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Physics 272
January 21
Spring 2014
http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html
Prof. Philip von Doetinchem
[email protected]
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Summary
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The electric fields of electric charges are
responsible for exerting the electric force on the
other charge
An electric field creates an electric force on a test
charge q0
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Summary
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Electric field always points away from a positive
charge and toward a negative charge
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vector field as a function of location
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electric charges act as sources for electric fields
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electric field in a conductor is 0
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Electric field lines
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A field line illustrates the direction of the electric field at a certain
point
If you draw the tangent to a point on a field line you get the direction
of the field at this point
Spacing of electric field lines is chosen such the density illustrates
the magnitude
Field lines do not intersect
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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
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Water – a not so normal liquid
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One of the lightest gases known
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as a liquid much denser than expectd
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As a solid much lighter than expected
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Molecular Hydrogen bonding plays an important role
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High freezing, high melting point
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Large heat capacity, high thermal conductivity → body
temperature control
Excellent solvent due to polarity
Water ionizes and allows easy proton exchange in
molecules → richness of ionic interactions in biology
Read more: http://www1.lsbu.ac.uk/water/anmlies.html
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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
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Potential energy of an electric dipole
φ=0: pot. energy minimal, stable equilibrium, dipole parallel to field
φ=π/2: pot. energy 0, dipole perpendicular to field
φ=π: 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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Review
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Electric charge, conductors, and insulators:
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Fundamental quantity in electrostatics
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Charge is conserved
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Protons carry positive charge and electrons negative
charge
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Conductors are materials in which charge moves easily.
Charge does not move easily in insulators.
Coulomb's law:
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Review
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The electric field is the force per unit charge exerted
on a test charge at any point. Electric field radially
points away from point charge.
Electric force and field can be superposed.
Electric field lines describe direction and magnitude
of the field at a certain point.
An electric dipole is a pair of positive and negative
charges of same magnitude, but opposite sign.
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Discussion
1) Your clothing tends to cling together after going through the dryer. Why?
Would you expect more or less clinging if all your clothing were made of the
same material than if you dried different kinds of clothing together?
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Tumbling motion produces static charges in dry air
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Charge transfer is easier between different materials
2) Good electrical conductors, such as metals, are typically good conductors of
heat; electrical insulators, such as wood, are typically poor conductors of heat.
Explain why there should be a relationship between electrical conduction and
heat conduction in these materials.
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Both types of conduction involves free electrons
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http://www.doitpoms.ac.uk/tlplib/thermal_electrical/metal_thermal.php
3) If you walk across a nylon rug and then touch a large metal object such as a
doorknob, you may get a spark and a shock. Why does this tend to happen
more on dry days than on humid days? Why are you less likely to get a shock
if you touch a small metal object, such as a paper clip?
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Charge builds up easier in dry air, humid air discharges easier
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Large objects can accept more electrons
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Gauß's law
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Assumption: any distribution of charge surrounded by
an imaginary surface:
Gauß's law is a relationship between the field at all
the points on the surface and the total charge
enclosed within the surface.
How much charge is inside the imaginary surface?
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Electric flux and enclosed charge
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Analogy: positive charges flow out of the surface
and negative charges flow into the surface.
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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Electric flux and enclosed charge
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Size of the enclosed surface does not matter and
only depends on the enclosed charge
Enclosing surface can have arbitrary shape.
→ Gauß's
law
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Calculating electric flux
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Electric flux: we make the analogy of a flowing fluid,
BUT electric flux is not actually flowing.
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How to calculate flux?
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How many field lines pass through the area?
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Flux of an uniform electric field
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Unit vector points outward from a closed surface
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Electric flux through a disk
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Flat surface in a uniform electric field
sanity check: the perpendicular value is the highest
value
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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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