Physics 272
February 5
Spring 2015
www.phys.hawaii.edu/~philipvd/pvd_15_spring_272_uhm
go.hawaii.edu/KO
Prof. Philip von Doetinchem
philipvd@hawaii.edu
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Capacitor
http://phet.colorado.edu/en/simulation/capacitor-lab
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Moving dielectric into capacitor
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Moving dielectric into capacitor
Battery connected → potential difference constant
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Moving dielectric into capacitor
Battery disconnected → charge constant
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Moving dielectric into capacitor
For small dx approximately 1
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Moving dielectric into capacitor
The charges on the plates exert force on the slab.
The relationship between electric potential energy
and force goes back to the following:
→ energy change equals the work done against
the force to move the slab
→ applied to this case:
When the plates are connected to
the battery, the plates plus slab are
not an isolated system. In addition to
the work done on the slab by the
charges on the plates, energy is also
transferred between the battery and
the plates.
Force exerted by the plates is in the direction of
moving the slab into the capacitor when the
battery is disconnected → slab feels pulled in
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Current
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So far: electrostatics: no motion of charges
Charges in motion from one region to another are
called an electric current
Charges in conducting path in a closed loop: electric
circuit
Transfer of electric potential energy from, e.g., a
battery to, e.g., a toaster or light bulb
Nervous system of your body is also an electric
circuit
In electrostatics: no net flow of free electrons inside
the conductor → no current
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Current
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Turn on electric field inside conductor (more later)
→ charged particle in conductor feels electric force
Charged particles feel the electric force, but also
bump into the positive ions of the conducting
material → random change of motion
As result electrons move at an average drift velocity
and produce a net current (~10 -4m/s)
Electric field turns on nearly with the speed of light
(~108m/s) → electrons move all along the wire
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Metallic conduction
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Classic model, no quantum effects for electrons
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each metal atom donates one electron
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Freely moving electrons
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Stationary ions
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Electrons follow straight lines without electric fields
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Random directions
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Electric field causes to bend electron tracks
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Electrons are slowed down in collisions
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Current
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Electric field does work on the moving charges
Kinetic energy is transferred to conductor by collisions
→ vibrational energy of ions
→ temperature increase
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In metals the moving charges are always electrons
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In ionized plasmas positive and negative ions can move
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Current is the net charge flow through an area and unit time
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Conductivity of ionized water
http://www.youtube.com/watch?v=Rf2mS4J0FNg
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Different applications have a wide
range of different typical current
values
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Engine starter: ~200A
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TV: mA
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Computers: 1pA-1nA
Source: http://en.wikipedia.org/wiki/Andr%C3%A9-Marie_Amp%C3%A8re
Current
André-Marie Ampère
(1775-1836)
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Current, drift velocity, current density
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Amount of charge flowing through an area:
Current in a conductor is the product of the density of moving
charged particles, the magnitude of charge of each such
particle, the magnitude of the drift velocity, and the crosssection area
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Current, drift velocity, current density
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Caution: current I is a scalar and current density is a vector
→ current describes how charges flow in an extended object
→ current density describes what is going on locally
Here only: direct currents with only one direction in the whole
circuit
→ we will cover alternating currents later
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Current density and drift velocity in a wire
What is the electron drift velocity?
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