Chapter 30
Potential & Field
Chapter 30. Reading Quizzes
2
1
What quantity is represented by
the symbol ?
What quantity is represented by
the symbol ?
A. Electronic potential
B. Excitation potential
C. EMF
D. Electric stopping power
E. Exosphericity
A. Electronic potential
B. Excitation potential
C. EMF
D. Electric stopping power
E. Exosphericity
3
4
What is the SI unit of capacitance?
What is the SI unit of capacitance?
A. Capaciton
B. Faraday
C. Hertz
D. Henry
E. Exciton
A. Capaciton
B. Faraday
C. Hertz
D. Henry
E. Exciton
5
6
The electric field
The electric field
A. is always perpendicular to an
equipotential surface.
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.
A. is always perpendicular to an
equipotential surface.
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
8
This chapter investigated
This chapter investigated
A.
B.
C.
D.
E.
A.
B.
C.
D.
E.
parallel capacitors
perpendicular capacitors
series capacitors.
Both a and b.
Both a and c.
parallel capacitors
perpendicular capacitors
series capacitors.
Both a and b.
Both a and c.
9
10
Finding Electric Field from
Potential and Vice Versa
Connecting Potential and Field
11
12
Finding the Electric Field from
the Potential
EXAMPLE 30.4 Finding E from
the slope of V
QUESTION:
In 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 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
Kirchoff’s Laws
Batteries and emf
1. Junction Law. Net current at a junction is zero
(Conservation of Charge)
The potential difference between the terminals of an ideal
battery is
∑I
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:
in
= ∑ I out
1. Loop Law. The sum of all potential differences around a
closed path is zero (Conservation of Energy)
21
22
Electrical Circuit
Potential and Current
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
where R = ρL/A
23
24
Electrical Circuit
Electrical Circuit
∆V
−
+
−
+
∆V
−
+
−
+
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.
Then the charge of the capacitor is
Q = C ∆V
∆V
−
−
+
−
+
Conducting wires.
In equilibrium all the points of the
wires have the same potential
+
If we disconnect the capacitor from the battery the
capacitor will still have the charge Q and potential
difference ∆V
25
Electrical Circuit
26
Capacitors in Parallel
∆V
∆V
−
+
+
C2
−
Q = C ∆V
∆V
−
∆V
+
+
−
−
∆V
+
If we connect the wires the charge will disappear
and there will be no potential difference
C1
All the points have
the same potential
All the points have
the same potential
−
∆V = 0
+
∆V
The capacitors 1 and 2 have the same potential difference
Then the charge of capacitor 1 is
27
The charge of capacitor 2 is
Q1 = C1∆V
Q2 = C2 ∆V
28
∆V
Capacitors in Parallel
Capacitors in Parallel
−
The total charge is
∆V
+
C2
The capacitors can be replaced with
one capacitor with a capacitance of Ceq
Q2 = C2 ∆V
Q = Q1 + Q2
Q = C1∆V + C2 ∆V = (C1 + C2 )∆V
−
∆V
+
The equivalent capacitor must have
exactly the same external effect on the
circuit as the original capacitors
Q1 = C1∆V
C1
This relation is equivalent to
the following one
Q = Ceq ∆V
Q = Ceq ∆V
Ceq
−
+
−
+
∆V
Ceq = C1 + C2
−
+
29
Capacitors
30
Capacitors in Series
∆V1
−
−
+
C2
C1
−
+
∆V2
+
The equivalence means that
−
Q = Ceq ∆V
+
∆V
−
∆V
∆V = ∆V1 + ∆V2
+
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32
Capacitors in Series
Capacitors in Series
Q1 = C1∆V
The total charge
is equal to 0
∆V1
−
−
+
C1
Q1 = Q2 = Q
The potential differences add up to the
battery voltage
Q Q
∆V = ∆V1 + ∆V2 =
+
C1 C2
∆V2
+
C2
∆V =
−
An equivalent capacitor can be found
that performs the same function as the
series combination
Q2 = C2 ∆V
Q
Ceq
1
1
1
=
+
Ceq C1 C2
+
∆V
Ceq =
C1C2
C1 + C2
33
Quiz: Find the equivalent capacitance for the circuit.
in parallel
34
Example
in parallel
Ceq = C1 + C2 = 1 + 3 = 4
Ceq = C1 + C2 = 1 + 3 = 4
Ceq = C1 + C2 = 6
Ceq = C1 + C2 = 8
Ceq = C1 + C2 = 6
Ceq = C1 + C2 = 8
in series
Ceq =
C1C2
8⋅8
=
=4
C1 + C2 8 + 8
in series
Ceq =
in parallel
in parallel
C1C2
8⋅8
=
=4
C1 + C2 8 + 8
in parallel
in parallel
35
36
Quiz: what are the charges stored?
Q = C ∆V
37
38
Energy Stored in a Capacitor
Assume the capacitor is being charged
and, at some point, has a charge q on it
The work needed to transfer a small
charge ∆q from one plate to the other is
equal to the change of potential energy
q
dW = ∆Vdq =
q
dq
C
−q
A
B
If the final charge of the capacitor is Q,
then the total work required is
W =∫
Q
0
39
q
Q2
dq =
C
2C
40
Energy Stored in a Capacitor
W =∫
Q
0
Energy Stored in a Capacitor: Application
q
Q2
dq =
C
2C
U=
The work done in charging the capacitor is
equal to the electric potential energy U of a
capacitor
One of the main application of capacitor:
Q = C ∆V
Q
U=
1
Q2 1
= Q∆V = C (∆V )2
2C 2
2
1
Q2 1
= Q∆V = C (∆V )2
2C 2
2
capacitors act as energy reservoirs that can be
slowly charged and then discharged quickly to
provide large amounts of energy in a short pulse
−Q
Q
This applies to a capacitor of any geometry
Q = C ∆V
−Q
41
42
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.
43
44
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.
• Filling a capacitor with a dielectric increases the
capacitance by a factor equal to the dielectric constant.
45
46
General Principles
Chapter 30. Summary Slides
General Principles
General Principles
Important Concepts
Important Concepts
Applications
Applications
What total potential difference is
created by these three batteries?
Chapter 30. Questions
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?
Which potential-energy
graph describes this
electric field?
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 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.
B.
C.
D.
E.
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.
B.
C.
D.
E.
V1 = V2 = V3 and E1 > E2 > E3
V1 > V2 > V3 and E1 = E2 = E3
V1 = V2 = V3 and E1 = E2 = E3
V1 > V2 > V3 and E1 > E2 > E3
V3 > V2 > V1 and E1 = E2 = E3
V1 = V2 = V3 and E1 > E2 > E3
V1 > V2 > V3 and E1 = E2 = E3
V1 = V2 = V3 and E1 = E2 = E3
V1 > V2 > V3 and E1 > E2 > E3
V3 > V2 > V1 and E1 = E2 = E3
Rank in order, from largest to smallest, the
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 (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