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Phys 102 – Lect. 29
Final exam review
1
Final exam study approaches
How should you study for the physics exam?
• Cramming DOES NOT work
• Emphasize understanding concepts & problem solving,
NOT memorization
• Review pre-lecture & lecture concepts
• Review problems: ACTs, HW, quizzes, practice exams
• Understand formula sheet (i.e. when to use and when NOT
to use an eq.) & know what each symbol means
• Do practice exam problems (time yourself!)
Phys. 102, Review 29, Slide 2
Review lecture ACTs
Some exam problems are inspired by ACTs.
EX2
30%
70%
Phys. 102, Review 29, Slide 3
Review homework questions
Some exam problems are inspired by the HW.
EX2
20%!
100%
Phys. 102, Review 29, Slide 4
Problem solving approaches
The not-so-good approaches:
EX2
“Reasoning by analogy”/memorization:
“I remember every time we’ve done RC
circuit problems, VC =  after a long time...”
The good approach:
Conceptual understanding /
reasoning from basic principles:
20%!
1.
2.
3.
4.
The capacitor is fully charged, so IC = 0
Resistor R3 is in series with C so I3 = 0
But, current can flow around inner loop, so I1 > 0
Algebra! KLR:  – I1R1 – VC = 0, therefore VC < 
Phys. 102, Review 29, Slide 5
Problem solving approaches
The not-so-good approaches:
EX2
The “magic” equation:
“What equation will solve this problem?
Req = R1+R2, V = IR?”
The good approach:
Conceptual understanding /
reasoning from basic principles:
70%
1.
2.
3.
4.
Redraw the circuit to make it clearer
The rightmost resistor is shorted, so no current
flows through it!
So, the current through the bottom resistor is I
Algebra! KLR: E – IR = 0
Phys. 102, Review 29, Slide 6
1. Electricity & circuits
Lects. 1 – 9
7
Relationship between F, E, UE, V
Vector
F
Number (“scalar”)
UE
[N]
Ex: F  k
q1q2
r2
WE  F r cos θ
 U E
Ex: U  k
V
[N/C]=[V/m]
Ex: E  k
q1q2
r
V  UE q
EF q
E
[J]
q
r2
E points from
high to low V
[J/C]=[V]
Ex: V  k
q
r
Phys. 102, Review 29, Slide 8
Circuits & components
Wire
Battery
Series and parallel
2
V1  V2  Veq
 Iin   Iout
Current In = Current Out
2
I1  I 2  I eq
Resistor
Basic principles:
Conservation of charge (KJR)
Conservation of energy (KLR)
1
1
Capacitor
I1  I 2  I eq
V1  V2  Veq
 V  0
Sum of voltages around loop = 0
Phys. 102, Review 29, Slide 9
RC Circuits
Charging:
Discharging:
Initially the capacitor is uncharged
At t = 0 we close switch S1
Initially the capacitor is fully charged
At t = 0 we close switch S2
Immediately after (t = 0):
No charge on C yet
Current IC,0 flows charge onto C
Immediately after (t = 0):
C still fully charged
Current IC,0 flows charge off of C
VC ,0
Q
 0  0 I C ,0  0
C
ε
C acts like a wire
After a long time (t = ):
Charge on C builds and saturates
Current decreases to zero
VC , 
Q
0
C
R
+
I C ,  0
C acts like an open circuit
+Q
–Q
S1
VC ,0 
IC
C acts like a battery
C
S2
Q0
 0 I C ,0  0
C
After a long time (t = ):
Charge dissipates to zero
Current decreases to zero
VC , 
Q
0
C
I C ,  0
C acts like an open circuit
Phys. 102, Review 29, Slide 10
2. Magnetism
Lects. 10 – 15
11
B
Magnetism summary
Type I: RHR for forces on moving
charges and currents
Type II: RHR for magnetic fields
generated by currents
B field from wire
Moving + charges and currents
v
I
+
Moving – charges
v
q
q
F
Thumb along v
Fingers along B
F on + q is out of palm
F  q vB sin θ
–
I
B
B
I
I
B
F
F
B field inside loop
B
B
I
B
I
Thumb along v
Fingers along B
F on – q is into palm
F  ILB sin θ
τloop  NIAB sin θ  μB sin θ
Thumb along I
Curl fingers along I
Curl fingers along B
Thumb along B
Bwire 
μ0 I
2πr
OR:
Thumb along I
Curl fingers along B
Bsol  μ0 nI
Phys. 102, Review 29, Slide 12
Lenz law
Induced EMF ε opposes change in flux 
1. Is  increasing, decreasing, or constant?
2. If  increases:
ε induces B field opposite external B field
If  decreases:
ε induces B field along external B field
Bext
Bext
Bext
Bext
I Bind
Bind
I
Bind
I
Bind
I
Top view
Top view
Side view
Side view
If  is constant:
ε is zero, no induced B field
Bind
I
3. Type II RHR gives current direction
Curl fingers along I
Thumb along Bind
I
Bind
Phys. 102, Review 29, Slide 13
Faraday’s law
Faraday’s law: “Induced EMF” = rate of change of magnetic flux
ε

t
Since   BA cos φ, 3 things can change 
1. Area of loop
2. Magnetic field B
3. Angle φ
B(t)
v
+1.0
B
ω
n
+0.5
0
B
t
0
10
20
-0.5
ε  BLv
-1.0
ε
B
A
t
ε (t )  ωNBA sin ωt
Phys. 102, Review 29, Slide 14
3. Light & optics
Lects. 16 – 23
15
Light summary
Properties of electromagnetic waves
Relation between E, B, f, λ
Energy density, power & intensity
Polarization Itrans  Iinc cos2 θ
I
P
A
2
 c utot  cε0 Erms
Ray model of light
Reflection θi  θr
Refraction n1 sin θ1  n2 sin θ2
1
1 1
Mirrors


f d o di
Lenses (alone, in combination)
The eye (nearsightedness, farsightedness)
m
hi
d
 i
ho
do
Interference
Constructive and destructive interference
Diffraction & resolution
Phys. 102, Review 29, Slide 16
Light as a wave (again)
Interference: phase shift & path length difference
θ
θ
Phase
shift
d
Constructive: phase shift of mλ
Destructive: phase shift of (m + ½)λ
Two & multiple slit maxima d sin θm  mλ
Two slit minima d sin θm  (m 
1
)λ
2
θ
d sin θ
m  0, 1,  2...
Single slit minima a sin θm  mλ m  1,  2...
Circular aperture minimum D sin θ1  1.22 λ
Phys. 102, Review 29, Slide 17
Example: Interference
Extra practice
Phys. 102, Review 29, Slide 18
4. Modern physics
Lects. 23 – 28
19
Quantum mechanics
Wave-particle duality
Matter waves – particle as a wave (de Broglie)
Photons – light as a particle (photoelectric effect)
λ
h
p
Bohr model
quantized orbits & energies, electronic transitions
n2
Z2
rn 
a0
En  13.6eV 2
Z
n
Quantum model
quantum numbers (n, ℓ, mℓ, ms), Pauli exclusion principle, magnetic
properties of atoms
Nuclear & particle physics
structure of nucleus & nucleons
decay processes (α, β, γ) & rates, binding energy
quark model
Phys. 102, Review 29, Slide 20
Example: wave-particle duality
Extra practice
Phys. 102, Review 29, Slide 21
Example: quantum numbers
Extra practice
Phys. 102, Review 29, Slide 22
Example: quantum atom
Extra practice
Phys. 102, Review 29, Slide 23
Example: nuclear decay
Extra practice
Phys. 102, Review 29, Slide 24