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Physics 272
February 7: Review
Spring 2017
http://go.hawaii.edu/j8M
Prof. Philip von Doetinchem
[email protected]
PHYS272 - Spring 17 - von Doetinchem – I/183
Coulomb's law with vectors
absolute charge values
unit vector along the direct connection
between charges q1 and q2
→ do not confuse the actual vector
and the unit vector of
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distance
between
charges
positive or negative
direction comes from
product of q1 and q2
Strength of electric force is proportional to 1/r2
The Magnitude of the electric force between two point charges is directly
proportional to the product of the charges and inversely proportional to the
square of the distance between them.
Direction is always along the line of the two charges
If both charges are positive: repulsive
If both charges are negative: repulsive
If have charges have opposite charge signs: attractive
PHYS272 - Spring 17 - von Doetinchem – I/184
Superposition of forces
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Total force is the vector sum of forces:
principle of superposition of forces:
PHYS272 - Spring 17 - von Doetinchem – I/185
Electric field of two point charges
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Electric field strength
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Electric field of two positively charged point charges
with the same magnitude of charge
Electric field as a function of x,y direction (z=0)
electric field strong
high potential
y direction
electric field strong
high potential
x direction
Electric field of
a point charge
PHYS272 - Spring 17 - von Doetinchem – I/186
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
PHYS272 - Spring 17 - von Doetinchem – I/187
Electron in a uniform field
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Release of an electron in a uniform electric field
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According to Newton's law:
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Electric potential energy of electron at rest is
converted into to kinetic energy:
PHYS272 - Spring 17 - von Doetinchem – I/188
Flux of an uniform electric field
PHYS272 - Spring 17 - von Doetinchem – I/189
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 17 - von Doetinchem – I/190
General form of Gauß's law
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Total electric field is the vector sum of the electric
fields of the individual charges inside the enclosed
surface
General form:
The total electric flux through a closed surface is
equal to the total (net) electric charge inside the
surface, divided by  0.
PHYS272 - Spring 17 - von Doetinchem – I/191
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
Conservative force
→ required work independent of exact path
Potential energy increases if charged particle moves in
opposite direction of electric force
PHYS272 - Spring 17 - von Doetinchem – I/192
Electric potential
← potential of a
point charge
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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.
Only the potential difference matters for the strength of the electric
field
PHYS272 - Spring 17 - von Doetinchem – I/193
Capacitors and capacitance
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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
Electric field is proportional
to the stored charge (the
same is true for the potential
difference)
Capacitance stays constant and only depends on the properties of
the capacitor and not the operational parameters:
← parallel plate
capacitor
PHYS272 - Spring 17 - von Doetinchem – I/194
Capacitors in series
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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 17 - von Doetinchem – I/195
Capacitors in parallel
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Charges can reach capacitors independently from the source
Imagine one big capacitor that you split into multiple smaller
capacitors
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 17 - von Doetinchem – I/196
Electric field energy
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Charging a capacitor: work against the electric field between the
plates
Energy is stored in the field in the region between the plates
PHYS272 - Spring 17 - von Doetinchem – I/197
Induced charge and polarization
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When dielectric is inserted and charge is
kept constant
→ potential difference drops
→ electric field drops
→ surface charge density drops, but not
the charge
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When dielectric is inserted and voltage is
kept constant
→ potential difference is constant
→ stored energy increases
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Redistribution of charges in dielectric
occurs: polarization
Induced charge:
PHYS272 - Spring 17 - von Doetinchem – I/198
Current, drift velocity, current density
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Amount of charge flowing through an area:
Current:
Current density:
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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
PHYS272 - Spring 17 - von Doetinchem – I/199
Resistivity
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Generally current density in conductor depends on
electric field and the properties of the material as
a function of temperature
Ohm's law:
Resistivity  of a material is the ratio of electric field
and current density
The greater the resistivity the greater the field has to
be to achieve the same current density
PHYS272 - Spring 17 - von Doetinchem – I/200
Resistance
Potential difference V
higher potential
lower potential
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Resistance
Current and potential difference are easier to
measure than current density and electric field
As current flows through electric potential difference
→ electric potential energy is lost
→ energy goes into the ions
PHYS272 - Spring 17 - von Doetinchem – I/201
Electromotive force and circuits
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Ideal source of emf
brings charge to higher
potential energy level
without increasing the
kinetic energy
Charge is not used up in
a circuit and is not
accumulating in the
circuit elements. Both
sides of the terminal of a
battery have the same
current for an ideal
source of emf.
PHYS272 - Spring 17 - von Doetinchem – I/202
Energy and power in electric circuits
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How fast is energy delivered or extracted?
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If a charge passes through a circuit element:
→ change of potential energy
BUT current stays the same → no gain of kinetic energy
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Potential energy change:
Power (energy transfer rate)
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Unit: 1J/s=1watt=1W
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Power for a pure resistance (rate of energy transfer into element):
PHYS272 - Spring 17 - von Doetinchem – I/203
Formulas provided for the midterm
PHYS272 - Spring 17 - von Doetinchem – I/204