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Physics II:
Electricity & Magnetism
Chapter 21
Section 21-5
Tuesday
(Day 5)
Warm-Up
Tues, Jan 27
 Complete Graphic Organizers for Sections 21-1 to 21-2
 Have you logged onto webassign.net?
 Place your homework on my desk:
 “Foundational Mathematics’ Skills of Physics” Packet
(Page 22 & 23)
 Future assignments:
 Electrostatics Lab #1 Packet and Conclusion
Questions (Due in 5 classes)
 Electrostatics Lab #2: Lab Report (Due in 5 classes)
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 compare and contrast the basic properties of an
insulator and a conductor?
 How do we describe and apply the concept of induced charge and
electrostatic shielding?
 How do we describe and apply Coulomb’s Law and the Principle
of Superposition?
Vocabulary
 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
 Test Charge
 Electric Field
 Field Lines
 Electric Dipole
 Dipole Moment
Foundational Mathematics
Skills in Physics Timeline
Day
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Day
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WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?
Agenda
 Review “Foundational Mathematics’ Skills of Physics”
Packet (Page 22 & 23) with answer guide.
 Discuss the quantized charge of electrons and protons
 Complete Electrostatic Labs #1 & 2
Section 21.5
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 use Coulomb’s Law and the
principle of superposition to determine the
force that acts between point charges?
21.5 Coulomb’s Law
Charge on the negative electron and
positive proton is:
e  1.602 x 10 19 C
The basic unit of charge is the
Coulomb, C. Electric charge is
quantized in whole number multiples
of the electron charge.
Q  n e (where n  1, 2, 3 , . . .)
Summary
 From Electrostatics Lab #2:
 What is the total positive charge of water (in Coulombs)?
 HW (Place in your agenda):
 “Foundational Mathematics’ Skills of Physics” Packet (Page
24)
 Web Assign Problems #1 & 2
 Future assignments:
 Electrostatics Lab #1 Packet and Conclusion
Questions (Due in 5 classes)
 Electrostatics Lab #2: Lab Report (Due in 5 classes)
Wednesday
(Day 6)
School closed due to inclement
weather
Thursday
(Day 6)
Two Hour Delay due to inclement
weather
Warm-Up
Thurs, Jan 29
 Complete Graphic Organizers for Sections 21-3 to 21-4
 For § 21-4: Identify how the process of charging by friction,
induction, and conduction applies to:
Walking across the carpet and touching a doorknob
A Van de Graaff Generator
Lightning
 Place your homework on my desk:
 “Foundational Mathematics’ Skills of Physics” Packet (Page 24)
 Web Assign Problems #1 & 2
Warm-Up
Thurs, Jan 29
Future assignments:
Electrostatics Lab #1 Packet and Conclusion Questions
(Due in 4 classes)
Electrostatics Lab #2: Lab Report (Due in 4 classes)
Teacher Assignment:
Acquire an IBM-Compatible computer for EM Field
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?
Vocabulary
 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
 Test Charge
 Electric Field
 Field Lines
 Electric Dipole
 Dipole Moment
Foundational Mathematics
Skills in Physics Timeline
Day
Pg(s)
Day
Pg(s)
Day
Pg(s)
Day
Pg(s)
1
1
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5
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WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?
Agenda
 Review “Foundational Mathematics’ Skills of Physics”
Packet (Page 24) with answer guide.
 Review select Electrostatic Lab #1 & 2 Results
 Discuss Coulomb’s Law, Newton’s Law of Gravitation,
and the Superposition Principle
 Apply Coulomb’s Law
 Begin The Four Circles Graphic Organizer
Section 21.5
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 use Coulomb’s Law and the
principle of superposition to determine the
force that acts between point charges?
21.5 Coulomb’s Law
Experiment shows that the electric force
between two charges is proportional to the
product of the charges and inversely
proportional to the distance between them.
How do we compare and contrast Coulomb’s Law and the Universal Law of Gravitation?
6.1 Newton’s Law of Gravitation
Experiment shows that the gravitational force
between two masses is proportional to the
product of the masses and inversely
proportional to the distance between them.
How do we compare and contrast Coulomb’s Law and the Universal Law of Gravitation?
21.5 Coulomb’s Law
Coulomb’s law:
This equation gives the magnitude of
the force.
How do we compare and contrast Coulomb’s Law and the Universal Law of Gravitation?
6.1 Newton’s Law of Gravitation
Newton’s Law of Gravitation:
m1 m2
F  G 2
r
This equation gives the magnitude of
the force.
How do we compare and contrast Coulomb’s Law and the Universal Law of Gravitation?
21.5 Coulomb’s Law
The electric force is along the line connecting the
charges, and is attractive if the charges are
opposite, and repulsive if they are the same.
How do we compare and contrast Coulomb’s Law and the Universal Law of Gravitation?
6.1 Newton’s Law of Gravitation
The gravitational force is along the line
connecting the masses and is always attractive
regardless of the size either mass.
How do we compare and contrast Coulomb’s Law and the Universal Law of Gravitation?
21.5 Coulomb’s Law
Unit of charge: coulomb, C
The proportionality constant in Coulomb’s
law is then:
Charges produced by rubbing are
typically around a microcoulomb:
How do we compare and contrast Coulomb’s Law and the Universal Law of Gravitation?
21.5 Coulomb’s Law
Unit of charge: coulomb, C
The proportionality constant in Coulomb’s
law is then:
Charges produced by rubbing are
typically around a microcoulomb:
How do we compare and contrast Coulomb’s Law and the Universal Law of Gravitation?
6.1 Newton’s Law of Gravitation
Unit of mass: kilogram, kg
The proportionality constant in Newton’s law
is:
NOTE: The Gravitational constant is
significantly less than the electrostatic
constant . . . Yes, we are going to
calculate this difference.
How do we compare and contrast Coulomb’s Law and the Universal Law of Gravitation?
Summary
 After comparing the force constants for electrostatics and gravity,
identify which Force is stronger.
 HW (Place in your agenda):
 †“Foundational Mathematics’ Skills of Physics” Packet (Page 12)
 Web Assign Problems #3
 Future assignments:
 Electrostatics Lab #1 Packet and Conclusion Questions (Due in 4
classes)
 Electrostatics Lab #2: Lab Report (Due in 4 classes)
How do we compare and contrast Coulomb’s Law and the Universal Law of Gravitation?
Friday
(Day 7)
Warm-Up
Fri, Jan 30
 Begin Graphic Organizer for Sections 21-5
 Place your homework on my desk:
 †“Foundational Mathematics’ Skills of Physics” Packet (Page 12)
 Future assignments:
 Electrostatics Lab #1 Packet and Conclusion Questions (Due in 3
classes)
 Electrostatics Lab #2: Lab Report (Due in 3 classes)
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?
Vocabulary
 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
 Test Charge
 Electric Field
 Field Lines
 Electric Dipole
 Dipole Moment
Foundational Mathematics
Skills in Physics Timeline
Day
Pg(s)
Day
Pg(s)
Day
Pg(s)
Day
Pg(s)
1
1
2
6
3
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21
2
13
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7
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10
5
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WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?
Agenda
 †Review “Foundational Mathematics’ Skills of Physics”
Packet (Page 12) with answer guide.
 Review select Electrostatic Lab #1 & 2 Results
 Coulomb’s Law & Vectors
 Applications of Coulomb’s Law
Section 21.5
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 use Coulomb’s Law and the
principle of superposition to determine the
force that acts between point charges?
21.5 Coulomb’s Law
The proportionality constant k can also be
written in terms of
, the permittivity of free
space:
How do we use Coulomb’s Law and the principle of superposition to determine the force that acts between point charges?
21.5 Coulomb’s Law
Coulomb’s law strictly applies only to point charges.
Superposition: for multiple point charges, the forces
on each charge from every other charge can be
calculated and then added as vectors.
How do we use Coulomb’s Law and the principle of superposition to determine the force that acts between point charges?
21.5 Solving Problems Involving
Coulomb’s Law and Vectors
The net force on a charge is the vector
sum of all the forces acting on it.
How do we use Coulomb’s Law and the principle of superposition to determine the force that acts between point charges?
21.5 Solving Problems Involving
Coulomb’s Law and Vectors
Vector addition review:
How do we use Coulomb’s Law and the principle of superposition to determine the force that acts between point charges?
3 Dimensional Axes & Unit
Vector Notation
How do we use Coulomb’s Law and the principle of superposition to determine the force that acts between point charges?
Steps for Solving Coulomb’s Law
Problems:
Determine the direction of the force
 Determine if your force vectors will
 represent all forces as repulsive. (NOTE: Since the
CORRECT direction of the force may NOT have been
established, the values of the charges, q, must be
entered as POSITIVE or NEGATIVE into Coulomb’s
Law. This is similar to substituting a=-9.8 m/s2 into
a kinematic equations): GENERAL CASE
OR
 Establish the direction of the force as repulsive or
attractive. (NOTE: Since the direction of the force is
now established in the correct direction, all charges,
q, will be POSITIVE values when entered into
Coulomb’s Law. This is similar to establishing a=-g
in the 2-D kinematic equations): SPECIFIC CASE
How do we use Coulomb’s Law and the principle of superposition to determine the force that acts between point charges?
Steps for Solving Coulomb’s Law
Problems:
Problem Solving
 Resolve the force vectors
 Sum up the force vectors in the x, y, and z
directions
 Use Pythagorean Theorem to determine the
magnitude of the resultant force vector
 Use SOH CAH TOA to determine the direction
of the resultant force vector
 Sounds simple, yah?
How do we use Coulomb’s Law and the principle of superposition to determine the force that acts between point charges?
Applying Coulomb’s Law
Three charge are placed are a fixed distance apart
shown on the following slide.
The charge on Q2 is +50 C located at the origin.
The charge on Q1 is -86 C located at 52 cm to the right
of Q2.
The charge on Q3 is +65 C located at 30 cm above Q2.
Calculate the net electrostatic force on charge Q3
due to charges Q1 and Q2.
How do we use Coulomb’s Law and the principle of superposition to determine the force that acts between point charges?
Applying Coulomb’s Law
How do we use Coulomb’s Law and the principle of superposition to determine the force that acts between point charges?
How do we use Coulomb’s Law and the principle of superposition to determine the force that acts between point charges?
How do we use Coulomb’s Law and the principle of superposition to determine the force that acts between point charges?
How do we use Coulomb’s Law and the principle of superposition to determine the force that acts between point charges?
How do we use Coulomb’s Law and the principle of superposition to determine the force that acts between point charges?
How do we use Coulomb’s Law and the principle of superposition to determine the force that acts between point charges?
Relationship between force
and distance
How would the force change IF the
distance were doubled?
FDistance 1  1
FDistance 2
r
 1
2
2r 
1
2
 1
4r
2
2
FDistance 2
r
1
4r

 2 
1 2
FDistance 1
4r
4
r
2
How do we use Coulomb’s Law and the principle of superposition to determine the force that acts between point charges?
Summary
 After comparing the force constants for electrostatics and gravity, identify
which Force is stronger.
 HW (Place in your agenda):
 “Foundational Mathematics’ Skills of Physics” Packet (Page 15)
 Web Assign Problems #3
 Future assignments:
 Electrostatics Lab #1 Packet and Conclusion Questions (Due in 3 classes)
 Electrostatics Lab #2: 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 8)
Warm-Up
Mon, Feb 2
 How many total moles of electrons would have to be removed from
the earth and the moon to cancel out the attractive gravitational force
between them?
 Place your homework on my desk:
 “Foundational Mathematics’ Skills of Physics” Packet (Page 12 & 15)
 Graphic Organizers for Sections 21-1 to 21-4
 Have you complete WebAssign Problems 21.1 - 21.3?
 Future assignments:
 Electrostatics Lab #1 Packet and Conclusion Questions (Due in 2 classes)
 Electrostatics Lab #2: Lab Report (Due in 2 classes)
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?
Vocabulary
 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
 Test Charge
 Electric Field
 Field Lines
 Electric Dipole
 Dipole Moment
Foundational Mathematics
Skills in Physics Timeline
Day
Pg(s)
Day
Pg(s)
Day
Pg(s)
Day
Pg(s)
1
1
2
6
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9
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10
5
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11
WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?
Agenda
 Review “Foundational Mathematics’ Skills of Physics”
Packet (Page 12 & 15) with answer guide.
 Butter Gun
 Applications of Coulomb’s Law
 Coulomb’s Law Lab
Section 21.5
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 use Coulomb’s Law and the
principle of superposition to determine the
force that acts between point charges?
Reviewing the warm-up:
Just a thought . . .
How many total moles of electrons
would have to be removed from
the earth and the moon to cancel
out the attractive gravitational
force between them?
592 615 508 moles of electrons each
1 185 231 015 moles of electrons total
How do we compare and contrast Coulomb’s Law and the Universal Law of Gravitation?
The Butter Gun
The Butter Gun
The Butter Gun
Applying Coulomb’s Law
Application #2
 (III) Three charge are placed are a fixed distance apart
shown on the following slide.
 The charge on Q2 is +50 C located at the origin.
 The charge on Q1 is -86 C located at 52 cm to the right of Q2.
 The charge on Q3 is +65 C located at 30 cm above Q2.
 Qualitatively identify the possible locations of a
POSITIVE 4th charge, Q4, of +1 C so it does not feel a
force due charges Q1, Q2, and Q3 using force diagrams.
 Where do you think it would be if the 4th charge were
NEGATIVE?
How do we use Coulomb’s Law and the principle of superposition to determine the force that acts between point charges?
Applying Coulomb’s Law
How do we use Coulomb’s Law and the principle of superposition to determine the force that acts between point charges?
Applying Coulomb’s Law
How do we use Coulomb’s Law and the principle of superposition to determine the force that acts between point charges?
Applying Coulomb’s Law
How do we use Coulomb’s Law and the principle of superposition to determine the force that acts between point charges?
Applying Coulomb’s Law
Application #3
 (III) IF two of the three charge are placed are a fixed
distance apart shown on the following slide.
 The charge on Q2 is +50 C located at the origin.
 The charge on Q1 is -86 C located at 52 cm to the right of Q2.
 The charge on Q3 is +65 C located at 30 cm above Q2.
 Identify the locations from the origin of a POSITIVE 4th
charge, Q4, of +1 C so it does not feel a force due to
charges
 Q1, and Q2.
 Q2 and Q3.
How do we use Coulomb’s Law and the principle of superposition to determine the force that acts between point charges?
Applying Coulomb’s Law
How do we use Coulomb’s Law and the principle of superposition to determine the force that acts between point charges?
Summary
 Coulomb’s Law Application #3: Determine the location(s) along the xaxis and y-axis for a positive particle to feel a Fnet = 0 N.
 HW (Place in your agenda):
 “Foundational Mathematics’ Skills of Physics” Packet (Page 3)
 Coulomb’s Law Application #3
 Future assignments:
 Electrostatics Lab #1 Packet and Conclusion Questions (Due in 2
classes)
 Electrostatics Lab #2: 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?
Tuesday
(Day 9)
Warm-Up
Tues, Feb 3
 Continue Graphic Organizer for Section 21-5
 Place your homework on my desk:
 “Foundational Mathematics’ Skills of Physics” Packet (Page 3)
 Graphic Organizers?
 Have you complete WebAssign Problems: 21.1 - 21.4?
 Future assignments:
 Electrostatics Lab #1 Packet and Conclusion Questions (Due in 1
class)
 Electrostatics Lab #2: Lab Report (Due in 1 class)
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?
Vocabulary
 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
 Test Charge
 Electric Field
 Field Lines
 Electric Dipole
 Dipole Moment
Foundational Mathematics
Skills in Physics Timeline
Day
Pg(s)
Day
Pg(s)
Day
Pg(s)
Day
Pg(s)
1
1
2
6
3
11
16
16
21
2
13
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7
4
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17
8
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8
5
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†12
9
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19
19
10
5
15
10
7
15
20
20
11
WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?
Agenda
 †Review “Foundational Mathematics’ Skills of Physics”
Packet (Page 3) with answer guide.
 Complete Coulomb’s Law Lab
 Complete Web Assign Problem #4
Summary
 Write down the answer to question 7 on Electrostatics Lab #3 (What happens
just before the balls touch?).
 HW (Place in your agenda):
 “Foundational Mathematics’ Skills of Physics” Packet (Page 4)
 Web Assign Problems #4
 Future assignments:
 Electrostatics Lab #1 Packet and Conclusion Questions (Due tomorrow)
 Electrostatics Lab #2: Lab Report (Postponed Due 1 class)
 Electrostatics Lab #3: Lab Report (Due in 5 classes)
How do we use Coulomb’s Law and the principle of superposition to determine the force that acts between point charges?
Wednesday
(Day 10)
Warm-Up
Wed, Feb 4
 Finish Graphic Organizer for Section 21-5
 Place your homework on my desk:
 “Foundational Mathematics’ Skills of Physics” Packet (Page 4)
 Electrostatics Lab #1 Packet and Conclusion Questions
 Have you complete WebAssign Problems: 21.1 - 21.4?
 Future assignments:
 Electrostatics Lab #2: Lab Report (POSTPONED - Due in 1 class)
 Electrostatics Lab #3: Lab Report (Due in 4 classes)
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?
Vocabulary
 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
 Test Charge
 Electric Field
 Field Lines
 Electric Dipole
 Dipole Moment
Foundational Mathematics
Skills in Physics Timeline
Day
Pg(s)
Day
Pg(s)
Day
Pg(s)
Day
Pg(s)
1
1
2
6
3
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21
2
13
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7
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†12
9
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19
10
5
15
10
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11
WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?
Agenda
 †Review “Foundational Mathematics’ Skills of Physics”




Packet (Page 4) with answer guide.
From “Foundational Mathematics’ Skills of Physics”
(Page 24): 3D Angles, Trigonometry, and xyzComponents
Complete Coulomb’s Law Lab
Begin The Four Circles Graphic Organizer
Complete Web Assign Problem #4
Applying Coulomb’s Law
Application #3
 (III) IF two of the three charge are placed are a fixed
distance apart shown on the following slide.
 The charge on Q2 is +50 C located at the origin.
 The charge on Q1 is -86 C located at 52 cm to the right of Q2.
 The charge on Q3 is +65 C located at 30 cm above Q2.
 Identify the locations from the origin of a POSITIVE 4th
charge, Q4, of +1 C so it does not feel a force due to
charges
 Q1, and Q2.
 Q2 and Q3.
How do we use Coulomb’s Law and the principle of superposition to determine the force that acts between point charges?
Applying Coulomb’s Law
How do we use Coulomb’s Law and the principle of superposition to determine the force that acts between point charges?
3D Angles, Trigonometry,
and xyz-Components
Fx  F cos  cos 
y
Fxz Fx
F
F Fxz
Fy  F sin 
l

F

x

l
l
z
Fy
F
Fx  F cos  sin 
Fyz Fz
F
F Fxz
Summary
 (Assignment from 2 classes ago) write down the locations for Coulomb’s Law
Application Question #3
 HW (Place in your agenda):
 “Foundational Mathematics’ Skills of Physics” Packet (Page 5)
 Web Assign Problems #4
 Future assignments:
 Electrostatics Lab #2: Lab Report (Due tomorrow)
 Electrostatics Lab #3: Lab Report (Due in 4 classes)
How do we use Coulomb’s Law and the principle of superposition to determine the force that acts between point charges?