Download Physics 272

Physics 272
January 27
Spring 2015
www.phys.hawaii.edu/~philipvd/pvd_15_spring_272_uhm
go.hawaii.edu/KO
Prof. Philip von Doetinchem
[email protected]
PHYS272 - Spring 15 - von Doetinchem - 128
Electric dipoles
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Pair of point charges
with equal magnitude
and opposite sign
Important from
molecules to antennas
Example water:
chemical bounds cause displacement of charge
→ water is a good solvent
(e.g., salt splits to Na+ and Cl- in water)
→ very important for biochemical reactions
PHYS272 - Spring 15 - von Doetinchem - 129
Force and torque of an electric dipole
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Electric dipole in a uniform external field
Electric dipole moment points from
the negative to the positive charge
PHYS272 - Spring 15 - von Doetinchem - 130
Potential energy of an electric dipole
(see chapter 10.4)
=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)
PHYS272 - Spring 15 - von Doetinchem - 131
Electric flux and enclosed charge
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All electric field lines that enter an enclosed surface have
to come out of the surface if there is no enclosed charge
The number of electric field lines going through an area
multiplied with the area is called flux
Charges outside the enclosed surface do not give a net
electric flux.
PHYS272 - Spring 15 - von Doetinchem - 134
Flux of an uniform electric field
PHYS272 - Spring 15 - von Doetinchem - 135
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
PHYS272 - Spring 15 - von Doetinchem - 136
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
PHYS272 - Spring 15 - von Doetinchem - 137
Electric flux through a sphere
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Radius cancels out → the flux through any surface enclosing a single
point charge is independent of the shape or size of the surface
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
PHYS272 - Spring 15 - von Doetinchem - 138
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
PHYS272 - Spring 15 - von Doetinchem - 139
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Total electric field is the vector
sum of the electric fields of the
individual charges inside a surface
General form:
Source: http://en.wikipedia.org/wiki/Carl_Gauss
Gauß's law
Carl Friedrich Gauß
(1777 - 1855)
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The total electric flux through a closed surface is
equal to the total (net) electric charge inside the
surface, divided by  0.
PHYS272 - Spring 15 - von Doetinchem - 140
Faraday's icepail experiment
http://www.youtube.com/watch?v=GNizWxAD-9M
http://youtu.be/GNizWxAD-9M?t=7m18s
PHYS272 - Spring 15 - von Doetinchem - 141
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
PHYS272 - Spring 15 - von Doetinchem - 142
Electric field of a conductor
Charged conducting object
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We know that the electric field inside a conductor is zero (excess charges would move
otherwise)
Charges can only sit on the surface:
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Construct Gaussian surface inside conducting object: electric field zero → no charge inside
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You can do this for an infinite number of Gaussian surfaces inside the conductor → charge is always
zero
→ Excess charges on a solid conductor resides entirely on the surface, and not in the
interior.
PHYS272 - Spring 15 - von Doetinchem - 145
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
PHYS272 - Spring 15 - von Doetinchem - 146
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)
PHYS272 - Spring 15 - von Doetinchem - 147
Van de Graaf generator
http://www.youtube.com/watch?v=sy05B32XTYY
PHYS272 - Spring 15 - von Doetinchem - 149
Van de Graaf generator
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Can be used to build
up very high charges
on top of shell surface
PHYS272 - Spring 15 - von Doetinchem - 150
Faraday cage
http://www.youtube.com/watch?v=WqvImbn9GG4
PHYS272 - Spring 15 - von Doetinchem - 151
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
PHYS272 - Spring 15 - von Doetinchem - 152
Electric field inside a Hydrogen atom
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Hydrogen atom: proton surrounded by electron (treat both point-like)
Electron moves → charge is smeared out → position probability
follows an exponential function
PHYS272 - Spring 15 - von Doetinchem - 153
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Ratio of electric field of
Hydrogen and the
proton alone
E/Eproton
Electric field inside a Hydrogen atom
Study the influence and
relative field strength
electron+proton field
goes much quicker to
zero than than proton
alone
r/a0
PHYS272 - Spring 15 - von Doetinchem - 154
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):
PHYS272 - Spring 15 - von Doetinchem - 155
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
PHYS272 - Spring 15 - von Doetinchem - 156
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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This constant reference point should be smartly chosen depending on
the problem
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Very often only the difference of two potential energy levels matter,
which makes the reference point irrelevant
Potential energy is a shared property of both charges
Electric field is the vector sum and the total potential energy is
the algebraic sum (potential energy is NOT a vector):
PHYS272 - Spring 15 - von Doetinchem - 157
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
PHYS272 - Spring 15 - von Doetinchem - 159
Finding electric potential from electric field
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If electric field is known or can be found easily:
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Potential does not depend on the exact path
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Moving with the direction of the electric field means
moving in the direction of decreasing potential
Moving a charge slowly against an electric field
requires an external force, equal and opposite to the
electric force.
PHYS272 - Spring 15 - von Doetinchem - 160
Electron volts
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Electric field unit:
1V/m = 1 Volt/meter = 1N/C = 1 Newton/Coulomb
Useful: electron charge → electron volt
unit of energy
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For instance, very important in particle physics and
to describe processes in atoms
PHYS272 - Spring 15 - von Doetinchem - 161
Electric force and electric potential
Proton moves in a uniform electric field:
Proton feels
electric force
=1 (because proton moves in the
direction ofPHYS272
the electric
lines)
- Springfield
15 - von
Doetinchem - 162
Electric force and electric potential
PHYS272 - Spring 15 - von Doetinchem - 163