can experience a net force in a
non-uniform electric field (polarization can happen due to electric field)
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Electric flux and enclosed charge
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If there is no enclosed charged: electric field flux
going into the surface cancels flux out of the
surface.
Charges outside the enclosed surface do not give a
net electric flux.
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Flux of an uniform electric field
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Flux of a nonuniform field
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General definition of electric flux:
If flux is not uniform and area is curved
→ just integrate over infinitesimal area elements
d
General electric flux definition
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Electric flux through a sphere
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Surface is not flat, electric field not uniform
→ make smart choice on enclosing surface to simplify the problem, make use of
symmetries
Electric field is perpendicular to surface
Radius cancels out
→ the flux through any surface enclosing a single point charge is independent of the
shape or size of the surface
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Gauß's law is an alternative to Coulomb's
law and is a different way to express the
relationship between electric charge and
electric field.
Source: http://en.wikipedia.org/wiki/Carl_Gauss
Gauß's law
Carl Friedrich Gauß
(1777 - 1855)
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Electric flux is independent
of exact radius and only
depends on enclosed charge.
If you increase the size of the sphere, the electric field gets smaller, but
the area increases → electric flux stays constant
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Point charge inside a nonspherical surface
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Electric flux is positive (negative) where the electric
field points out (into) of the surface
Electric field lines can begin or end inside a region
of space only when there is charge in that region
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General form of Gauß's law
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Surface encloses multiple charges
Total electric field is the vector sum of the electric
fields of the individual charges
General form:
The total electric flux through a closed surface is
equal to the total (net) electric charge inside the
surface, divided by  0.
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Faraday's icepail experiment
http://www.youtube.com/watch?v=GNizWxAD-9M
http://youtu.be/GNizWxAD-9M?t=7m18s
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Faraday's icepail experiment
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Rod inside pail:
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Position of rod does not
matter: reading of electroscope
does not change
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Charge on inside wall opposite
of outside wall
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Charge of pail is the same as
the rod
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Take rod out: electroscope
reads zero
remove electrons on surface
(e.g., by touching)
remove rod
Conducting ball touches pail:
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Charge transfers to surface of
pail
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Take ball out: no charge on
ball, but charge on pail surface
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Applications of Gauß's Law
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If charge distribution is known and has enough symmetry the
integral can be evaluated
If we know the field we can find the charge distribution.
Typical question: what is the electric field caused by a charge
distribution on a conductor.
Excess charge at rest on a solid conductor resides entirely
on the surface, and not in the interior.
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Field of a charged conducting sphere
surface integral
apply Gauss' law
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Field inside is zero in a conductor
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Field outside is the same as for a point charge
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Field of a charged insulating sphere
apply Gauss' law
surface integral
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Electric field is a continuous function of the radius
(in contrast to conductor)
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Faraday cage
http://www.youtube.com/watch?v=WqvImbn9GG4
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Faraday cage
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Faraday cages protect against the external
influence of electric fields
All charges in a conductor reside on
the outer surface, and always
rearrange themselves
to cancel out the electric
field in the interior.
Vacuum chamber:
Electric noise from pumps
→ distorts measurement
Sensitive silicon detector
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Electric potential energy
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Charged particle moving in a field: field exerts work on particle
Work can be expressed as potential energy: position of a charge in an
electric field
Use electric potential to describe potential electric energy
→ potential differences are important for understanding of electric circuits
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Work done on a particle to move from a to b:
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change of potential energy for a conservative force (reversible):
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Electric potential energy in an uniform field
a
d
b
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Conservative force → independent of exact path
Potential energy decreases if a charged particle moves in the direction
of the electric field
If the displacement of a positive charge is in the direction of the electric
field the work is positive
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Electric potential energy of two point charges
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Potential energy of two point charges
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Potential energy defined to some reference point
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Shared property of both charges
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Electric field is the vector sum and the total potential
energy is the algebraic sum (potential energy is
NOT a vector):
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Electric potential
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Describe potential energy on
a “per unit charge” basis
(like the electric field describes
force per unit charge)
Determination of electric field is
often easier by using the potential
Source: http://de.wikipedia.org/wiki/Alessandro_Volta
Alessandro Volta
1745-1825
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Potential energy and potential are scalars
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Potential difference in circuits is often called voltage
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