Physics II:Electricity & Magnetism
Physics II:Electricity & Magnetism
Chapter 22Chapter 22
Friday (Day 1)Friday (Day 1)
Add 21.9 Figure: E-field in a conductor.
Fix derivations for uniform charge density (dr is wrong, etc)
Add EM Field Activities
Add 21.9 Figure: E-field in a conductor.
Fix derivations for uniform charge density (dr is wrong, etc)
Add EM Field Activities
Warm-UpWarm-Up
Fri, Feb 20
Write down the steps you give a visually-disabled individual to explain to how to fill a coffee cup with water.
Place your homework on my desk: “Foundational Mathematics’ Skills of Physics” Packet (Page 9)
For future assignments - check online at www.plutonium-239.com
Fri, Feb 20
Write down the steps you give a visually-disabled individual to explain to how to fill a coffee cup with water.
Place your homework on my desk: “Foundational Mathematics’ Skills of Physics” Packet (Page 9)
For future assignments - check online at www.plutonium-239.com
Essential Question(s)Essential Question(s) WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE
NECESSARY IN PHYSICS II? HOW DO WE DESCRIBE THE NATURE OF ELECTROSTATICS AND
APPLY IT TO VARIOUS SITUATIONS?How do we describe and apply the concept of electric field?How do we describe and apply the electric field created by uniformly
charged objects?How do we describe and apply the relationship between the electric
field and electric flux?How do we describe and apply Gauss’s Law?How do we describe and apply the nature of electric fields in and
around conductors?How do we describe and apply the concept of induced charge and
electrostatic shielding?
WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?
HOW DO WE DESCRIBE THE NATURE OF ELECTROSTATICS AND APPLY IT TO VARIOUS SITUATIONS?
How do we describe and apply the concept of electric field?How do we describe and apply the electric field created by uniformly
charged objects?How do we describe and apply the relationship between the electric
field and electric flux?How do we describe and apply Gauss’s Law?How do we describe and apply the nature of electric fields in and
around conductors?How do we describe and apply the concept of induced charge and
electrostatic shielding?
VocabularyVocabulary
FluxElectric FluxFlux LinesSurface AreaPerpendicularOrthogonalNormalDot Product
FluxElectric FluxFlux LinesSurface AreaPerpendicularOrthogonalNormalDot Product
Gauss’s LawCharge Density
Gauss’s LawCharge Density
Foundational Mathematics Skills in Physics Timeline
Foundational Mathematics Skills in Physics Timeline
Day Pg(s) Day Pg(s) Day Pg(s) Day Pg(s)
11
26 3 11 16 16 21
213
147 4 12 17 17 8
322
238 5 13 18 18 9
424
†129 6 14 19 19 10
5 15 10 7 15 20 20 11
WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?
AgendaAgenda
Review “Foundational Mathematics’ Skills of Physics” Packet (Page 9) with answer guide.
Review electric fields, electrons, and conductorsDiscuss the following:
Electric Flux
Work Day:Chapter 21 Web Assign ProblemsUniform Charge Distribution DerivationsChapter 22 Web Assign Problems 22.1 - 22.4
Review “Foundational Mathematics’ Skills of Physics” Packet (Page 9) with answer guide.
Review electric fields, electrons, and conductorsDiscuss the following:
Electric Flux
Work Day:Chapter 21 Web Assign ProblemsUniform Charge Distribution DerivationsChapter 22 Web Assign Problems 22.1 - 22.4
A Review of Electric Fields and Conductors
The electric field is perpendicular to the surface of a conductor – again, if it were not, charges would move.
Chapter 22
Gauss’s Law
Main Points of Chapter 22
• Electric flux
• Gauss’ law
• Using Gauss’ law to determine electric fields
• Conductors and electric fields
• Testing Gauss’ and Coulomb’s laws
Section 22.1Section 22.1
Given a diagram where the electric field is represented by flux lines, how do wedetermine the direction of the field at a given point? identify the locations where the field is strong and where it is
weak? identify where the positive and negative charges must be
present?
How do we use the relationship between the electric field and electric flux to calculate the flux of a uniform electric field E through an arbitrary surface?
Given a diagram where the electric field is represented by flux lines, how do wedetermine the direction of the field at a given point? identify the locations where the field is strong and where it is
weak? identify where the positive and negative charges must be
present?
How do we use the relationship between the electric field and electric flux to calculate the flux of a uniform electric field E through an arbitrary surface?
Section 22.1Section 22.1
How do we use the relationship between the electric field and electric flux to calculate the flux of a uniform electric field E through a curved surface when E is uniform in magnitude and perpendicular to the surface?
How do we use the relationship between the electric field and electric flux to calculate the flux of a uniform electric field E through a rectangle when E is perpendicular to the rectangle and a function of one coordinate only?
How do we state and apply the relationship of between electric flux and lines of force?
How do we use the relationship between the electric field and electric flux to calculate the flux of a uniform electric field E through a curved surface when E is uniform in magnitude and perpendicular to the surface?
How do we use the relationship between the electric field and electric flux to calculate the flux of a uniform electric field E through a rectangle when E is perpendicular to the rectangle and a function of one coordinate only?
How do we state and apply the relationship of between electric flux and lines of force?
22.1 Electric Flux
Electric flux:
Electric flux through an area is proportional to the total number of field lines crossing the area.
A
ΦE = E Acosθ
ΦE = E⊥A =E A⊥
A
22.1 Electric Flux
Electric flux:
ΦE = EgA
ΦE = E Acosθ
When = 0°, the flux (field lines) passing through the area is maximized and when = 90°, the flux (field lines) is zero. Therefore, for mathematical simplicity, it is important to note that the area A of a surface will represented by a vector A whose magnitude is A but whose direction is perpendicular to it surface.
A
22.1 Electric Flux
Flux through a closed surface:
EM Field 6EM Field 6
Using EM Field, determine the flux through a closed surface (represented by a 2-D cross-section) by counting the number of field lines entering the area and subtracting it from the number of field lines exiting the area.This is because the area vector A for a
closed surface is always directed outward. i.e. cos (0°) = 1 and cos (180°) = -1
Using EM Field, determine the flux through a closed surface (represented by a 2-D cross-section) by counting the number of field lines entering the area and subtracting it from the number of field lines exiting the area.This is because the area vector A for a
closed surface is always directed outward. i.e. cos (0°) = 1 and cos (180°) = -1
EM Field 6EM Field 6
How can we draw a surface that has more field lines entering or exiting the closed surface?
How can we draw a surface that has more field lines entering or exiting the closed surface?
EM Field 6EM Field 6
The following are examples of the Flux calculations using EM Field 6.
Besides its relation to the number of field lines entering and exiting the closed surface, how does the flux calculation relate to charge?
The following are examples of the Flux calculations using EM Field 6.
Besides its relation to the number of field lines entering and exiting the closed surface, how does the flux calculation relate to charge?
SummarySummary
How does flux relate to the charge enclosed by a closed surface?
HW (Place in your agenda): “Foundational Mathematics’ Skills of Physics” Packet (Page 10) The final copies for all Uniformly Charged Objects: 1 derivation with
reasons for each mathematical step and 3 additional derivations: (*Refer to rubric)
Web Assign Final Copies: Chapter 21 Web Assign Problems: Chapter 22.1 & 22.2
How does flux relate to the charge enclosed by a closed surface?
HW (Place in your agenda): “Foundational Mathematics’ Skills of Physics” Packet (Page 10) The final copies for all Uniformly Charged Objects: 1 derivation with
reasons for each mathematical step and 3 additional derivations: (*Refer to rubric)
Web Assign Final Copies: Chapter 21 Web Assign Problems: Chapter 22.1 & 22.2
How do we apply integration and the Principle of Superposition to uniformly charged objects? How do we identify and apply the fields of highly symmetric charge distributions?
How do we describe and apply the electric field created by uniformly charged objects?
Monday (Day 2)Monday (Day 2)
Warm-UpWarm-UpMon, Feb 23
For an electric field raining straight down into an imaginary box . . . What is the direction of E? What is the direction of A for the (1) bottom, (2) top, and (3) side surfaces? What is the angle, , between E and A for the (1) bottom, (2) top, and (3) side
surfaces? What is value of cos for the (1) bottom, (2) top, and (3) side surfaces?
Place your homework on my desk: “Foundational Mathematics’ Skills of Physics” Packet (Page 10) - POSTPONED The final copies for all Uniformly Charged Objects: 1 derivation with reasons for
each mathematical step and 3 additional derivations: (*Refer to rubric) Web Assign Final Copies: Chapter 21
For future assignments - check online at www.plutonium-239.com
Mon, Feb 23 For an electric field raining straight down into an imaginary box . . .
What is the direction of E? What is the direction of A for the (1) bottom, (2) top, and (3) side surfaces? What is the angle, , between E and A for the (1) bottom, (2) top, and (3) side
surfaces? What is value of cos for the (1) bottom, (2) top, and (3) side surfaces?
Place your homework on my desk: “Foundational Mathematics’ Skills of Physics” Packet (Page 10) - POSTPONED The final copies for all Uniformly Charged Objects: 1 derivation with reasons for
each mathematical step and 3 additional derivations: (*Refer to rubric) Web Assign Final Copies: Chapter 21
For future assignments - check online at www.plutonium-239.com
Application:Electric Flux
Application:Electric Flux
Warm-up: What is the direction of E? What is the direction of A
for the (1) bottom, (2) top, and (3) side surfaces?
What is the angle, , between E and A for the (1) bottom, (2) top, and (3) side surfaces?
What is value of cos for the (1) bottom, (2) top, and (3) side surfaces?
Warm-up: What is the direction of E? What is the direction of A
for the (1) bottom, (2) top, and (3) side surfaces?
What is the angle, , between E and A for the (1) bottom, (2) top, and (3) side surfaces?
What is value of cos for the (1) bottom, (2) top, and (3) side surfaces?
E
A
E
Application:Electric Flux
Application:Electric Flux
Eout
Abottom
ΦEbottom= Eout Abottom cosθ
Abottom
The bottom square flux is
ΦE =EAcos 0°( )= EA
Ein
Atop
ΦEtop= Ein Atop cosθ
Atop
= −EA
ΦEtop= Ein Aside cosθ
Aside = 0
The net flux, Φnet, isΦnet = Φ top +Φbottom + Φsides
Φnet = −EA + EA + 0 = 0
Essential Question(s)Essential Question(s) WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE
NECESSARY IN PHYSICS II? HOW DO WE DESCRIBE THE NATURE OF ELECTROSTATICS AND
APPLY IT TO VARIOUS SITUATIONS?How do we describe and apply the concept of electric field?How do we describe and apply the electric field created by uniformly
charged objects?How do we describe and apply the relationship between the electric
field and electric flux?How do we describe and apply Gauss’s Law?How do we describe and apply the nature of electric fields in and
around conductors?How do we describe and apply the concept of induced charge and
electrostatic shielding?
WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?
HOW DO WE DESCRIBE THE NATURE OF ELECTROSTATICS AND APPLY IT TO VARIOUS SITUATIONS?
How do we describe and apply the concept of electric field?How do we describe and apply the electric field created by uniformly
charged objects?How do we describe and apply the relationship between the electric
field and electric flux?How do we describe and apply Gauss’s Law?How do we describe and apply the nature of electric fields in and
around conductors?How do we describe and apply the concept of induced charge and
electrostatic shielding?
VocabularyVocabulary
FluxElectric FluxFlux LinesSurface AreaPerpendicularOrthogonalNormalDot Product
FluxElectric FluxFlux LinesSurface AreaPerpendicularOrthogonalNormalDot Product
Gauss’s LawCharge Density
Gauss’s LawCharge Density
Foundational Mathematics Skills in Physics Timeline
Foundational Mathematics Skills in Physics Timeline
Day Pg(s) Day Pg(s) Day Pg(s) Day Pg(s)
11
26 3 11 16 16 21
213
147 4 12 17 17 8
322
238 5 13 18 18 9
424
†129 6 14 19 19 10
5 15 10 7 15 20 20 11
WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?
AgendaAgenda
Review “Foundational Mathematics’ Skills of Physics” Packet (Page 10) with answer guide. - POSTPONED
Review electric fluxDiscuss the following:
Gauss’s Law Applications of Gauss’s Law
Spherical Conductor, Point Charge, & Line Charges
Work Time: Web Assign Problems 22.1 - 22.5
Review “Foundational Mathematics’ Skills of Physics” Packet (Page 10) with answer guide. - POSTPONED
Review electric fluxDiscuss the following:
Gauss’s Law Applications of Gauss’s Law
Spherical Conductor, Point Charge, & Line Charges
Work Time: Web Assign Problems 22.1 - 22.5
Section 22.2Section 22.2
How do we state Gauss’s Law in integral form and apply it qualitatively to relate electric flux and electric charge for a specified surface?
How do we state Gauss’s Law in integral form and apply it qualitatively to relate electric flux and electric charge for a specified surface?
22-2 What Does Gauss’ Law Do?
Imagine field lines emanating from a positive charge.
Now imagine a sphere of tissue paper around the charge. How many field lines penetrate the tissue? It doesn’t really matter how many we draw in the first place, as long as we are consistent; they all go through.
Now imagine the charge being off-center; all the lines still go through:
22-2 What Does Gauss’ Law Do?
Suppose the tissue is some shape other than spherical, but still surrounds the charge.
All the field lines still go through:
Now, imagine the paper is crinkled and overlaps itself; how shall we deal with the lines that pierce the tissue three times?
Notice that they go out twice and in once – if we subtract the “ins” from the “outs” we are left with one line going out, which is consistent with the other situations.
22-2 What Does Gauss’ Law Do?
Now, look at an open (flat) sheet. If it is perpendicular to the field, the maximum number of lines penetrates:
If it is at an angle, fewer lines penetrate:
22-2 What Does Gauss’ Law Do?
The number of field lines piercing the surface is proportional to the surface area, the orientation, and the field strength. If we stop counting lines and just use the field strength itself, we can define the electric flux through an infinitesimal area:
Integrating gives the total flux:
22-2 What Does Gauss’ Law Do?
For a closed surface, we can uniquely define the direction of the normal to the surface as pointing outwards and define:
Then:
Note the circle on the integral sign, which means that the integration is over a closed surface.
22-2 What Does Gauss’ Law Do?
Note that the surface does not have to be made of real matter – it is a surface that we can imagine, but that does not have to exist in reality.
This kind of imaginary surface is called a Gaussian surface. We can imagine it to be any shape we want; it is very useful to choose one that makes the problem you are trying to solve as easy as possible.
22-2 Gauss’ Law
The electric flux through a closed surface that encloses a net charge is equal to the net
charge divided by the permittivity of free space.
Without further ado, we can state Gauss’ law:
22-2 Gauss’ Law
The electric flux through a closed surface that encloses no net charge is zero.
22.2 Gauss’s Law
Restating Gauss’ Law, the net number of field lines through the surface is proportional to the charge enclosed, and also to the flux:
Gauss’ Law can easily be used to find the electric field in situations with a high degree of symmetry.
ΦE = E⋅dA—∫ =
Qencl
ε0
E-Field for a Sphere or Point Charge
E-Field for a Sphere or Point Charge
Spherical ConductorSpherical Conductor
+
+
+
++
+
+
+
E
A1
r1
At radius r1 r > r0( ),
E⋅dA—∫
dAsphere
=EA1 cosθ =EA1=E 4π r2( ) =
Qencl
ε 0
Therefore, Eoutside =1
4πε0
Qr12
To calculate the electric field inside of a
conductor, we look at radius r2 r < r0( ),
r0
A2
r2
E⋅dA—∫ =EA2 cosθ =EA2=E 4π r2
( ) =Qencl
ε 0Because the enclosed charge inside
of a conductor is zero, Einside =0
22-2 Gauss’ Law for a Point Charge
The electric field through a Gaussian sphere with a single point charge at the center is easily calculated using:
ΦE = E ⋅dA—∫ =
Qencl
ε 0
ΦE = E 4π r2( ) =
Qencl
ε 0
Recall that F =qE.Therefore,
F =q21
4πε0
q1
r2
⎛
⎝⎜⎞
⎠⎟⇒ F =
1
4πε 0
q1q2
r2
This is Coulomb's Law!
22-2 Gauss’ LawBut the result would be the same if the surface was not spherical, or if the charge was anywhere inside it!
Therefore, we can quickly generalize this to any surface and any charge distribution; all can be considered as a collection of point or infinitesimal charges:
Here, Q is the total net charge enclosed by the surface.
Applications of Gauss’ LawApplications of Gauss’ Law
22-3 Using Gauss’ Law to Determine Electric Fields
Problem-solving techniques:
1. Make a sketch.
2. Identify any symmetries.
3. Choose a Gaussian surface that matches the symmetry – that is, the electric field is either parallel to the surface or constant and perpendicular to it.
4. The correct choice in 3 should allow you to get the field outside the integral. Then solve.
Section 22.3Section 22.3
How do we describe the electric field of a long, uniformly charged wire?
How do we describe the electric field of a thin spherical shell?
How do we use superposition to determine the electric fields of coaxial cylinders?
How do we use superposition to determine the electric fields of concentric spheres?
How do we describe the electric field of a long, uniformly charged wire?
How do we describe the electric field of a thin spherical shell?
How do we use superposition to determine the electric fields of coaxial cylinders?
How do we use superposition to determine the electric fields of concentric spheres?
Section 22.3Section 22.3
How do we apply Gauss’s Law, along with symmetry arguments, to determine the electric field inside a uniformly charged long cylinder? outside a uniformly charged long cylinder? inside a uniformly charged cylindrical shell? outside a uniformly charged cylindrical shell? inside a uniformly charged sphere? outside a uniformly charged sphere? inside a uniformly charged spherical shell?
outside a uniformly charged spherical shell?
How do we apply Gauss’s Law, along with symmetry arguments, to determine the electric field inside a uniformly charged long cylinder? outside a uniformly charged long cylinder? inside a uniformly charged cylindrical shell? outside a uniformly charged cylindrical shell? inside a uniformly charged sphere? outside a uniformly charged sphere? inside a uniformly charged spherical shell?
outside a uniformly charged spherical shell?
Section 22.3Section 22.3 How do we apply Gauss’s Law to determine the charge density on a surface in
terms of the electric field near the surface? How do we apply Gauss’s Law to determine the total charge on a surface in
terms of the electric field near the surface? How do we prove and apply the relationship between the surface charge
density on a conductor and the electric field strength near its surface? How do we qualitatively explain why there can be no electric field in a
charge-free region completely surrounded by a single conductor? How do we qualitatively explain why the electric field outside of a closed
conducting surface cannot depend on the precise location of charge in the space enclosed by the conductor?
What is the significance of why the electric field outside of a closed conducting surface cannot depend on the precise location of charge in the space enclosed by the conductor?
How do we apply Gauss’s Law to determine the charge density on a surface in terms of the electric field near the surface?
How do we apply Gauss’s Law to determine the total charge on a surface in terms of the electric field near the surface?
How do we prove and apply the relationship between the surface charge density on a conductor and the electric field strength near its surface?
How do we qualitatively explain why there can be no electric field in a charge-free region completely surrounded by a single conductor?
How do we qualitatively explain why the electric field outside of a closed conducting surface cannot depend on the precise location of charge in the space enclosed by the conductor?
What is the significance of why the electric field outside of a closed conducting surface cannot depend on the precise location of charge in the space enclosed by the conductor?
E-Field for a Line of Charge
E-Field for a Line of Charge
Long Uniform Line of Charge
Long Uniform Line of Charge
E
E
E⋅dA—∫ =EAtop
dAtop
+EAtube
dAtube
+EAbottom
dAbottom
Note: There is no electric field lines
going through the top or bottom of
the cylinder.
=E Atube =E 2π rL( )
=Qencl
ε 0
E 2πrL( ) =Qencl
ε0
⇒ Ewire =1
2πε 0
Q
rL
Uniformly ChargedVertical Wire (–∞+∞)
Uniformly ChargedVertical Wire (–∞+∞)
-∞
∞dy
y
x
h = x2 + y2
dE
dEx=dE cosθ
dE =1
4πε0
dqh2 ; dEx =dEcos =dE
x
h=
1
4πε 0
x
h3 dq
λ =Q
l=
Q
y⇒ Q = λ y
λ =dq
dl=
dq
dy⇒ dq = λ dy
Ex = dEx0
Etot
∫ =
1
4πε 0
x
h3 dq=λ dy{0
Qtot
∫
=1
4πε 0
x
hx2 +y2
{3 λ dy
−∞
∞
∫ =1
4πε 0
λ x1
x2 + y2( )
32
dy−∞
∞
∫
Ex =1
4πε0
λxy
x2 x2 + y2
⎡
⎣⎢⎢
⎤
⎦⎥⎥−∞
∞
=1
4πε 0
λ
x
y
x2 + y2
⎡
⎣⎢⎢
⎤
⎦⎥⎥
−∞
∞
=1
2πε 0
λ
x
Ex =1
2πε0
λx
yy
=1
2πε 0
Q
xy=
1
2πε 0
Q
rLNote: "r" replaced "x" and "L" replaced "y"( )
Do they agree?
SummarySummary
What does the closed integral sign mean in Gauss’ Law?
HW (Place in your agenda): “Foundational Mathematics’ Skills of Physics” Packet (Page 10)†“Foundational Mathematics’ Skills of Physics” Packet (Page 11)Web Assign 22.1 - 22.5
What does the closed integral sign mean in Gauss’ Law?
HW (Place in your agenda): “Foundational Mathematics’ Skills of Physics” Packet (Page 10)†“Foundational Mathematics’ Skills of Physics” Packet (Page 11)Web Assign 22.1 - 22.5
How do we apply integration and the Principle of Superposition to uniformly charged objects? How do we identify and apply the fields of highly symmetric charge distributions?
How do we describe and apply the electric field created by uniformly charged objects?
Tuesday (Day 3)
Tuesday (Day 3)
Warm-UpWarm-Up
Tues, Feb 24
Calculate the electric flux for a charged object on the following slide.
Place your homework on my desk: “Foundational Mathematics’ Skills of Physics” Packet (Page 10) †“Foundational Mathematics’ Skills of Physics” Packet (Page 11) -
POSTPONED Web Assign Problems 22.1 - 22.5
For future assignments - check online at www.plutonium-239.com
Tues, Feb 24
Calculate the electric flux for a charged object on the following slide.
Place your homework on my desk: “Foundational Mathematics’ Skills of Physics” Packet (Page 10) †“Foundational Mathematics’ Skills of Physics” Packet (Page 11) -
POSTPONED Web Assign Problems 22.1 - 22.5
For future assignments - check online at www.plutonium-239.com
Application: Electric FluxApplication: Electric Flux
Two objects, O1 and O2, have charges +1 C and -2.0 C, respectively, and a third object, O3, is electrically neutral. (a) What is the electric flux through the surface A1 that encloses all three objects?(b) What is the electric flux through the surface A2 that encloses the third object only?
ΦA1
= E ⋅d—∫ A =Qencl
ε 0
=1.0μC + −2.0μC( )( )
8.85 x 10−12 C2 N ⋅m2 =1.13 x 105 N ⋅m2 C
ΦA2
= E ⋅d—∫ A=Qencl
ε 0
=0 μC( )
8.85 x 10−12 C2 N ⋅m2 =0 N ⋅m2 C
Essential Question(s)Essential Question(s) WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE
NECESSARY IN PHYSICS II? HOW DO WE DESCRIBE THE NATURE OF ELECTROSTATICS AND
APPLY IT TO VARIOUS SITUATIONS?How do we describe and apply the concept of electric field?How do we describe and apply the electric field created by uniformly
charged objects?How do we describe and apply the relationship between the electric
field and electric flux?How do we describe and apply Gauss’s Law?How do we describe and apply the nature of electric fields in and
around conductors?How do we describe and apply the concept of induced charge and
electrostatic shielding?
WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?
HOW DO WE DESCRIBE THE NATURE OF ELECTROSTATICS AND APPLY IT TO VARIOUS SITUATIONS?
How do we describe and apply the concept of electric field?How do we describe and apply the electric field created by uniformly
charged objects?How do we describe and apply the relationship between the electric
field and electric flux?How do we describe and apply Gauss’s Law?How do we describe and apply the nature of electric fields in and
around conductors?How do we describe and apply the concept of induced charge and
electrostatic shielding?
VocabularyVocabulary
FluxElectric FluxFlux LinesSurface AreaPerpendicularOrthogonalNormalDot Product
FluxElectric FluxFlux LinesSurface AreaPerpendicularOrthogonalNormalDot Product
Gauss’s LawCharge Density
Gauss’s LawCharge Density
Foundational Mathematics Skills in Physics Timeline
Foundational Mathematics Skills in Physics Timeline
Day Pg(s) Day Pg(s) Day Pg(s) Day Pg(s)
11
26 3 11 16 16 21
213
147 4 12 17 17 8
322
238 5 13 18 18 9
424
†129 6 14 19 19 10
5 15 10 7 15 20 20 11
WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?
AgendaAgenda
Review “Foundational Mathematics’ Skills of Physics” Packet (Page 11) with answer guide.
Discuss the following:Applications of Gauss’ Law
Charged Plate(s), Charged Surfaces, & Charged Spherical Insulators
Conductors in Electric FieldsExperimental Basis of Gauss’ and Coulomb’s Law
Work Time: Web Assign Problems 22.6 - 22.15
Review “Foundational Mathematics’ Skills of Physics” Packet (Page 11) with answer guide.
Discuss the following:Applications of Gauss’ Law
Charged Plate(s), Charged Surfaces, & Charged Spherical Insulators
Conductors in Electric FieldsExperimental Basis of Gauss’ and Coulomb’s Law
Work Time: Web Assign Problems 22.6 - 22.15
Section 22.3Section 22.3
How do we apply Gauss’s Law, along with symmetry arguments, to determine the electric field? near a large, uniformly charged plane?
How do we apply Gauss’s Law, along with symmetry arguments, to determine the electric field? near a large, uniformly charged plane?
Section 22.3Section 22.3 How do we apply Gauss’s Law to determine the charge density on a surface in
terms of the electric field near the surface? How do we apply Gauss’s Law to determine the total charge on a surface in
terms of the electric field near the surface? How do we prove and apply the relationship between the surface charge
density on a conductor and the electric field strength near its surface? How do we qualitatively explain why there can be no electric field in a
charge-free region completely surrounded by a single conductor? How do we qualitatively explain why the electric field outside of a closed
conducting surface cannot depend on the precise location of charge in the space enclosed by the conductor?
What is the significance of why the electric field outside of a closed conducting surface cannot depend on the precise location of charge in the space enclosed by the conductor?
How do we apply Gauss’s Law to determine the charge density on a surface in terms of the electric field near the surface?
How do we apply Gauss’s Law to determine the total charge on a surface in terms of the electric field near the surface?
How do we prove and apply the relationship between the surface charge density on a conductor and the electric field strength near its surface?
How do we qualitatively explain why there can be no electric field in a charge-free region completely surrounded by a single conductor?
How do we qualitatively explain why the electric field outside of a closed conducting surface cannot depend on the precise location of charge in the space enclosed by the conductor?
What is the significance of why the electric field outside of a closed conducting surface cannot depend on the precise location of charge in the space enclosed by the conductor?
Infinite Plane of Charge(nonconducting uniform )
Infinite Plane of Charge(nonconducting uniform )
EA
E
E⋅dA—∫
dA
dA
=Qencl
ε 0
=A
ε 0
Also Note: The electric field, E,
is in the direction of dA and exists
on both sides of the charged plate.
Therefore,
Anet = Atop + Abottom = 2Acircle
E 2A( ) =Aε0
⇒ E =σ
2ε 0
for each plate
Enet = En∑ =E1 + E2=
2ε 0
+σ
2ε 0
=ε0
dAtube
Infinite Plane of Charge(nonconducting uniform )
Infinite Plane of Charge(nonconducting uniform )
EA
E
E⋅dA—∫
dA
dA
=Qencl
ε 0
=A
ε 0
Also Note: The electric field, E,
is in the direction of dA and exists
on both sides of the charged plate.
Therefore, dAtube
ΦE = E ⋅dA
=EAtop
{top∫ + E ⋅dA
=0{
tube∫ + E ⋅dA
=EAbottom
{bottom∫
ΦE = 2EAcircle
2EA =Aε0
⇒ E =σ
2ε 0
for each side
For two oppositely charged plates:
Enet = En∑ =E1 + E2 =
2ε 0
+σ
2ε 0
=ε0
Uniformly Charged Disk (0∞)
Uniformly Charged Disk (0∞)
R
dr
r
z
h = r2 + z2
dE
dEz=dE cosθ
dE =1
4πε0
dqh2 ; dEz =dEcos =dE
z
h=
1
4πε 0
z
h3 dq
=Q
A=
Q
π r2 ⇒ Q = π r2σ
dA
dr=2πr ⇒ dA = 2π rdr
=dq
dA=
dq
2π rdr⇒ dq = 2π rσ dr
Ez = dEz0
Etot
∫ =
1
4πε 0
z
h3 dq=2π rσ dr
{0
Qtot
∫
=1
4πε 0
z
hz2 +r2
{3 2π rσ dr
0
∞
∫
Ez =1
4πε0
2πzr
z2 + r2( )32dr
0
∞
∫ =1
2ε 0
σ z −1
z2 + r2
⎡
⎣⎢
⎤
⎦⎥
0
∞
=1
2ε 0
σ z1
z2 + r2
⎡
⎣⎢
⎤
⎦⎥
∞
0
Ez =12ε0
z1z−
1
z2 +∞2
⎡
⎣⎢
⎤
⎦⎥ =
2ε 0
z
z⎡⎣⎢
⎤⎦⎥=
2ε 0
Uniformly ChargedInfinite Plate
Uniformly ChargedInfinite Plate
-∞ ∞-∞
∞
dxdyx
yr = x2 + y2
z h = r2 + z2
= x2 + y2 + z2
dE
dEz=dE cosθdE =
14πε0
dqh2 ; dEz =dEcos =dE
z
h=
1
4πε 0
z
h3 dq
=Q
A=
Q
xy⇒ Q = σ xy
dA =dxdy
=dq
dA=
dq
dx dy⇒ dq = σ dx dy
Ez = dEz0
Etot
∫ =
1
4πε 0
z
h3 dq=σ dx dy{0
Qtot
∫
Ez =1
4πε0
zh
x2+y2+z2{
3 dx−∞
∞
∫−∞
∞
∫ dy=1
4πε 0
σ z1
x2 + y2 + z2( )
32
dx−∞
∞
∫ dy−∞
∞
∫
Ez =1
4πε0
z2
y2 + z2dy
−∞
∞
∫ =1
4πε 0
σ z2π
z⎡⎣⎢
⎤⎦⎥=
2ε 0
No radius?!? What does that mean?!?
21-7 The Field of a Continuous Distribution
From the electric field due to a nonconducting uniform sheet of charge, we can calculate what would happen if we put two oppositely-charged sheets next to each other:The individual fields:
The superposition:
The result:
How do we apply integration and the Principle of Superposition to uniformly charged objects? How do we identify and apply the fields of highly symmetric charge distributions?
How do we describe and apply the electric field created by uniformly charged objects?
21.8 Field Lines
The electric field between two closely spaced, oppositely charged parallel plates is constant.
E-Field at the Surface of a Conductor
E-Field at the Surface of a Conductor
Surface of a ConductorSurface of a Conductor
+
+ +
+ + +
+ + + +
+ + +
+ +
+
E
A
E⋅dA—∫
dA
=Qencl
ε 0
=A
ε 0
Note: Since we are Gaussian surface
is just below the surface of the
conductor, the electric field, E,
is only in the direction of dA and
does not exist within the conductor.
= EAcircle
EA =Aε0
⇒ E =σ
ε 0
for the surface
dAtube
So why are the E-Fields different for the plate and
the surface?
So why are the E-Fields different for the plate and
the surface?Nonconducting: Charge remains
localized (ie. +2Q remains fixed)Conducting: Like charges repel (ie.
+2Q total -> +Q move to each side and conduct=1/2 insulator )
Therefore, both E-fields will have the same magnitude and direction.
Nonconducting: Charge remains localized (ie. +2Q remains fixed)
Conducting: Like charges repel (ie. +2Q total -> +Q move to each side and conduct=1/2 insulator )
Therefore, both E-fields will have the same magnitude and direction.
EM Field 6EM Field 6
Find the field lines for:2 Parallel Oppositely Charged Plates2 Parallel Plates of the Same Charge
Find the field lines for:2 Parallel Oppositely Charged Plates2 Parallel Plates of the Same Charge
Spherical Insulator (Uniformly distributed charge)
Spherical Insulator (Uniformly distributed charge)
++
+
+
++
++
E
A1
r1
At radius r1 r > r0( ),
E⋅dA—∫
dA1= dAsphere
=EA1 cosθ =EA1=E 4π r2( ) =
Qencl
ε 0
Therefore, Eoutside =1
4πε0
Qr12
At radius r2 r < r0( ),r0
A2
r2
E⋅dA—∫
+
+
+
++ +
+
+
+dA2
=EA2 cosθ =EA2=E 4π r2( ) =
Qencl
ε 0Note: Since the enclosed charge density is
evenly distributed, ρE =Qtot
Vtot
=dQ
dV=constant
Then, ρE =Qtot
Vtot
=Qencl
Vencl
⇒ Qencl =Vencl
Vtot
Qtot =r3
r03 Qtot
E⋅dA—∫ =E 4π r2
( )=Qencl
ε 0
=r3
r03
Qtot
ε 0
Therefore, Einside =1
4πε0
Qtot
r03 r
22-3 Conductors and Electric Fields
In conductors, the charges are free to move if there is an external electric field exerting a force on them.
• Therefore, in equilibrium, there is no static field inside a conductor. This also means that the external electric field is perpendicular to the conductor at its surface.
22-3 Conductors and Electric Fields
What if the conductor is charged – where does the excess charge go?
• By making a Gaussian surface very close to, but just under, the surface of the conductor, we see that any excess charge must lie on the outside of the conductor.
22-3 Conductors and Electric Fields
What if there is a cavity inside the conductor, and that cavity has charges in it?
The field inside the conductor must still be zero, so charges will be induced on the inner surface of the cavity and the outer surface of the conductor:
22-3 Conductors and Electric FieldsElectrostatic Fields Near Conductors
Looking at the electrostatic field very near a conductor, we find:
and therefore:
The electric field is perpendicular to the surface, and where the charge density is higher, the field is larger.
23-3 Conductors and Electric Fields
1. The electrostatic field inside a conductor is zero.
2. The electrostatic field immediately outside a conductor is perpendicular to the surface and has the value σ/ε0 where σ is the local surface charge density.
3. A conductor in electrostatic equilibrium—even one that contains nonconducting cavities—can have charge only on its outer surface, as long as the cavities contain no net charge. If there is a net charge within the cavity, then an equal and opposite charge will be distributed on the surface of the conductor that surrounds the cavity.
To summarize:
22-4 Are Gauss’ and Coulomb’s Laws Correct?
An experiment to validate Gauss’ law (that there is no charge within a conductor) can be done as follows:
Need a hollow conducing sphere, a small conducting ball on an insulating rod, and an electroscope attached to the surface of the conductor.
22-4 Are Gauss’ and Coulomb’s Laws Correct?
Charge the small sphere and hold it inside the shell without touching. Induced charge will be on outside of shell and on electroscope.
Now touch the inside of the shell with the small sphere. Charge will flow onto it until it is neutral, leaving the shell with a net positive charge.
22-4 Are Gauss’ and Coulomb’s Laws Correct?
Finally, remove the rod. The electroscope leaves do not move, indicating that the excess charge resides on the outside of the shell.
22-4 Are Gauss’ and Coulomb’s Laws Correct?
This table shows the results of such experiments looking for a deviation from an inverse-square law:
22-4 Are Gauss’ and Coulomb’s Laws Correct?
One problem with the above experiments is that they have all been done at short range, 1 meter or so.
Other experiments, more sensitive to cosmic-scale distances, have been done, testing whether Coulomb’s law has the form:
No evidence for a nonzero μ has been found.
Summary of Chapter 22
• Electric flux due to field intersecting a surface S:
• Gauss’ law relates flux through a closed surface to charge enclosed:
• Can use Gauss’ law to find electric field in situations with a high degree of symmetry
ΦS = E ⋅dAS∫
Summary of Chapter 22
• Electric flux:
• Gauss’s law:
E⋅dA—∫ =
Qencl
ε0
Summary of Chapter 22 (con’t)
• Properties of conductors:
1. Electric field is zero inside
2. Field just outside conductor is perpendicular to surface
3. Excess charge resides on the outside of a conductor, unless there is a nonconducting cavity in it; in that case, there is an induced charge on both surfaces
• Gauss’ law has been verified to a very high degree of accuracy
SummarySummary
In a conductor, what happens to an electron in the presence of an electric field?
What happens to the electric field in the presence of an conductor?
HW (Place in your agenda): “Foundational Mathematics’ Skills of Physics” Packet (Page 10)†“Foundational Mathematics’ Skills of Physics” Packet (Page 11)
LAST ONE!!!!!!!!
Web Assign 22.6 - 22.15
In a conductor, what happens to an electron in the presence of an electric field?
What happens to the electric field in the presence of an conductor?
HW (Place in your agenda): “Foundational Mathematics’ Skills of Physics” Packet (Page 10)†“Foundational Mathematics’ Skills of Physics” Packet (Page 11)
LAST ONE!!!!!!!!
Web Assign 22.6 - 22.15
How do we apply integration and the Principle of Superposition to uniformly charged objects? How do we identify and apply the fields of highly symmetric charge distributions?
How do we describe and apply the electric field created by uniformly charged objects?
Wednesday (Day 4)
Wednesday (Day 4)
Warm-UpWarm-Up
Wed, Feb 25
Two thin concentric spherical shells of radii r1 and r2 (r1 < r2) contain a uniform surface charge densities 1 and 2, respectively. Determine the electric field for (a) r < r1, (b) r1 < r < r2, and (c) r > r2. (d) Under what conditions will E = 0 for r > r2? (e) Under what conditions will E = 0 for r1 < r < r2?
Place your homework on my desk: †“Foundational Mathematics’ Skills of Physics” Packet (Page 11) Web Assign Problems 22.6 - 22.15
For future assignments - check online at www.plutonium-239.com
Wed, Feb 25
Two thin concentric spherical shells of radii r1 and r2 (r1 < r2) contain a uniform surface charge densities 1 and 2, respectively. Determine the electric field for (a) r < r1, (b) r1 < r < r2, and (c) r > r2. (d) Under what conditions will E = 0 for r > r2? (e) Under what conditions will E = 0 for r1 < r < r2?
Place your homework on my desk: †“Foundational Mathematics’ Skills of Physics” Packet (Page 11) Web Assign Problems 22.6 - 22.15
For future assignments - check online at www.plutonium-239.com
Essential Question(s)Essential Question(s)
HOW DO WE DESCRIBE THE NATURE OF ELECTROSTATICS AND APPLY IT TO VARIOUS SITUATIONS?
How do we describe and apply the concept of electric field?How do we describe and apply the electric field created by
uniformly charged objects?How do we describe and apply the relationship between the
electric field and electric flux?How do we describe and apply Gauss’s Law?How do we describe and apply the nature of electric fields in
and around conductors?How do we describe and apply the concept of induced charge
and electrostatic shielding?
HOW DO WE DESCRIBE THE NATURE OF ELECTROSTATICS AND APPLY IT TO VARIOUS SITUATIONS?
How do we describe and apply the concept of electric field?How do we describe and apply the electric field created by
uniformly charged objects?How do we describe and apply the relationship between the
electric field and electric flux?How do we describe and apply Gauss’s Law?How do we describe and apply the nature of electric fields in
and around conductors?How do we describe and apply the concept of induced charge
and electrostatic shielding?
VocabularyVocabulary
FluxElectric FluxFlux LinesSurface AreaPerpendicularOrthogonalNormalDot Product
FluxElectric FluxFlux LinesSurface AreaPerpendicularOrthogonalNormalDot Product
Gauss’s LawCharge Density
Gauss’s LawCharge Density
AgendaAgenda
Review “Foundational Mathematics’ Skills of Physics” Packet (Page 11) with answer guide.
Complete the Gauss’ Law lab using EM Field 6Complete Web Assign Problems 22.6 - 22.15
Review “Foundational Mathematics’ Skills of Physics” Packet (Page 11) with answer guide.
Complete the Gauss’ Law lab using EM Field 6Complete Web Assign Problems 22.6 - 22.15
SummarySummary
What did you learn about drawing Gaussian surfaces when using EM Field?
HW (Place in your agenda): Electrostatics Lab #4 Report (Due in 5 Classes) Web Assign 22.6 - 22.15
What did you learn about drawing Gaussian surfaces when using EM Field?
HW (Place in your agenda): Electrostatics Lab #4 Report (Due in 5 Classes) Web Assign 22.6 - 22.15
How do we apply integration and the Principle of Superposition to uniformly charged objects? How do we identify and apply the fields of highly symmetric charge distributions?
How do we describe and apply the electric field created by uniformly charged objects?
Thursday (Day 5)
Thursday (Day 5)
Warm-UpWarm-Up
Thurs, Feb 26
Complete Chapter 22 Graphic Organizers
Place your homework on your desk: Web Assign Problems 22.6 - 22.15
For future assignments - check online at www.plutonium-239.com
Thurs, Feb 26
Complete Chapter 22 Graphic Organizers
Place your homework on your desk: Web Assign Problems 22.6 - 22.15
For future assignments - check online at www.plutonium-239.com
Essential Question(s)Essential Question(s)
HOW DO WE DESCRIBE THE NATURE OF ELECTROSTATICS AND APPLY IT TO VARIOUS SITUATIONS?
How do we describe and apply the concept of electric field?How do we describe and apply the electric field created by
uniformly charged objects?How do we describe and apply the relationship between the
electric field and electric flux?How do we describe and apply Gauss’s Law?How do we describe and apply the nature of electric fields in
and around conductors?How do we describe and apply the concept of induced charge
and electrostatic shielding?
HOW DO WE DESCRIBE THE NATURE OF ELECTROSTATICS AND APPLY IT TO VARIOUS SITUATIONS?
How do we describe and apply the concept of electric field?How do we describe and apply the electric field created by
uniformly charged objects?How do we describe and apply the relationship between the
electric field and electric flux?How do we describe and apply Gauss’s Law?How do we describe and apply the nature of electric fields in
and around conductors?How do we describe and apply the concept of induced charge
and electrostatic shielding?
VocabularyVocabulary
FluxElectric FluxFlux LinesSurface AreaPerpendicularOrthogonalNormalDot Product
FluxElectric FluxFlux LinesSurface AreaPerpendicularOrthogonalNormalDot Product
Gauss’s LawCharge Density
Gauss’s LawCharge Density
AgendaAgenda
Complete the Gauss’ Law lab using EM Field 6Complete Web Assign Problems 22.6 - 22.15
Complete the Gauss’ Law lab using EM Field 6Complete Web Assign Problems 22.6 - 22.15
SummarySummary
Would Gauss’ Law be helpful in determining the electric field due to an electric dipole?
HW (Place in your agenda): Electrostatics Lab #4 Report (Due in 4 Classes) Web Assign 22.6 - 22.15
Would Gauss’ Law be helpful in determining the electric field due to an electric dipole?
HW (Place in your agenda): Electrostatics Lab #4 Report (Due in 4 Classes) Web Assign 22.6 - 22.15
How do we apply integration and the Principle of Superposition to uniformly charged objects? How do we identify and apply the fields of highly symmetric charge distributions?
How do we describe and apply the electric field created by uniformly charged objects?