Logic Eleanor Roosevelt High School Geometry Mr. Chin-Sung Lin.
Lesson 17 Electric Fields and Potential Eleanor Roosevelt High School Chin-Sung Lin.
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Transcript of Lesson 17 Electric Fields and Potential Eleanor Roosevelt High School Chin-Sung Lin.
Lesson 17
Electric Fields and Potential
Eleanor Roosevelt High School
Chin-Sung Lin
Electric Fields
Law of Universal Gravitation
Coulomb’s Law
Gravitational & Electric Forces
What are the formulas for the following physics laws?
Gravitational & Electric Forces
Fg = G m1 m2
r2
Law of Universal Gravitation
Coulomb’s Law
Fe = k q1 q2
r2
Gravitational Field What’s the definition of gravitational field?
Gravitational Field
• Fg: gravitational force (N)
• m: mass (kg)
• g: gravitational field strength (N/kg, or m/s2)
g = Fg
m
Gravitational Field: Force per unit mass
Electric Field
• Fe: electric force (N)
• q: charge (C)
• E: electric field strength (N/C)
E = Fe
q
Electric Field: Force per unit charge
Gravitational & Electric Fields
E = Fe
q
Electric Field
g = Fg
m
Gravitational Field
Electric Field
Source Charge
+q+QFe
Fe
qE =
Test Charge
r
Electric Field
Source Charge
Fe
qE =
Test Charge
+q–Q Fer
Electric Field Electric field is a vector
A vector includes ___________ and ____________
Source Charge
Test Charge
+q+QFe
r Fe
qE =
+q–Q Fer
Electric Field Electric field is a vector
A vector includes direction and magnitude
Source Charge
Test Charge
+q+QFe
r Fe
qE =
+q–Q Fer
Electric Field
E = Fe
q
Can you apply Coulomb’s law to this formula and then simplify it?
Source Charge
+q+QFe
Test Charge
r
= ???
Electric Field
• Fe: electric force (N)
• q: test charge (C)
• Q: source charge (C)
• E: electric field strength (N/C)
• r: distance between charges (m)
• k: electrostatic constant (N m2/C2)
Electric Field: Force per unit charge
E = Fe
q= k
q Q
r2 q= k
Q
r2
Electric Field Example
What is the magnitude of the electric field strength when an electron experiences a 5.0N force?
Electric Field Example
E = Fe / q
E = 5 N / (1.6 x 10-19 C)
= 3.13 x 1019 N/C
What is the magnitude of the electric field strength when an electron experiences a 5.0N force?
Electric Field Example
What are the magnitude and direction of the electric field 1.5 m away from a positive charge of 2.1*10-9 C?
Electric Field Example
What are the magnitude and direction of the electric field 1.5 m away from a positive charge of 2.1*10-9 C?
E = k Q / r2
E = (8.99 x 109 N m2/C2) (2.1 x 10-9 C) / (1.5 m)2
= 8.4 N/C
Direction: away from the positive charge
Electric Field Exercise
There is a negative charged particle of 0.32 C in the free space. (a) What are the magnitude and direction of the electric field 2.0 m away from the particle? (b) What are the magnitude and direction of the electric force when an electron is placed 2.0 m away from this particle?
[3 minutes] e –– 0.32 C2.0 m
Electric Field Exercise
There is a negative charged particle of 0.32 C in the free space. (a) What are the magnitude and direction of the electric field 2.0 m away from the particle?
E = k Q / r2
E = (8.99 x 109 N m2/C2) (0.32 C) / (2.0 m)2
= 7.2 x 108 N/C
Direction: toward the negative charge
Electric Field Exercise
There is a negative charged particle of 0.32 C in the free space. (b) What are the magnitude and direction of the electric force when an electron is placed 2.0 m away from this particle? E = Fe / q Fe = q E
Fe = (1.6 x 10-19 C) (7.2 x 108 N/C)
= 1.15 x 10-10 N
Aim: Electric Field
DoNow: (4 minutes)
Write down the definition of Electric Field in words
Write down the formulas of Electric Field in two different forms
Define every symbol in the formula and identify their units
Identify the relationships between Electric Field and other variables
Aim: Electric Field
Electric Field
• Fe: electric force (N)
• q: test charge (C)
• Q: source charge (C)
• E: electric field strength (N/C)
• r: distance between charges (m)
• k: electrostatic constant (N m2/C2)
Electric Field: Force per unit charge
E = Fe
q= k
Q
r2
Electric Field
• Fe: electric force (N)
• q: test charge (C)
• Q: source charge (C)
• E: electric field strength (N/C)
• r: distance between charges (m)
• k: electrostatic constant (N m2/C2)
Electric Field: Force per unit charge
E ~ Fe E ~ 1r2
E ~ Q 1qE ~
Electric Field
Source Charge
+q+QFe
Fe
qE =
Test Charge
If you shift the test charge around, where can you find the electric field with the same magnitude?
Electric Field
Source Charge
+q+QFe
Test Charge
Fe
Fe
Fe
E
E
E
E
Electric Field
Source Charge
Test Charge
+q+QFe
Fe
Fe
Fe
E
E
E
E
What will happen if you move the test charges away from the source charge?
Electric Field
Source Charge
+q+QFe
Test Charge
Fe
Fe
Fe
E
E
E
E
Electric Field
Fe
Fe
Source Charge
+q+QFe
Test Charge
Fe
Fe
E
E
E
E
Fe
Fe
Fe
E
E
E
E
Electric Field
Source Charge
+q+QFe
Test Charge
Fe
Fe
Fe
E
E
E
E
Fe
Fe
Fe
Fe
E
E
E
E
Test Charge
+q
Vector representation
-+
Electric Field Representation
Line-of-Force representation
-+
Electric Field Representation
Electric Field Representation
-+
How do you decide the strength of electric field?
Electric Field Representation
-+
When the field lines are denser, the field is stronger
Electric Field Representation Where can you find the the strongest
electric field?
A
B
C
D
E
Electric Field: Point Charge
Line-of-Force representation
-+
Electric Field: Pair of Charges
Line-of-Force representation
Electric Field: Pair of Charges
Sketch the electric field for like charges?
++
Electric Field: Pair of Charges
Line-of-Force representation
++
Electric Field: Pair of Charges
Line-of-Force representation
Electric Field: Parallel Plates
Line-of-Force representation
Electric Field: Parallel Plates
Anything special for the electric field between the parallel plates charged with opposite charges?
Electric Field: Parallel Plates
The electric field between the parallel plates is uniform except at both ends
Electric Field Example
A charged droplet of mass 5.87 x 10-10 kg is hovering motionless between two parallel plates. The parallel plates have a electric field of 1.2 x 107 N/C and are 2.00 mm apart. (a) What is the charge on the particle? (b) By how many electrons is the particle deficient?
Electric Field Example
A charged droplet of mass 5.87 x 10-10 kg is hovering motionless between two parallel plates. The parallel plates have a electric field of 1.2 x 107 N/C and are 2.00 mm apart. (a) What is the charge on the particle? E = Fe / q Fe = E q Fg = m g Fe = Fg
E q = m g
(1.2 x 107 N/C) q = (5.87 x 10-10 kg) (9.81 m/s2)
q = 4.80 x 10-16 C
Electric Field Example
A charged droplet of mass 5.87 x 10-10 kg is hovering motionless between two parallel plates. The parallel plates have a electric field of 1.2 x 107 N/C and are 2.00 mm apart. (b) By how many electrons is the particle deficient?e - = 1.6 x 10-19 C
number of e - = 4.80 x 10-16 C / 1.6 x 10-19 C = 3000 e –
Electric Field Exercise
A charged droplet of mass 5.87 x 10-10 kg is hovering motionless between two parallel plates. The parallel plates have a electric field of 9.6 x 106 N/C and are 2.00 mm apart. What is the charge on the particle?
Electric Field Exercise
A charged droplet of mass 5.87 x 10-10 kg is hovering motionless between two parallel plates. The parallel plates have a electric field of 9.6 x 106 N/C and are 2.00 mm apart. What is the charge on the particle? E = Fe / q Fe = E q Fg = m g Fe = Fg
E q = m g
(9.6 x 106 N/C) q = (5.87 x 10-10 kg) (9.81 m/s2)
q = 6.0 x 10-16 C
Electric Field Exercise
A positively charged ball with mass 20 g is hanging between two charged parallel plates from the ceiling through an insulating wire with length 0.1 m. The electric field strength of the charged parallel plates is 4.2 x 109 N/C. When the ball is in balance, the wire and the vertical line form an angle of 60o. What is the charge of the ball?
Electric Fields
Electric Fields
Electric Fields
Electric Fields
Electric Fields
Electric Fields and Shielding
E = 0Electric Shielding
Electric Fields and Shielding
Cancellation of electric force
The electric forces of area A and area B on P completely cancel out
A BP
Electric Potential
Aim: Electric PotentialDoNow: (3 minutes)
Write down the formulas of Electric Field
Draw the electric field surrounding a pair of opposite charge
Draw the electric field surrounding a pair of charged parallel plates
Aim: Electric Potential
Electric Field
• Fe: electric force (N)
• q: test charge (C)
• Q: source charge (C)
• E: electric field strength (N/C)
• r: distance between charges (m)
• k: electrostatic constant (N m2/C2)
Electric Field: Force per unit charge
E = Fe
q= k
Q
r2
Electric Field: Pair of Charges
Line-of-Force representation
Electric Field: Parallel Plates
Line-of-Force representation
Gravitational Potential Energy (GPE)
Gravitational Potential Energy (GPE)
What happens in the picture?
What types of energy have been converted?
Gravitational Potential Energy (GPE)
What happens in the picture?
What types of energy have been converted?
If we want to pull the weight up back to its original position, what should we do?
Gravitational Potential Energy (GPE)
What happens in the picture?
What types of energy have been converted?
If we want to pull the weight up back to its original position, what should we do?
How much work do we need?
Electric Potential Energy (EPE)
++
++
-----
What are they in common?
Electric Potential Energy (EPE)
++
++
-----
What happens in the picture?
What types of energy have been converted?
If we want to pull the weight up back to its original position, what should we do?
How much work do we need?
Electric Potential Energy (EPE)
++
++
-----
What are they different?
Electric Potential Energy
What did the monkey do in order to bring a positively charged ball toward a
positively charged object?
Electric Potential Energy
What did the monkey do in order to bring a positively charged ball toward a
positively charged object?
When the ball was released, what happened to the ball? Why?
Gravitational Potential Energy
The work performed in taking a mass from height A to height B does not depend on the path
B
A A
Electric Potential Energy
B
A
The work performed in taking a charge from A to B does not depend on the path
Gravitational Potential Energy
x2
What happens when we double the mass?
Gravitational Potential Energy
x2
When mass is doubled, the gravitational potential energy is also doubled
PE2 = (2m)gh = 2(mgh) = 2PE1
Electric Potential Energy
++
++
---
x2
What did we double here?
Electric Potential Energy
++
++
---
x2
We doubled the charge.
What happens when we double the charge?
Electric Potential Energy
++
++
---
x2
When charge is doubled, the electric potential energy is also doubled
Electric Potential Energy
• W: electric (potential) energy aka work (J)
W is a scalar (not a vector)
W or EPE
Potential Energy – Capability to Do Work
Electric Potential Energy
• W: electric (potential) energy aka work (J)
W or EPE
Potential Energy – Capability to Do Work
W ~ q
Electric Potential
• W: electric (potential) energy, aka work (J)
• V: electric potential, aka potential difference,
aka voltage (V, Volts)
• q: charge (C)
V = Wq
Electric potential energy per unit charge
Electric Potential
Electric potential (V) is based on a zero reference point
Only the potential difference matters Electric potential (Voltage, V) is the work
(W) required to bring a unit charge (1 C) from the zero reference point
V is a scalar (not a vector)
W = qV
Electric Potential Example
How much work is required to move 3.0 C of positive charge from the negative terminal of a 12-volt battery to the positive terminal?
Electric Potential Example
How much work is required to move 3.0 C of positive charge from the negative terminal of a 12-volt battery to the positive terminal?
V = W / q W = q V
W = (3.0 C) (12.0 V) = 36.0 J
Electric Potential Example
If an electron loses 1.4 x 10-15 J of energy in traveling from the cathode to the screen of a computer monitor, across what potential difference must it travel?
Electric Potential Example
If an electron loses 1.4 x 10-15 J of energy in traveling from the cathode to the screen of a computer monitor, across what potential difference must it travel?
V = W / q W = q V
V = (1.4 x 10-15 J) / (1.6 x 10-19 C) = 8750 V
Electric Potential Example
Can you make up a question using the definition of electric potential?
Electric Potential Example
Electric Potential: Parallel Plates
What is special about the electric field between the charged parallel plates?
Electric Potential: Parallel Plates
Electric Field (E): is uniform due to uniform density of the electric field lines
E E E
Electric Potential: Parallel Plates
If we place test charge at different locations between the charged parallel plates, compare the forces experienced by these test charges
E E E
Electric Potential: Parallel Plates
Electric Force (Fe): experienced by a test charge is constant due to Fe = qE
E E E
Fe
FeFe
Electric Potential: Parallel Plates
Compare the work required to move test charges from the negative plate to the positive plate
E E EFe dFeFe
Electric Potential: Parallel Plates
Electric potential energy / work (W): required to move a test charge from negative plate to positive plate is constant due to W = Fe d
E E EFe dFe Fe
Electric Potential: Parallel Plates
V = Wq
Given the following formulas, can you derive the formula for Electric potential (V) and Electric field (E)?
W = Fe d
Fe = q E
Electric Potential: Parallel Plates
V = Wq
Electric potential (V):
W = Fe d and Fe = q E
W = q E d
V = E d or
= q E dq = E d
E = Vd
Electric Potential: Parallel Plates
Electric potential (V): relative to the negative plate is proportional to the distance to it due to V = E d
E E E
dV
Equipotential Lines: Parallel Plates
Equipotential Lines: on an equipotential line, voltages are all the same
Equipotential lines are perpendicular to field lines
E E E
d1
V1V1V1
V2V2V2
d2
Equipotential Lines: Point Charge
Equipotential Lines for a point charge:
Equipotential Lines: Point Charge
Equipotential Lines for a charge pair
Electric Field and Potential
• E: electric field (N/C or V/m)• V: electric potential / potential difference /
voltage (V, Volts)• d: distance between parallel plates (m)• q: charge (C)
Electric field
E = Vd =
Fe
q
Electric Potential Example
A charged droplet of mass 5.87x 10-10 kg is hovering motionless between two parallel plates. The parallel plates have a potential difference of 24000 V and are 2.00 mm apart. What is the charge on the particle?
A charged droplet of mass 5.87x 10-10 kg is hovering motionless between two parallel plates. The parallel plates have a potential difference of 24000 V and are 2.00 mm apart. What is the charge on the particle?
E = Fe / q Fe = E q Fg = m g Fe = Fg
E q = m g E = V / d V q / d = m g
(24000 V) q / ((0.002 m) = (5.87 x 10-10 kg) (9.81 m/s2)
q = 4.80 x 10-16 C
Electric Potential Example
The End