Transcript Equipotential Lines - Tenafly Public Schools

-Electric Potential due to a Charged
Conductor
-The Millikan Oil Drop Experiment
-Applications of Electrostatics
AP Physics C
Mrs. Coyle
Electric Potential –What we used so far!
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Electric Potential
U
V
qo
B
U
V 
   E  ds
A
qo
Potential Difference
q
V  ke
r
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Potential for a point charge
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Potential for multiple point charges
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Potential for continuous charge
distribution
qi
V  ke 
i ri
dq
V  ke 
r
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Is the surface of a charged conductor an
equipotential?
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Is the electric potential constant everywhere
inside a charged conductor and equal to its
value at the surface?
Electric Potential Difference on the Surface of
a Charged Conductor in Equilibrium
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Let A and B be points on the
surface of the charged
conductor
Let ds be the displacement from
A to B.
E is always perpendicular to the
displacement ds.
So, E · ds = 0
Therefore, the potential
difference between A and B is
also zero
B
V    E  ds  0
A
Electric Potential Difference on the
Surface of a Charged Conductor in
Equilibrium
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V is constant everywhere on the surface of a
charged conductor in equilibrium
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ΔV = 0 between any two points on the surface
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The surface of any charged conductor in
electrostatic equilibrium is an equipotential
surface
What about the inside of a charged
conductor?
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E=0 inside the conductor in equilibrium
E · ds = 0
B
V    E  ds  0
A
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Therefore, the electric potential is constant
everywhere inside the conductor and
equal to the value at the surface.
Solid Conducting
Sphere
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r<R
V=kq/R
E=0
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r=R
V=kq/R
E=kQ/R2
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r>R
V=kq/r
E=kQ/r2
Note:
 V is a Scalar related to energy
 E is a Vector related to force.
Irregularly Shaped Conductors
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The charge density is high
where the radius of
curvature is small
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The electric field is high at
sharp points
Irregularly Shaped Conductors
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The field lines are
perpendicular to the
conducting surface
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The equipotential
surfaces are
perpendicular to the
field lines
Quick Quiz 25.10
Draw a graph of the electric potential as a function of position
relative to the center of the left sphere. (Left sphere 1, radius a),
(Right sphere 2, radius c)
The centers of
the spheres are
a distance b
apart.
Quick Quiz 25.10
Answer: See below. Notice the flat plateaus at each conductor,
representing the constant electric potential inside a solid conductor.
Ex 25.9: Two Connected
Charged Spheres
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The separation distance of
the spheres is much greater
than the radius of either
sphere so their fields do not
affect each other.
Show
E1 r2
E2

r1
ΔV= O in a Cavity in a Conductor, so
Equipotential to Body of Conductor
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Assume no charges are
inside the cavity
E=0 inside the conductor
B
VB  VA    E  ds  0
A
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The electric field inside
does not depend on the
charge distribution on
the outside surface of
the conductor
Corona Discharge
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If the electric field near a conductor is sufficiently
strong, electrons resulting from random ionizations of
air molecules near the conductor accelerate away
from their parent molecules
These electrons can ionize additional molecules near
the conductor
Corona Discharge
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The glow that is observed
near a charged conductor of
a strong E-field.
It results from the
recombination of freed
electrons with the ionized air
molecules
Most likely to occur near
very sharp points
Millikan Oil-Drop Experiment
Millikan Oil-Drop Experiment
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Robert Millikan measured e, the charge of
the electron e = 1.60 x 10-19 C
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He also demonstrated the quantized nature
of this charge
Oil-Drop Experiment
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With no electric field
between the plates:
The drop reaches
terminal velocity
with FD = mg
Oil-Drop Experiment
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When an electric field is
set up between the plates
the drop moves upwards
and reaches a new
terminal velocity
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Fe = mg +FD =qE
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Solve for q
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Observed thousands of
times and always found
e=multiple of 1.6x10-19 C
Van de Graaff
Generator
Electrostatic Precipitator
On
Off
Electrostatic Precipitator
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It removes particulate
matter like ashes from
combustion gases
Corona discharge
ionizes particles of air
Most of the dirt
particles are negatively
charged and are drawn
to the walls by the
electric field of the
negative potential coil.
Xerography: uses photoconductive
material coating(Selenium) a drum