Download Electric potential

Physics 272
February 4
Spring 2014
http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html
Prof. Philip von Doetinchem
[email protected]
Phys272 - Spring 14 - von Doetinchem - 179
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Phys272 - Spring 14 - von Doetinchem - 180
Electric potential energy in an uniform field
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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 14 - von Doetinchem - 182
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 14 - von Doetinchem - 187
Calculating electric potential
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Potential of a continuous charge distribution:
Potential is zero at points that are infinitely far away
from all the charges creating the potential
Electric potential at a certain point is the
potential energy that would be associated with a
unit charge placed at that point.
Phys272 - Spring 14 - von Doetinchem - 188
Equipotential surfaces
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Equipotential lines
are similar to field
lines
→ they help us to
visualize a potential
Similar to a
topographic map: line
corresponds to same
potential
Electric field lines
Equipotential lines
Charge can be moved
Source: http://de.wikipedia.org/wiki/%C3%84quipotentialfl%C3%A4che
around this potential line
without exerting electric force
→ force must be perpendicular to equipotential line
→ field lines are perpendicular to potential lines
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Lines are closer to each other for steeper gradients
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Equipotential lines cannot intersect
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Electric field is generally not constant over an equipotential line
Phys272 - Spring 14 - von Doetinchem - 192
Potential gradient
Phys272 - Spring 14 - von Doetinchem - 194
Potential gradient
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Vector electric field can be calculated from scalar electric potential
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Potential gradient points towards the most rapid change in position.
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The shortest way to the next equipotential line is perpendicular to the old line:
→ electric field perpendicular to equipotential lines
Absolute value of potential is not important for electric field, only the local change.
Phys272 - Spring 14 - von Doetinchem - 195
Electric potential energy and electric potential
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Electric potential energy:
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Electric force is conservative
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Work done by an electric force is represented by the change in
potential energy
Electric potential:
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Potential energy per unit charge
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Potential difference between two points equals the amount of
work to move a test charge between those points.
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Potential difference between two points is given by the line
integral along the electric field
Equipotential lines are lines of constant potential. Electric
field lines and equipotential lines are perpendicular.
The electric field can be calculated from the potential
gradient of the electric potential.
Phys272 - Spring 14 - von Doetinchem - 198
Capacitance and dielectrics
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Capacitor stores electric potential and electric charge
Capacitor: just insulate two conductors (with same amount
of negative and positive charge)
Work must be done to move charges through the resulting
potential → stored electric potential energy
Applications: flashs, electronic devices
Capacitor has a certain capacitance depending on its
properties: size, shape, material
Capacitance increases when using an insulating material
between the negative and positive side (polarization)
Electric field can be seen as a store-house of electric
potential energy
Phys272 - Spring 14 - von Doetinchem - 199
Capacitors and capacitance
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Charging capacitor:
conductors initially
uncharged
Transfer electrons from
one side to the other
Net charge on capacitor
is zero
Common way of charging:
connect sides to different
terminals of a battery
Electric field is proportional to the stored charge (the same is true for the
potential difference)
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Capacitance stays constant:
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Capacitance is a measure of the ability of a capacitor to store energy.
Phys272 - Spring 14 - von Doetinchem - 200
Calculating capactiance: capacitors in vacuum
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Nothing between oppositely charged conductors
condenser microphone: capacitance changes due to flexible plate moved by sound
waves → current flow
One farad is a very large amount:
typical values:
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flash unit in a camera: microfarad (µF, 10-6)
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radio tuning unit: 10-100 picofarad (pF, 10 -12)
Phys272 - Spring 14 - von Doetinchem - 202
Spherical capacitor
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Outer sphere makes no contribution to the field
between the sphere
Phys272 - Spring 14 - von Doetinchem - 204
Cylindrical capacitor
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Important property of parallel-plate, spherical, an cylindrical
capacitors: capacitance just depends on dimensions
Phys272 - Spring 14 - von Doetinchem - 205
Capacitors in series
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Combining capacities
helps you to get the
capacitance you need
for your application
Series connection:
capacitors are connected
one after the other
Charges on all plates have
the same magnitude
Equivalent capacitance of a series combination of
capacitors is always less than any individual capacitance.
Charges on plates are the same, but if the dimensions are
different
→ potential for each capacitor different
Phys272 - Spring 14 - von Doetinchem - 208
Capacitors in parallel
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Charges can reach capacitors independently from the source
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Imagine one big capacitor that you split into multiple smaller capacitors
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The parallel combination of capacitors always has a higher capacitance than
the individual capacitances
Charges are generally not the same on each capacitor
Phys272 - Spring 14 - von Doetinchem - 209
Equivalent capacitance
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Make a drawing of the arrangement
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Identify groups of parallel and series connections
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Series connection: capacitors have same charge,
different potential difference
Parallel connection: same potential difference,
different charge
Phys272 - Spring 14 - von Doetinchem - 210
Capacitor network
Phys272 - Spring 14 - von Doetinchem - 211