Transcript Powerpoint

Chapter 21
Electric Potential
Topics:
• Electric potential energy
• Electric potential
• Conservation of energy
Sample question:
Shown is the electric potential measured on the surface of a patient.
This potential is caused by electrical signals originating in the beating
heart. Why does the potential have this pattern, and what do these
measurements tell us about the heart’s condition?
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Slide 21-16
How many of you are in lab?
A - Yes
B - No
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Slide 21-16
Reading Quiz
3. The electric potential inside a parallel-plate capacitor
A.
B.
C.
D.
E.
is constant.
increases linearly from the negative to the positive plate.
decreases linearly from the negative to the positive plate.
decreases inversely with distance from the negative
plate.
decreases inversely with the square of the distance from
the negative plate.
Slide 21-10
Answer
3. The electric potential inside a parallel-plate capacitor
A.
B.
C.
D.
E.
is constant.
increases linearly from the negative to the positive
plate.
decreases linearly from the negative to the positive plate.
decreases inversely with distance from the negative
plate.
decreases inversely with the square of the distance from
the negative plate.
Slide 21-11
The Potential Inside a Parallel-Plate Capacitor
Uelec
Q
V
 Ex 
x
q
0 A
Slide 21-25
Reading Quiz
4. The electric field
A.
B.
C.
D.
is always perpendicular to an equipotential surface.
is always tangent to an equipotential surface.
always bisects an equipotential surface.
makes an angle to an equipotential surface that depends
on the amount of charge.
Slide 21-12
Answer
4. The electric field
A.
B.
C.
D.
is always perpendicular to an equipotential surface.
is always tangent to an equipotential surface.
always bisects an equipotential surface.
makes an angle to an equipotential surface that depends
on the amount of charge.
Slide 21-13
Connecting Potential and Field
Slide 21-31
Equipotential Maps (Contour Maps)
1.Describe the charges that
could create equipotential lines
such as those shown above.
2.
2.Describe the forces a proton
would feel at locations A and B.
3. Describe the forces an
electron would feel at locations
A and B
4.
4.Where could an electron be
placed
that is
it would
not
5. At
whichsopoint
the magnitude
of the electric field the greatest?
move?
6. Is it possible to have a zero electric field, but a non-zero electric potential?
7. Is it possible to have a zero electric potential, but a non-zero electric field?
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Slide 21-16
3D view
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Slide 21-16
Electric Potential of a Point Charge
Slide 21-27
Electric Potential: Charged Sphere
Outside of a sphere of charge Q the potential has the same form as
for a point charge Q:
If the sphere has radius R and the potential at its surface is V0, then
the potential a distance r from its center can also be written
R
V  V0
r
Slide 21-28
Graphical Representations of Electric Potential
Slide 21-13
Assembling a square of charges
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Slide 21-16
Analyzing a square of charges
Energy to Assemble
Wme = PEE = PEEf - PEEi
(PEEi = 0 J)
PEEf = q1Vnc@1 + q2V1@2 + q3V12@3 + q4V123@4
V123@4 = V1@4 +V2@4 + V3@4
Energy to move
(Move 2q from Corner to Center)
Wme = PEE = PEEf - PEEi
= q2qV123@center - q2qV123@corner
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Slide 21-16
Example Problem
Source charges create the electric
potential shown.
A. What is the potential at point
A? At which point, A, B, or C,
does the electric field have its
largest magnitude?
B. Is the magnitude of the electric
field at A greater than, equal
to, or less than at point D?
C. What is the approximate magnitude of the electric field at
point C?
D. What is the approximate direction of the electric field at
point C?
Slide 21-33
Example Problem
A proton is released from rest at point a. It then travels past point
b. What is its speed at point b?
Slide 21-23
Example Problem
A parallel-plate capacitor is held at a potential difference of 250 V.
A proton is fired toward a small hole in the negative plate with a
speed of 3.0 x 105 m/s. What is its speed when it emerges through
the hole in the positive plate? (Hint: The electric potential outside
of a parallel-plate capacitor is zero).
Slide 21-26
Example Problem
What is Q2?
Slide 21-35
Electric Potential Energy Example Problem
The electric field between two
charged plates is uniform with a
strength of 4 N/C.
a. Draw several electric field lines in the
region between the plates.
b. Determine the change in electrical
potential energy in moving a positive
4 microCoulomb charge from A to B.
c. Determine the change in electrical potential energy in moving a
negative 12 microCoulomb charge from A to B.
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Slide 21-16
Gravitational Potential Energy: Example Problem 2
A spacecraft is launched away from earth
a. Draw several gravitational field lines
in the region around Earth.
b. Determine the change in
gravitational potential energy when
the spacecraft moves from A to B,
where A is 10 million miles from
Earth and B is 30 million miles from
Earth.
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Slide 21-16
Electric Potential Energy: Example Problem 3
A small charge moves farther from a
positive source charge.
a. Draw several electric field lines in the region
around the source charge.
b. Determine the change in electrical potential
energy in moving a positive 4 nC charge
from A to B, where A is 3 cm from the source
charge and B is 10 cm away.
c. Determine the change in electrical potential
energy in moving a negative 4 nC charge
from A to B.
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Slide 21-16
Electric Potential Energy & Electric Potential:
Example Problem 4
A proton has a speed of 3.5 x 105 m/s at a point where the
electrical potential is 600 V. It moves through a point where the
electric potential is 1000 V. What is its speed at this second point?
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Slide 21-16