physics ii: electricity & magnetism
DESCRIPTION
Physics II: Electricity & Magnetism. Binomial Expansions, Riemann Sums, Sections 21.6 & 21.8. Friday (Day 12). Warm-Up. Fri, Feb 6 Calculate the velocity of the electron moving around the hydrogen nucleus (r = 0.53 x 10 -10 m) Place your homework on my desk: - PowerPoint PPT PresentationTRANSCRIPT
Physics II:Electricity & Magnetism
Physics II:Electricity & Magnetism
Binomial Expansions, Riemann Sums, Sections 21.6
& 21.8
Binomial Expansions, Riemann Sums, Sections 21.6
& 21.8
Friday (Day 12)Friday
(Day 12)
Warm-UpWarm-Up
Fri, Feb 6 Calculate the velocity of the electron moving around the hydrogen nucleus (r
= 0.53 x 10-10 m)
Place your homework on my desk: “Foundational Mathematics’ Skills of Physics” Packet (Page 6) Derivative Practice
For future assignments - check online at www.plutonium-239.com
Fri, Feb 6 Calculate the velocity of the electron moving around the hydrogen nucleus (r
= 0.53 x 10-10 m)
Place your homework on my desk: “Foundational Mathematics’ Skills of Physics” Packet (Page 6) Derivative Practice
For future assignments - check online at www.plutonium-239.com
Warm-Up ReviewWarm-Up Review
Calculate the velocity of the electron moving around the hydrogen nucleus (r = 0.53 x 10-10 m)
Calculate the velocity of the electron moving around the hydrogen nucleus (r = 0.53 x 10-10 m)
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 Coulomb’s Law and the Principle
of Superposition?
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 Coulomb’s Law and the Principle
of Superposition?
VocabularyVocabulary Static Electricity Electric Charge Positive / Negative Attraction / Repulsion Charging / Discharging Friction Induction Conduction Law of Conservation of Electric
Charge Non-polar Molecules
Static Electricity Electric Charge Positive / Negative Attraction / Repulsion Charging / Discharging Friction Induction Conduction Law of Conservation of Electric
Charge Non-polar Molecules
Polar Molecules Ion Ionic Compounds Force Derivative Integration (Integrals) Test Charge Electric Field Field Lines Electric Dipole Dipole Moment
Polar Molecules Ion Ionic Compounds Force Derivative Integration (Integrals) Test Charge Electric Field Field Lines Electric Dipole Dipole Moment
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†12
9 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 6) with answer guide.
Review Derivative Practice INTEGRAL PROOF USING RIEMANN SUMS Integral Practice
MONDAY: Discuss Electric Fields & Gravitational Field Apply Electric Fields Continue with The Four Circles Graphic Organizer
Review “Foundational Mathematics’ Skills of Physics” Packet (Page 6) with answer guide.
Review Derivative Practice INTEGRAL PROOF USING RIEMANN SUMS Integral Practice
MONDAY: Discuss Electric Fields & Gravitational Field Apply Electric Fields Continue with The Four Circles Graphic Organizer
Topic #1: Determine the slope at point A for f(x)=xn
Topic #1: Determine the slope at point A for f(x)=xn
y = 1/2 x
WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?
Topic #1: Determine the slope at point A for f(x)=xn
Topic #1: Determine the slope at point A for f(x)=xn
y = 1/4 x2
WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?
SummarySummary
Identify one section that in the Integral Proof using Riemann Sums that was confusing?
HW (Place in your agenda): “Foundational Mathematics’ Skills of Physics” Packet (Page 7) Go through the Riemann sum derivation - determine what you do not
understand. Integral Practice
Future assignments: Electrostatics Lab #3: Lab Report (Due in 3 classes)
Identify one section that in the Integral Proof using Riemann Sums that was confusing?
HW (Place in your agenda): “Foundational Mathematics’ Skills of Physics” Packet (Page 7) Go through the Riemann sum derivation - determine what you do not
understand. Integral Practice
Future assignments: Electrostatics Lab #3: Lab Report (Due in 3 classes)
How do we use Coulomb’s Law and the principle of superposition to determine the force that acts between point charges?
Monday (Day 13)Monday (Day 13)
Warm-UpWarm-UpMon, Feb 9
1. If I measured the distance of each step I took and summed them all together, what would I have calculated?
2. If I was driving in a car on the turnpike at a constant speed and I multiplied my speed by the time I was traveling, what would I have calculated?
3. Now make it more complex, what if my speed was slowly changing and I1. Wrote down my velocity and the amount of time I was traveling at that velocity;2. Multiplied those two numbers together;3. Added those new numbers together; What would I have calculated?
Place your homework on my desk: “Foundational Mathematics’ Skills of Physics” Packet (Page 7) Integral Practice
1. For future assignments - check online at www.plutonium-239.com
Mon, Feb 91. If I measured the distance of each step I took and summed them all together, what
would I have calculated?2. If I was driving in a car on the turnpike at a constant speed and I multiplied my speed
by the time I was traveling, what would I have calculated?3. Now make it more complex, what if my speed was slowly changing and I
1. Wrote down my velocity and the amount of time I was traveling at that velocity;2. Multiplied those two numbers together;3. Added those new numbers together; What would I have calculated?
Place your homework on my desk: “Foundational Mathematics’ Skills of Physics” Packet (Page 7) Integral Practice
1. For future assignments - check online at www.plutonium-239.com
Warm-UpWarm-Up
Mon, Feb 91. If I measured the distance of each step I took and summed them all
together, what would I have calculated?2. If I was driving in a car on the turnpike at a constant speed and I
multiplied my speed by the time I was traveling, what would I have calculated?
3. Now make it more complex, what if my speed was slowly changing and I
1. Wrote down my velocity and the amount of time I was traveling at that velocity;
2. Multiplied those two numbers together;3. Added those new numbers together; What would I have calculated?
Mon, Feb 91. If I measured the distance of each step I took and summed them all
together, what would I have calculated?2. If I was driving in a car on the turnpike at a constant speed and I
multiplied my speed by the time I was traveling, what would I have calculated?
3. Now make it more complex, what if my speed was slowly changing and I
1. Wrote down my velocity and the amount of time I was traveling at that velocity;
2. Multiplied those two numbers together;3. Added those new numbers together; What would I have calculated?
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 Coulomb’s Law and the Principle
of Superposition?
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 Coulomb’s Law and the Principle
of Superposition?
VocabularyVocabulary Static Electricity Electric Charge Positive / Negative Attraction / Repulsion Charging / Discharging Friction Induction Conduction Law of Conservation of Electric
Charge Non-polar Molecules
Static Electricity Electric Charge Positive / Negative Attraction / Repulsion Charging / Discharging Friction Induction Conduction Law of Conservation of Electric
Charge Non-polar Molecules
Polar Molecules Ion Ionic Compounds Force Derivative Integration (Integrals) Test Charge Electric Field Field Lines Electric Dipole Dipole Moment
Polar Molecules Ion Ionic Compounds Force Derivative Integration (Integrals) Test Charge Electric Field Field Lines Electric Dipole Dipole Moment
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†12
9 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 7) with answer guide.
Complete the Integral Proof using Riemann Sums Review Integral Practice Discuss
Electric Fields Gravitational Field Field Lines
Continue with The Four Circles Graphic Organizer Apply Electric Fields
Review “Foundational Mathematics’ Skills of Physics” Packet (Page 7) with answer guide.
Complete the Integral Proof using Riemann Sums Review Integral Practice Discuss
Electric Fields Gravitational Field Field Lines
Continue with The Four Circles Graphic Organizer Apply Electric Fields
Riemann Sums ProofRiemann Sums Proof
ADD RIEMANN SUMS PROOF HEREADD RIEMANN SUMS PROOF HERE
Riemann SumsRiemann Sums
Riemann Sums Related to RealityRiemann Sums Related to Reality
Big Picture Ideas and RelationshipsBig Picture Ideas and Relationships
If F(x) is written as x(t) (aka. Displacement as a function of time)
Then slope of the graph, F’(x), can be written as x’(t) (aka v(t), the velocity as a function of time)
And F(b) - F(a) is the really the just the xfinal - xinitial.
This is also equal to the summation of all velocity x time calculations [f(ci)(xi-xi-1)] or rewritten as [v(ci)(ti-ti-1)]
If F(x) is written as x(t) (aka. Displacement as a function of time)
Then slope of the graph, F’(x), can be written as x’(t) (aka v(t), the velocity as a function of time)
And F(b) - F(a) is the really the just the xfinal - xinitial.
This is also equal to the summation of all velocity x time calculations [f(ci)(xi-xi-1)] or rewritten as [v(ci)(ti-ti-1)]
The graph of y(x)Referred to as F(x) [or x(t)]
The graph of y(x)Referred to as F(x) [or x(t)]
x(a)
x(b)
x ti−1( )
x(ti )ti −ti−1
x(ti )−x ti−1( )ti −ti−1
′x (ci ) = v(ci )
Δt Δt
The graph of y’(x);Called F’ (x); [or x’ (t)]
The graph of y’(x);Called F’ (x); [or x’ (t)]
The graph of F’(x) is renamed f(x); [or x’ (t) is renamed v(t)]The graph of F’(x) is renamed f(x); [or x’ (t) is renamed v(t)]
Riemann Sum with only 1 approximation (Δt: large)Riemann Sum with only 1 approximation (Δt: large)
tt
x
x(a)
x(b)
x ti−1( )
x(ti )
ti −ti−1
x(ti )−x ti−1( )ti −ti−1
′x (ci ) = v(ci )
x(ci ) only a reference point; not the "height"
Riemann Sum with only 2 approximations (Δt: still large)
Riemann Sum with only 2 approximations (Δt: still large)
t
x
x(a)
x(b)
x ti−1( )
x(ti )
ti −ti−1
x(ti )−x ti−1( )ti −ti−1
′x (ci ) = v(ci )
Riemann Sum with 9 approximations (Δt: medium)
Riemann Sum with 9 approximations (Δt: medium)
t
x
x(a)
x(b)
x ti−1( )
x(ti )
ti −ti−1
x(ti )−x ti−1( )ti −ti−1
′x (ci ) = v(ci )
Δt
Δt
Riemann Sum with 17 approximations (Δt: small)
Riemann Sum with 17 approximations (Δt: small)
t
x
x(a)
x(b)
x ti−1( )x(ti )
ti −ti−1
x(ti )−x ti−1( )ti −ti−1
′x (ci ) = v(ci )
Δt
Riemann Sum with only 33 approximations (Δt: smaller)Riemann Sum with only 33 approximations (Δt: smaller)
t
x
Riemann SumsRiemann Sums
Confusing Points:x(ci) is only a point of reference, not the “height” to which
the Δt is multiplied to get the area under the curve. In fact, it is the area under the v(t) graph that we are trying
to find in order to determine the total displacement.
Confusing Points:x(ci) is only a point of reference, not the “height” to which
the Δt is multiplied to get the area under the curve. In fact, it is the area under the v(t) graph that we are trying
to find in order to determine the total displacement.
Riemann SumsRiemann Sums
As Δt decreases, your approximations become more accurate.
Note: Summing up all of the “slope of x vs t times Δt” (aka. “velocity x time”) calculations will equal the
total displacement (aka. The final position minus the starting position).
As Δt decreases, your approximations become more accurate.
Note: Summing up all of the “slope of x vs t times Δt” (aka. “velocity x time”) calculations will equal the
total displacement (aka. The final position minus the starting position).
Section 21.6Section 21.6
How do we describe and apply the concept of electric field?How do we define electric fields in terms of the
force on a test charge?
How do we describe and apply the concept of electric field?How do we define electric fields in terms of the
force on a test charge?
Section 21.6Section 21.6
How do we describe and apply Coulomb’s Law and the Principle of Superposition?How do we use Coulomb’s Law to describe the
electric field of a single point charge?How do we use vector addition to determine
the electric field produced by two or more point charges?
How do we describe and apply Coulomb’s Law and the Principle of Superposition?How do we use Coulomb’s Law to describe the
electric field of a single point charge?How do we use vector addition to determine
the electric field produced by two or more point charges?
21.6 The Electric Field
The electric field is the force on a small charge, divided by the charge:
21.6 The Electric Field
For a point charge:
21.6 The Electric Field
Force on a point charge in an electric field:
Superposition principle for electric fields:
21.6 The Electric Field
Problem solving in electrostatics: electric forces and electric fields
1. Draw a diagram; show all charges, with signs, and electric fields and forces with directions
2. Calculate forces using Coulomb’s law
3. Add forces vectorially to get result
Section 21.8Section 21.8
How do we describe and apply Coulomb’s Law and the Principle of Superposition?How do we compare and contrast Coulomb’s
Law and the Universal Law of Gravitation?
How do we describe and apply Coulomb’s Law and the Principle of Superposition?How do we compare and contrast Coulomb’s
Law and the Universal Law of Gravitation?
21.8 Field Lines
The electric field can be represented by field lines. These lines start on a positive charge and end on a negative charge.
Electric Field created by a spherically charged objectElectric Field created by a spherically charged object
Electric Field created by a spherically charged objectElectric Field created by a spherically charged object
21.8 Field Lines
The number of field lines starting (ending) on a positive (negative) charge is proportional to the magnitude of the charge.
The electric field is stronger where the field lines are closer together.
21.8 Field Lines
Electric dipole: two equal charges, opposite in sign:
21.8 Field Lines
Summary of field lines:
1. Field lines indicate the direction of the field; the field is tangent to the line.
2. The magnitude of the field is proportional to the density of the lines.
3. Field lines start on positive charges and end on negative charges; the number is proportional to the magnitude of the charge.
21.8 Field Lines
Summary of field lines:
4. Field lines never cross because the electric field cannot have two values for the same point.
EM Field uses color to represent the field strength (ie. Red is stronger; blue is weaker). Each charge below is ±10q. EM Field uses color to represent the field strength (ie. Red is stronger; blue is weaker). Each charge below is ±10q.
SummarySummary
Using Newton’s Second Law, what the formula for force?
HW (Place in your agenda): “Foundational Mathematics’ Skills of Physics” Packet (Page 16) Web Assign 21.5 - 21.7
Future assignments: Electrostatics Lab #3: Lab Report (Due in 2 classes)
Using Newton’s Second Law, what the formula for force?
HW (Place in your agenda): “Foundational Mathematics’ Skills of Physics” Packet (Page 16) Web Assign 21.5 - 21.7
Future assignments: Electrostatics Lab #3: Lab Report (Due in 2 classes)
How do we use Coulomb’s Law and the principle of superposition to determine the force that acts between point charges?