View
217
Download
3
Category
Preview:
Citation preview
Potential & Field
Chapter 30
1
Potential & Field Chapter 30. Reading QuizzesChapter 30. Reading Quizzes
2
What quantity is represented by
the symbol ?
A. Electronic potential
B. Excitation potential
C. EMF
D. Electric stopping power
E. Exosphericity
3
What quantity is represented by
the symbol ?
A. Electronic potential
B. Excitation potential
C. EMF
D. Electric stopping power
E. Exosphericity
4
What is the SI unit of capacitance?
A. CapacitonA. Capaciton
B. Faraday
C. Hertz
D. Henry
E. Exciton
5
What is the SI unit of capacitance?
A. CapacitonA. Capaciton
B. Faraday
C. Hertz
D. Henry
E. Exciton
6
The electric field
A. is always perpendicular to an
equipotential surface.
B. is always tangent to an B. is always tangent to an
equipotential surface.
C. always bisects an equipotential
surface.
D. makes an angle to an equipotential
surface that depends on the amount
of charge.7
The electric field
A. is always perpendicular to an
equipotential surface.
B. is always tangent to an B. is always tangent to an
equipotential surface.
C. always bisects an equipotential
surface.
D. makes an angle to an equipotential
surface that depends on the amount
of charge.8
This chapter investigated
A. parallel capacitors A. parallel capacitors
B. perpendicular capacitors
C. series capacitors.
D. Both a and b.
E. Both a and c.
9
This chapter investigated
A. parallel capacitors A. parallel capacitors
B. perpendicular capacitors
C. series capacitors.
D. Both a and b.
E. Both a and c.
10
Connecting Potential and Field
11
Finding Electric Field from
Potential and Vice Versa
12
Finding the Electric Field from
the PotentialIn terms of the potential, the component of the electric field
in the s-direction is
Now we have reversed Equation 30.3 and have a way to
find the electric field from the potential.
EXAMPLE 30.4 Finding E from
the slope of VQUESTION:
EXAMPLE 30.4 Finding E from
the slope of V
EXAMPLE 30.4 Finding E from
the slope of V
EXAMPLE 30.4 Finding E from
the slope of V
EXAMPLE 30.4 Finding E from
the slope of V
EXAMPLE 30.4 Finding E from
the slope of V
20
Batteries and emfThe potential difference between the terminals of an ideal
battery is
In other words, a battery constructed to have an emf of In other words, a battery constructed to have an emf of
1.5V creates a 1.5 V potential difference between its
positive and negative terminals.
The total potential difference of batteries in series is simply
the sum of their individual terminal voltages:
21
Kirchoff’s Laws
∑∑ =outin
II
1. Junction Law. Net current at a junction is zero
(Conservation of Charge)
22
1. Loop Law. The sum of all potential differences around a
closed path is zero (Conservation of Energy)
Potential and Current
where R = ρL/A
23
where R = ρL/A
Electrical Circuit
� A circuit diagram is a simplified
representation of an actual circuit
� Circuit symbols are used to
represent the various elements
� Lines are used to represent wires
� The battery’s positive terminal is
indicated by the longer line
24
indicated by the longer line
Electrical Circuit
25
+−
+−
+−
+−
Conducting wires.
In equilibrium all the points of the
wires have the same potential
Electrical Circuit
+−
+− The battery is characterized by the voltage –
the potential difference between the contacts of
the battery
In equilibrium this potential difference is equal to
the potential difference between the plates of the
capacitor.
V∆
26
V∆ capacitor.
Then the charge of the capacitor is
Q C V= ∆
If we disconnect the capacitor from the battery the
capacitor will still have the charge Q and potential
difference V∆
+−
V∆
Electrical Circuit
+−
+−
V∆
Q C V= ∆
If we connect the wires the charge will disappear
+−
V∆
27
V∆If we connect the wires the charge will disappear
and there will be no potential difference
0V∆ =
Capacitors in Parallel
+−
V∆
+−
V∆
1C
2C
28
+−
V∆
All the points have
the same potentialAll the points have
the same potential
The capacitors 1 and 2 have the same potential difference V∆
Then the charge of capacitor 1 is 1 1Q C V= ∆
The charge of capacitor 2 is 2 2Q C V= ∆
Capacitors in Parallel
+−
V∆
+−V∆
1C
2CThe total charge is
1 1Q C V= ∆
2 2Q C V= ∆
1 2Q Q Q= +
1 2 1 2( )Q C V C V C C V= ∆ + ∆ = + ∆
29
+−
V∆
eqQ C V= ∆
This relation is equivalent to
the following one
1 2eqC C C= +
+−
+−
eqC
Capacitors in Parallel
� The capacitors can be replaced with
one capacitor with a capacitance of
� The equivalent capacitor must have
exactly the same external effect on the
circuit as the original capacitors
eqC
30
eqQ C V= ∆
Capacitors
31
+−
+−
V∆
eqQ C V= ∆
The equivalence means that
Capacitors in Series
+−
1V∆
+−
2V∆
1C 2C
32
+−
V∆
1C
1 2V V V∆ = ∆ + ∆
Capacitors in Series
+−
1V∆
+−
2V∆
C
1 2
1 2
Q QV V V
C C∆ = ∆ + ∆ = +
The total charge
is equal to 01 2Q Q Q= =
1 1Q C V= ∆2 2Q C V= ∆
33
+−
V∆
1C 2C
eq
QV
C∆ =
1 2
1 1 1
eqC C C= +
1 2
1 2
eq
C CC
C C=
+
Capacitors in Series
� An equivalent capacitor can be found
that performs the same function as the
series combination
� The potential differences add up to the
battery voltage
34
Quiz: Find the equivalent capacitance for the circuit.
in parallel
1 2 1 3 4eqC C C= + = + =
6C C C= + =
35
in parallel
1 2 8eqC C C= + =
in series
1 2
1 2
8 84
8 8eq
C CC
C C
⋅= = =
+ +in parallel
1 2 6eqC C C= + =
Example
in parallel
1 2 1 3 4eqC C C= + = + =
6C C C= + =
36
in parallel
1 2 8eqC C C= + =
in series
1 2
1 2
8 84
8 8eq
C CC
C C
⋅= = =
+ +in parallel
1 2 6eqC C C= + =
Q C V= ∆
37
Quiz: what are the charges stored?
38
39
� Assume the capacitor is being charged
and, at some point, has a charge q on it
� The work needed to transfer a small
charge from one plate to the other is
equal to the change of potential energy
Energy Stored in a Capacitor
q A
q∆
q
40
� If the final charge of the capacitor is Q,
then the total work required is
q− B
qdW Vdq dq
C= ∆ =
2
0 2
Q q QW dq
C C= =∫
� The work done in charging the capacitor is
equal to the electric potential energy U of a
capacitor
Energy Stored in a Capacitor
Q
2
0 2
Q q QW dq
C C= =∫
Q C V= ∆
41
This applies to a capacitor of any geometry
Q−
221 1
( )2 2 2
QU Q V C V
C= = ∆ = ∆
One of the main application of capacitor:
� capacitors act as energy reservoirs that can be
slowly charged and then discharged quickly to
Energy Stored in a Capacitor: Application
221 1
( )2 2 2
QU Q V C V
C= = ∆ = ∆
42
provide large amounts of energy in a short pulse
Q
Q−
Q C V= ∆
43
The Energy in the Electric
Field
The energy density of an electric field, such as the one
inside a capacitor, is
The energy density has units J/m3.
44
45
Dielectrics• The dielectric constant, like density or specific heat, is a
property of a material.
• Easily polarized materials have larger dielectric constants
than materials not easily polarized.
• Vacuum has κ = 1 exactly.• Vacuum has κ = 1 exactly.
• Filling a capacitor with a dielectric increases the
capacitance by a factor equal to the dielectric constant.
46
Chapter 30. Summary SlidesChapter 30. Summary Slides
General Principles
General Principles General Principles
Important Concepts Important Concepts
Applications Applications
Chapter 30. QuestionsChapter 30. Questions
What total potential difference is
created by these three batteries?
A. 1.0 V
B. 2.0 V
C. 5.0 V
D. 6.0 V
E. 7.0 V
What total potential difference is
created by these three batteries?
A. 1.0 V
B. 2.0 V
C. 5.0 V
D. 6.0 V
E. 7.0 V
Which potential-energy
graph describes this
electric field?
Which potential-energy
graph describes this
electric field? Which set of equipotential surfaces
matches this electric field?
Which set of equipotential surfaces
matches this electric field?
Three charged, metal
spheres of different radii
are connected by a thin
metal wire. The potential
and electric field at the
surface of each sphere
are V and E. Which of
the following is true?
A. V1 = V2 = V3 and E1 > E2 > E3
B. V1 > V2 > V3 and E1 = E2 = E3
C. V1 = V2 = V3 and E1 = E2 = E3
D. V1 > V2 > V3 and E1 > E2 > E3
E. V3 > V2 > V1 and E1 = E2 = E3
the following is true?
Three charged, metal
spheres of different radii
are connected by a thin
metal wire. The potential
and electric field at the
surface of each sphere
are V and E. Which of
the following is true?
A. V1 = V2 = V3 and E1 > E2 > E3
B. V1 > V2 > V3 and E1 = E2 = E3
C. V1 = V2 = V3 and E1 = E2 = E3
D. V1 > V2 > V3 and E1 > E2 > E3
E. V3 > V2 > V1 and E1 = E2 = E3
the following is true?Rank in order, from largest to smallest, the
equivalent capacitance (C ) to (C ) of equivalent capacitance (Ceq)a to (Ceq)d of
circuits a to d.A. (Ceq)d > (Ceq)b > (Ceq)a > (Ceq)c
B. (Ceq)d > (Ceq)b = (Ceq)c > (Ceq)a
C. (Ceq)a > (Ceq)b = (Ceq)c > (Ceq)d
D. (Ceq)b > (Ceq)a = (Ceq)d > (Ceq)c
E. (Ceq)c > (Ceq)a = (Ceq)d > (Ceq)b
Rank in order, from largest to smallest, the
equivalent capacitance (C ) to (C ) of
A. (Ceq)d > (Ceq)b > (Ceq)a > (Ceq)c
B. (Ceq)d > (Ceq)b = (Ceq)c > (Ceq)a
C. (Ceq)a > (Ceq)b = (Ceq)c > (Ceq)d
D. (Ceq)b > (Ceq)a = (Ceq)d > (Ceq)c
E. (Ceq)c > (Ceq)a = (Ceq)d > (Ceq)b
equivalent capacitance (Ceq)a to (Ceq)d of
circuits a to d.
Recommended