College Physics II. Electric Field & Electric Charge II. Greg Anderson Department of Physics & Astronomy. January 2012
Northeastern Illinois University
College Physics II Electric Field & Electric Charge II Greg Anderson Department of Physics & Astronomy Northeastern ...
College Physics II Electric Field & Electric Charge II Greg Anderson Department of Physics & Astronomy Northeastern Illinois University January 2012
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College Physics II
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Overview
Electric Charge Electrostatic Forces Electric Fields
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Outline Electro-Magnetic Forces
Outline ◆ Review: Electric charges & forces
Electric Charge
■ Electric charge, conserved and quantized.
Electrostatic Forces
■ Coulomb’s Law
Electric Fields
◆ Coulomb’s Law
■ Attraction & Repulsion ■ Adding Force Vectors ◆ The Electric Field
■ Electric Field Lines ■ Electric Monopoles ■ Electric Dipoles c
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Outline Electro-Magnetic Forces Electric Charge Electrostatic Forces
Electro-Magnetic Forces With the exception gravity, almost every force that you witness in everyday life is electro-magnetic in origin. ◆ EM forces binding atoms together.
Electric Fields
◆ EM forces binding atoms into molecules. ◆ EM forces bind molecules together.
Electric forces are produced by electric charges.
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Outline Electro-Magnetic Forces Electric Charge Electric Charge Quantization Electric Charge Quantization II Charged Constituents Electric Charged is Conserved Charge Conservation Examples
Electric Charge
Electrostatic Forces Electric Fields
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Outline Electro-Magnetic Forces Electric Charge Electric Charge Quantization Electric Charge Quantization II Charged Constituents Electric Charged is Conserved Charge Conservation Examples Electrostatic Forces
Electric Charge Quantization Electric charge is quantized: A charged object has a surplus or deficit in the number of electrons relative to protons. ◆ e = fundamental unit of charge
Qproton = +e,
Qelectron = −e
◆ For any charge:
Electric Fields
Q = ne,
n = 0, ±1, ±2, . . .
SI Units: [Charge] = Coulomb = C e = 1.6 × 10−19 C. c
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Outline Electro-Magnetic Forces Electric Charge Electric Charge Quantization Electric Charge Quantization II Charged Constituents Electric Charged is Conserved Charge Conservation Examples Electrostatic Forces
Electric Charge Quantization II Electric charge is quantized: A charged object has a surplus or deficit in the number of electrons relative to protons. For any charged object: Q = ne,
n = 0, ±1, ±2, . . .
◆ Let Ne be the number of electrons in an object ◆ Let Np be the number of protons in an object.
Electric Fields
n = Np − N e
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Outline Electro-Magnetic Forces Electric Charge Electric Charge Quantization Electric Charge Quantization II Charged Constituents Electric Charged is Conserved Charge Conservation Examples Electrostatic Forces
Charge & Charged Constituents The total charge of any composite object is the sum of the charges of its charged constituents: electrons and protons. ◆ Ne electrons, each with charge −e contribute:
Qelectrons = Ne (−e) = −Ne e
◆ Np protons, each with charge +e contribute:
Electric Fields
Qprotons = Np e Example
Together they give a total charge: Q = (Np − Ne )e c
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− +
− +
+ Np = 3
−
Ne = 4
− Q = −1e
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Outline Electro-Magnetic Forces Electric Charge Electric Charge Quantization Electric Charge Quantization II Charged Constituents Electric Charged is Conserved Charge Conservation Examples
Electric Charged is Conserved Electric Charge is Conserved: The total charge of an isolated system never changes.
For an Isolated System:
Qinitial = Qfinal
Electrostatic Forces Electric Fields
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Charge Conservation Examples
Outline Electro-Magnetic Forces
Examples of electric charge conservation:
Electric Charge Electric Charge Quantization Electric Charge Quantization II Charged Constituents Electric Charged is Conserved Charge Conservation Examples
Outline Electro-Magnetic Forces Electric Charge Electrostatic Forces The Electric Force Active Learning Active Learning Adding Two Forces: F = F1 + F2 Example: Adding two forces
Electrostatic Forces
Electric Fields
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Outline Electro-Magnetic Forces
The Electric Force Charges of opposite sign attract.
Electric Charge Electrostatic Forces The Electric Force Active Learning Active Learning Adding Two Forces: F = F1 + F2 Example: Adding two forces Electric Fields
Coulomb’s law: −
+ F
F
1 Q1 Q2 Q1 Q2 F =k 2 = r 4πǫ0 r2 k ≃ 9 × 109 Nm2 /C2
Charges of the same sign reǫ0 = permittivity of free space. pel.
+ F
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+ F
1 ǫ0 = = 8.85×10−12 C2 /Nm2 4πk
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Outline Electro-Magnetic Forces Electric Charge Electrostatic Forces The Electric Force Active Learning Active Learning Adding Two Forces: F = F1 + F2 Example: Adding two forces
Active Learning Two equal mass pith balls are both charged. They hang on strings as shown in the figure. What can we say about the two charges charges?
Electric Fields
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a. Q1 = Q2 b. Q1 = −Q2 θ
Q1
θ
Q2
c. | Q1 |=| Q2 | d. not enough information
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Outline Electro-Magnetic Forces Electric Charge Electrostatic Forces The Electric Force Active Learning Active Learning Adding Two Forces: F = F1 + F2 Example: Adding two forces
Active Learning Two equal mass pith balls are both charged. They hang on strings as shown in the figure. What can we say about the two charges charges?
Electric Fields
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a. Q1 = Q2 b. Q1 = −Q2 θ
Q1
θ
Q2
c. | Q1 |=| Q2 | d. not enough tion
informa-
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Outline Electro-Magnetic Forces Electric Charge Electrostatic Forces The Electric Force Active Learning Active Learning Adding Two Forces: F = F1 + F2 Example: Adding two forces
Active Learning Two equal mass pith balls are both charged. They hang on strings as shown in the figure. What can we say about the sign of the two charges? a. One is + the other is −. b. Both are −. c. Both are +. θ
θ
Electric Fields
Q1
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Q2
d. The charges are the same sign, but we can’t tell if they are + or −.
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Outline Electro-Magnetic Forces Electric Charge Electrostatic Forces The Electric Force Active Learning Active Learning Adding Two Forces: F = F1 + F2 Example: Adding two forces
Active Learning Two equal mass pith balls are both charged. They hang on strings as shown in the figure. What can we say about the sign of the two charges? a. One is + the other is −. b. Both are −. c. Both are +. θ
Electric Fields
Q1
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θ
Q2
d. The charges are the same sign, but we can’t tell if they are + or −.
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Outline Electro-Magnetic Forces Electric Charge
Adding Two Forces: F = F1 + F2 Graphical Method Algebraic Method
Electrostatic Forces The Electric Force Active Learning Active Learning Adding Two Forces: F = F1 + F2 Example: Adding two forces Electric Fields
F1x F1y F2x F2y
= = = =
F1 cos θ1 F1 sin θ1 F2 cos θ2 F2 sin θ2
Fx Fy F tan θ
= = = =
F1x + F2x F F2y p1y + Fx2 + Fy2 Fy /Fx
F F2 θ2 θ
F1 θ1
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Example: Adding two forces
Find the net force on q: y
3m
q=3C
Q1 = 2 C
Algebraic Method 3m
F = k Qq r2 x
Q2 = −4 C
F = F1 + F2
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Example: Adding two forces
Find the net force on q: y
3m
q=3C
F1 Algebraic Method
Q1 = 2 C
F1 = k Qr12q 9 Nm2 (2 C)(3 C) = (9 × 10 C2 ) 9 m2 = 6 × 109 N.
3m x
(F1 )x = 6 × 109 N,
(F1 )y = 0
Q2 = −4 C
F = F1 + F2
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Example: Adding two forces
Find the net force on q: y
3m
q=3C
Q1 = 2 C
(F1 )x = 6 × 109 N,
F2
3m
x Q2 = −4 C
Algebraic Method (F1 )y = 0
F2 = k |Qr22|q 9 Nm2 (4 C)(3 C) = (9 × 10 C2 ) 18 m2 = 6 × 109 N
F = F1 + F2
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Example: Adding two forces
Find the net force on q: y
3m Q1 = 2 C
q=3C 45◦
F2
3m
(F1 )x = 6 × 109 N,
(F1 )y = 0
F2 = 6 × 109 N x
Q2 = −4 C
Algebraic Method
(F2 )x = −F2 cos 45◦ = −4.24 × 109 N (F2 )y = −F2 sin 45◦ = −4.24 × 109 N
F = F1 + F2
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Example: Adding two forces
Find the net force on q: y
3m Q1 = 2 C
F2
3m
Algebraic Method q=3C 45◦
F1
(F1 )x = 6 × 109 N,
(F1 )y = 0
(F2 )x = −F2 cos 45◦ = −4.24 × 109 N
F
(F2 )y = −F2 sin 45◦ = −4.24 × 109 N x
Q2 = −4 C
Fx = (F1 )x + (F2 )x = 1.76 × 109 N Fy = (F1 )y + (F2 )y = −4.24 × 109 N
F = F1 + F2
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Outline Electro-Magnetic Forces Electric Charge Electrostatic Forces Electric Fields Electric Field Physics & Geometry Electric Field From a Point Charge Monopole + Monopole − Electric Field Lines Net Electric Field Active Learning Active Learning The Electric Dipole Electric Field Lines Electric Monopoles and Dipoles The Capacitor Next Time c
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Electric Fields
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Outline Electro-Magnetic Forces
Electric Field The electric field is the force/unit charge.
Electric Charge
Newtons/ Coulomb
E = F/q
Electrostatic Forces
F
Electric Fields Electric Field Physics & Geometry Electric Field From a Point Charge Monopole + Monopole − Electric Field Lines Net Electric Field Active Learning Active Learning The Electric Dipole Electric Field Lines Electric Monopoles and Dipoles The Capacitor Next Time c
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q
Electric field produced by Q Q
E
Q 1 Q E=k 2 = r 4πǫ0 r2
Compute the electric field, then find the force on q: F = qE
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Outline Electro-Magnetic Forces
Physics & Geometry Imaginary sphere of radius r At a distance r from Q:
Electric Charge Electrostatic Forces Electric Fields Electric Field Physics & Geometry Electric Field From a Point Charge Monopole + Monopole − Electric Field Lines Net Electric Field Active Learning Active Learning The Electric Dipole Electric Field Lines Electric Monopoles and Dipoles The Capacitor Next Time c
Electric Field From a Point Charge The electric field is a vector field. Magnitude:
Electric Charge Electrostatic Forces Electric Fields Electric Field Physics & Geometry Electric Field From a Point Charge Monopole + Monopole − Electric Field Lines Net Electric Field Active Learning Active Learning The Electric Dipole Electric Field Lines Electric Monopoles and Dipoles The Capacitor Next Time c
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1 Q Q E=k 2 = r 4πǫ0 r2
|E |
where:
r
◆ Q charge producing E-field. ◆ r distance between charge and point where E is
measured.
◆ E points away from + charge (source). ◆ E points toward − charge (sink).
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Electric Monopole Field +
Outline Electro-Magnetic Forces Electric Charge Electrostatic Forces Electric Fields Electric Field Physics & Geometry Electric Field From a Point Charge Monopole + Monopole − Electric Field Lines Net Electric Field Active Learning Active Learning The Electric Dipole Electric Field Lines Electric Monopoles and Dipoles The Capacitor Next Time c
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Electric Monopole Field +
Outline Electro-Magnetic Forces Electric Charge Electrostatic Forces Electric Fields Electric Field Physics & Geometry Electric Field From a Point Charge Monopole + Monopole − Electric Field Lines Net Electric Field Active Learning Active Learning The Electric Dipole Electric Field Lines Electric Monopoles and Dipoles The Capacitor Next Time c
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+
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Electric Monopole Field +
Outline Electro-Magnetic Forces Electric Charge Electrostatic Forces Electric Fields Electric Field Physics & Geometry Electric Field From a Point Charge Monopole + Monopole − Electric Field Lines Net Electric Field Active Learning Active Learning The Electric Dipole Electric Field Lines Electric Monopoles and Dipoles The Capacitor Next Time c
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+
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Electric Monopole Field −
Outline Electro-Magnetic Forces Electric Charge Electrostatic Forces Electric Fields Electric Field Physics & Geometry Electric Field From a Point Charge Monopole + Monopole − Electric Field Lines Net Electric Field Active Learning Active Learning The Electric Dipole Electric Field Lines Electric Monopoles and Dipoles The Capacitor Next Time c
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Electric Monopole Field −
Outline Electro-Magnetic Forces Electric Charge Electrostatic Forces Electric Fields Electric Field Physics & Geometry Electric Field From a Point Charge Monopole + Monopole − Electric Field Lines Net Electric Field Active Learning Active Learning The Electric Dipole Electric Field Lines Electric Monopoles and Dipoles The Capacitor Next Time c
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Electric Monopole Field −
Outline Electro-Magnetic Forces Electric Charge Electrostatic Forces Electric Fields Electric Field Physics & Geometry Electric Field From a Point Charge Monopole + Monopole − Electric Field Lines Net Electric Field Active Learning Active Learning The Electric Dipole Electric Field Lines Electric Monopoles and Dipoles The Capacitor Next Time c
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Outline Electro-Magnetic Forces Electric Charge Electrostatic Forces
Electric Field Lines ◮ Positive charges are sources of electric field lines. ◮ Negative charges are sinks of electric field lines. ◮ Otherwise electric field lines are continuous.
Electric Fields Electric Field Physics & Geometry Electric Field From a Point Charge Monopole + Monopole − Electric Field Lines Net Electric Field Active Learning Active Learning The Electric Dipole Electric Field Lines Electric Monopoles and Dipoles The Capacitor Next Time c
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◮ The closer electric field lines are together, the stronger the electric field. ◮ At any point, the electric field is tangent to the electric field lines. ◮ Electric field lines do not cross.
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Outline Electro-Magnetic Forces Electric Charge Electrostatic Forces
Net Electric Field 1 Q Q ˆr point charge E = k 2 ˆr = 2 r 4πǫ0 r For several charges add the electric field vectors produced by each charge.
Electric Fields Electric Field Physics & Geometry Electric Field From a Point Charge Monopole + Monopole − Electric Field Lines Net Electric Field Active Learning Active Learning 1 The Electric Dipole Electric Field Lines Electric Monopoles and Dipoles The Capacitor Next Time c
