1

Phys 102 – Lect. 29Final exam review

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

Phys. 102, Review 29, Slide 3

Review lecture ACTs

70%

EX2

Some exam problems are inspired by ACTs.

30%

Review homework questions

Phys. 102, Review 29, Slide 4

20%!

EX2

Some exam problems are inspired by the HW.

100%

Problem solving approachesThe not-so-good approaches:

Conceptual understanding / reasoning from basic principles:

“Reasoning by analogy”/memorization:“I remember every time we’ve done RC circuit problems, VC = after a long time...”

1. The capacitor is fully charged, so IC = 0 2. Resistor R3 is in series with C so I3 = 03. But, current can flow around inner loop, so I1 > 0 4. Algebra! KLR: – I1R1 – VC = 0, therefore VC <

The good approach:

Phys. 102, Review 29, Slide 5

20%!

EX2

Problem solving approachesThe not-so-good approaches:

The “magic” equation:

Conceptual understanding / reasoning from basic principles:

“What equation will solve this problem?Req = R1+R2, V = IR?”

1. Redraw the circuit to make it clearer2. The rightmost resistor is shorted, so no current

flows through it!3. So, the current through the bottom resistor is I4. Algebra! KLR: E – IR = 0

The good approach:

Phys. 102, Review 29, Slide 6

EX2

70%

7

1. Electricity & circuitsLects. 1 – 9

Vector Number (“scalar”)

Property

of

interacting c

harges

Property

of

point in sp

ace

Ex:

Ex:Ex:

Ex:

F

E V

UE[N] [J]

[N/C]=[V/m] [J/C]=[V]

Relationship between F, E, UE, V

EV U qqE F

1 22

q qF k

r 1 2q q

U kr

2

qE k

r

qV k

rE points from

high to low V

cosE

E

W F r θU

Phys. 102, Review 29, Slide 8

Wire Battery

Circuits & componentsCapacitor Resistor

Series and parallelBasic principles:Conservation of charge (KJR) Conservation of energy (KLR)

21

1

2 Current In = Current Out

Sum of voltages around loop = 0

0V

in outI I

Phys. 102, Review 29, Slide 9

1 2 eqI I I

1 2 eqV V V 1 2 eqV V V 1 2 eqI I I

RC Circuits

Phys. 102, Review 29, Slide 10

Charging:Initially the capacitor is uncharged At t = 0 we close switch S1

0,0 0C

QV

C

After a long time (t = ):Charge on C builds and saturatesCurrent decreases to zero

,0 0CI

, 0C

QV

C

, 0CI

C acts like a wire

C acts like an open circuit

+ε

IC

R

S1

C

S2

+Q

–Q

Immediately after (t = 0):No charge on C yetCurrent IC,0 flows charge onto C

Discharging:Initially the capacitor is fully charged At t = 0 we close switch S2

Immediately after (t = 0):C still fully chargedCurrent IC,0 flows charge off of C

After a long time (t = ):Charge dissipates to zero Current decreases to zero

0,0 0C

QV

C ,0 0CI

, 0C

QV

C

, 0CI

C acts like a battery

C acts like an open circuit

11

2. MagnetismLects. 10 – 15

I

Type I: RHR for forces on moving charges and currents

Type II: RHR for magnetic fields generated by currents

I

I

Thumb along I

Curl fingers alongB

Curl fingers along I

Thumb alongB

B field from wire B field inside loop

vThumb along BFingers along

F on + q is out of palmF on – q is into palm

+q

F

B

OR:

v

I

F

–F

v

q

Moving + charges and currents Moving – charges

vThumb alongBFingers along

B

B

B

B

B

I I

Thumb along I

Curl fingers alongB

B

Magnetism summary

0

2wireμ I

Bπr

0solB μ nIsinF q vB θ sinF ILB θ

sinloopτ NIAB θ sinμB θPhys. 102, Review 29, Slide 12

1. Is increasing, decreasing, or constant?

2. If increases: ε induces B field opposite external B field

3. Type II RHR gives current direction

BindBind

Induced EMF ε opposes change in flux

Side viewTop view

Bind

Bext

Bext

If decreases:ε induces B field along external B field

Top view

Bext

Bind

Bext

Side view

If is constant:ε is zero, no induced B field

I

I

Curl fingers along IThumb along Bind

Bind

Bind

II

II

Lenz law

Phys. 102, Review 29, Slide 13

2. Magnetic field B

cosBA φ

εt

Since , 3 things can change F

Faraday’s law: “Induced EMF” = rate of change of magnetic flux

ε BLv ( ) sinε t ωNBA ωt

1. Area of loop 3. Angle φ

v

10 20t

B(t)

+1.0

-1.0

0

+0.5

-0.5

0

Bε A

t

BnωB

Faraday’s law

Phys. 102, Review 29, Slide 14

15

3. Light & opticsLects. 16 – 23

Light summary

Properties of electromagnetic wavesRelation between E, B, f, λEnergy density, power & intensityPolarization

Ray model of lightReflectionRefractionMirrorsLenses (alone, in combination)The eye (nearsightedness, farsightedness)

InterferenceConstructive and destructive interferenceDiffraction & resolution

Phys. 102, Review 29, Slide 16

20tot rms

PI c u cε E

A

2costrans incI I θ

i i

o o

h dm

h d

1 1 1

o if d d

i rθ θ1 1 2 2sin sinn θ n θ

Light as a wave (again)Interference: phase shift & path length difference

θ

θ

d

sind θ

θ

Constructive: phase shift of mλDestructive: phase shift of (m + ½)λ

Phase shift

sin md θ mλ

12sin ( )md θ m λ

Two & multiple slit maxima

Two slit minima

sin ma θ mλSingle slit minima

0, 1, 2...m

1, 2...m

1sin 1.22D θ λCircular aperture minimum Phys. 102, Review 29, Slide 17

Example: Interference

Phys. 102, Review 29, Slide 18

Extra practice

19

4. Modern physicsLects. 23 – 28

Quantum mechanics

Wave-particle dualityMatter waves – particle as a wave (de Broglie)Photons – light as a particle (photoelectric effect)

Bohr modelquantized orbits & energies, electronic transitions

Nuclear & particle physicsstructure of nucleus & nucleonsdecay processes (α, β, γ) & rates, binding energyquark model

hλ

p

2

0nn

r aZ

2

213.6eVn

ZE

n

Quantum modelquantum numbers (n, ℓ, mℓ, ms), Pauli exclusion principle, magnetic properties of atoms

Phys. 102, Review 29, Slide 20

Example: wave-particle duality

Phys. 102, Review 29, Slide 21

Extra practice

Example: quantum numbersExtra practice

Phys. 102, Review 29, Slide 22

Example: quantum atomExtra practice

Phys. 102, Review 29, Slide 23

Example: nuclear decayExtra practice

Phys. 102, Review 29, Slide 24