Download 14.1-14.4

Course Organization
• Syllabus
• Lesson Plan
• Grading
• Participation Bonus
• Textbook (M&I II Electricity and Magnetism …)
• Quest
• i-Clickers (register on Quest)
What you need to remember from 303K
Vectors
𝐴+𝐵
𝐴
𝜃
𝐴 ∙ 𝐵 = 𝐴 𝐵 𝑐𝑜𝑠 𝜃
𝐵
𝐴 × 𝐵 = 𝐴 𝐵 𝑠𝑖𝑛 𝜃
𝐵
Right Hand Rule
𝐴
How particles move and are affected by forces
Momentum: 𝑝~ 𝑚𝑣
𝑝 = 𝛾𝑚𝑣 ; 𝛾 =
1
1−
Newton’s
2nd
Law: 𝐹 =
𝑑𝑝
𝑑𝑡
𝑣 2
𝑐
; 𝐹 = 𝑚𝑎 ; 𝑝𝑓 = 𝑝𝑖 + 𝐹∆𝑡
Work and Energy: 𝑊 = 𝐹 ∙ ∆𝑟 = ∆𝐾 =
1
𝑚𝑣𝑓2
2
−
1
𝑚𝑣𝑖2
2
Clicker Question 1
𝐴 =< 2, 1, 0 > and 𝐵 =< 1, 1, 0 > . What are 𝐴 and 𝐵 ?
Choice
𝐴
𝑩
A
5
2
B
5
3
3
2
2
C
D
2
Clicker Question 2
𝐴 =< 2, 1, 0 > and 𝐵 =< 1, 1, 0 > . What is 𝐴 ∙ 𝐵 ?
Recall: 𝐴 ∙ 𝐵 = 𝐴 𝐵 𝑐𝑜𝑠 𝜃 = 𝐴𝑥 𝐵𝑥 + 𝐴𝑦 𝐵𝑦 + 𝐴𝑧 𝐵𝑧
Choice
A
B
C
Use your results to find 𝑐𝑜𝑠 𝜃 .
𝐴∙ 𝐵
2
3
4
Choice
A
𝒄𝒐𝒔(𝜽)
B
3/ 2
C
3/ 10
3/ 5
What will you learn?
Interaction of Matter and
Electromagnetic Fields
aurora borealis
Backpacking in
Alaska
𝐵
𝑝
• Sun spits out Charged Particles (Solar Wind)
• Earth’s Magnetic Field extends out into space
and collects charged solar wind.
• Charged particles are concentrated at poles
• Collisions of these high velocity charges with air
makes the light of the aurora
More Mathematically …
The interactions between matter and Electric and Magnetic fields
can be explained with just a few equations.
Maxwell equations:
r
div( E ) = Ñ × E =
e0
div( B) = Ñ × B = 0
¶B
curl(E) = Ñ ´ E = ¶t
é
¶E ù
curl( B ) = Ñ ´ B = m0 ê J + e 0
ú
¶
t
ë
û
Lorentz force:
F = qE + qv ´ B
Point Charges
• Two types: positive and negative
• Like charges: repel
• Opposite charges: attract
• Charge is quantized in units of e
Millikan’s oil drop experiment (1910-1913)
• Point charge: Size is small compared to the distance between
it and other objects of interest
• Electric charge is an intrinsic property of the fundamental
particles that everything is made of
The Coulomb Force Law
Q1Q2
F =F=
2
4pe 0 r
1
"The magnitude of the electrostatic force between two
point charges is directly proportional to the
magnitudes of each charge and inversely proportional
to the square of the distance between the charges."
Q1
Q2
F
F
Charles-Augustin de Coulomb
(1736 - 1806)
The Coulomb Force Law
1 Q1Q2
F=
r̂
2
4pe 0 r
r
+
+
2
0 = permittivity constant
F21
Force on “2” by “1”
1
Force repulsive
r
+
F21
-
2
1
Force attractive
Units and Constants
SI units of electric charge: Coulomb, C
1 Q1Q2
F =F=
Constants:
2
4
pe
r
0
1/40 = 9x109 N.m2/C2
0 = 8.85x10-12 C2/N.m2 permittivity constant
e = 1.602x10-19 C
1 C = 6.24x1018 elementary charges
Particle
electron
positron
proton
antiproton
muon
pion
neutron
Charge
-e
+e
+e
-e
+e or –e
+e or –e or 0
0
Structure of Atom
Matter consists of atoms
1 cm3 : ~1024 atoms
Nucleus:
~104 times smaller than electron cloud,
~104 times heavier than electron.
1Å=10-10m
Example: nucleus of the iron atom
Size: ~10–15 m, mass: ~10-25 kg
Nucleus charge = +Ze, atom with Z electrons is neutral.
The Concept of Electric Field
Accelerates at 9.8 m/s2 – why?
Accelerates at 1011 m/s2 – why?
There are many possible
configurations of charges
to produce the observed
effect.
Electric Field
There is something in space
waiting for a charged particle to
interact with it!
This virtual force is called
electric field.
An electric field created by charge is present throughout
space at all times, whether or not there is another charge
around to feel its effect.
Force between Charges
𝑘𝑄𝑞
𝑘𝑄
𝐹=
𝑟=
𝑟 𝑞
2
2
𝑟
𝑟
+
+
𝑟
q
Q
The Electric field of
the Point Charge Q
𝑘𝑄
𝐸 = 2𝑟
𝑟
𝐹 = 𝑞𝐸
Electrical Field is convenient tool
turns out to be measurable … so really exists
Electric Field of Point Charge
𝐸
𝐸
+
𝐸
𝐸
𝐸
+
𝐸
𝐸
𝐸
Spherically
Symmetric
Draw the E field for a Negative Charge
𝐸
𝐸
_
𝐸
𝐸
_
𝐸
𝐸
𝐸
𝐸
E Field Lines
Direction of Electric Field Points along Line
Field Lines
+
+
_
Isolated
Positive Charge
Isolated
Positive Charge
+
Begin and End on Charges or Infinity; Never Cross
Things to do
• Homework on Quest: Ch14-h1; review Ch14-h0
• Read Ch14.1-14.8
• i-Clickers (register on Quest)
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