Review ofChapters 20, 26, 27

Hint: Be able to do the homework (both theproblems to turn in AND the recommended ones)you’ll do fine on the exam!

Monday, May 10, 1999 10:30am - 11:20amChs. 20, 26, and 27

You may bring one 3”X5” index card (hand-writtenon both sides), a pencil or pen, and a scientificcalculator with you. Same format!

Hint: Review notes from my review lectures! Tryto do some of the old homework recommendedhomework, and exam problems.

Monday, May 10, 1999 11:30am - 12:30pm

everything we’ve covered

You may bring one 8.5”X11” sheet (hand-writtenon both sides), a pencil or pen, and a scientificcalculator with you.

Monday, December 15, 1997 11:30am - 12:30pm

everything we’ve covered

Format: 5 problems, 1 multiple-choice, pick 4.

1 problem on each of the following topics:

Electrostatics Circuits Magnetism

Optics Modern

Magnetic Flux Induced EMF Motional EMF Inductance

Wien’s Law Photoelectric Effect Heisenberg Uncertainty Principle de Broglie Wavelength

Length Contraction Time DilationRelativistic Energy Relativistic Momentum Rest Energy Michelson-Morley Exp.

Magnetic Flux Induced EMF Motional EMF Inductance

Wien’s Law Photoelectric Effect Heisenberg Uncertainty Principle de Broglie Wavelength

Length Contraction Time DilationRelativistic Energy Relativistic Momentum Rest Energy Michelson-Morley Exp.

30o

60o

top view

Btot

B B||

This is also the direction of the normal to the loop!

=| |A =| |AB B cos

The induced current triesto maintain the original flux through the circuit.

The polarity of the induced emf is such thatit produces a current whose magnetic fieldopposes the change in magnetic flux throughthe loop.

Nt

Emf!

AI

S N

LN

A0

2

lU LI

1

22

L is the inductance and is defined to be

FOR A SOLENOID!!!!B = onI

LI

tL N

I

V R+

_L

= the time constant = L / R

I I( ) ( )/t e t max 1

Imax V R/

VR ( ) ( )/t e t V 1

VL ( ) ( )/ /t e et t V V V1

x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x

Lv

++++++

------

F+

F-

FE = FB

FE = q EFB = q v B

E = v B

|V| = E d = B L v

x x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x x

R Lv

II

BLv

R

Blackbody Observations

Wavelength

Inte

ns

ity

IncreasingTemperature

max

max

max

max .T 0 2898 10 2 mK

I Thc

ehc kT( , )

( )/

8

15

h 6 626 10 34. Js E nhfn

V+

_ V

A

A

C evacuatedchamber

-6 -4 -2 0 2 4 6 8 10

Applied Voltage

Cu

rren

t

High intensity

Low intensity

Stopping potentia

l

Applied Voltage

Cu

rren

t

frequencyfc

stop

pin

gp

oten

tial

Cut-off frequency

KE hfmax energy of theincident light

The work function:Energy required to escape the metal.Characteristic of the metal!

Explains thephotoelectric

effect

Explains thephotoelectric

effect

Where V0 is the stopping potential and KEmax is the maximum kinetic

energy of the emitted electrons

KEmax = e Vo

Photoelectric effect, light actslike particle. Einstein saysphotons carry energy given by

E = h f

If light does act as a particle, it should carrymomentum…(and using relativity, we canderive the momentum of a photon of light)

de Broglie’s hypothesis was that any particle with momentum p should also exhibit wave properties with characteristic wavelength ...

Here, p is the momentum and c the speed of light.

E pc

Recalling that E = hf, we find that ph

p mv h

mv

x ph

4

E th

4

Albert Einstein

GM R/R

Physics

Rules

u

SThe “lab” frame. It’s theone “at rest.”

S’

u

the movingframeMoves with a velocity

u relative to frame S.

The world BEFORE Einstein...

x’ = x - ut

Positions of stationary objects

y’ = y z’ = z

t’ = tTime is the samein both frames...

v’ = v - uAn object moving with velocity v in the lab frame appears to move with velocity v’ in a frame which moves with velocity u

1) absolute, uniform motion cannot be detected

Einstein’s AssumptionsEinstein’s Assumptions

2) c always is 3 X 108 m/s in vacuum

y’ = y z’ = zxx ut

u c'

/

1 2 2

Absolute time on clocks (NOTthe duration of events). Thiswill NOT be on the exam.

tt ux c

u c'

/

/

2

2 21

m0 is the rest mass (the massin the frame in which theobject is at rest).

mm

v c

0

2 21 /

t0 is the proper time (thetime between events asmeasured in the rest frameof the experiment).

TIME DILATIONTIME DILATION

tt

v ct

0

2 2 01 /

1

1 2 2v c/

LENGTHCONTRACTION

LENGTHCONTRACTION

L0 is the proper length(the length measuredin the rest frame ofthe object).

LL

0

m0 rest massL0 proper lengtht0 proper time

m0 rest massL0 proper lengtht0 proper time

In the rest frameof the object:

In the rest frameof the object:

In the lab (wherethe observer is):In the lab (wherethe observer is):

m massL lengtht time

m massL lengtht time

GM R/R

Physics

Rules

u

So, whether we sit on the boxcar or stand alongside the tracks, light from the two paths will appear to arrive at the detector simultaneously.

tL c

c

L c

c

2

1

2

12 2 2 2

|| /

( / )

/

( / )u u

Using our relativistic formula for lengthcontraction, we now get t = 0, as observed.Using our relativistic formula for lengthcontraction, we now get t = 0, as observed.

where

m m 0p = m v

Kinetic energy:

E m c0 02Rest energy:

E mc m c 20

2 Total energy:

KE m c ( ) 1 02

(Total Energy)2 = (momentum)2c2+(rest energy)2(Total Energy)2 = (momentum)2c2+(rest energy)2

Finally, we can relate Total Energy to Momentum using:

E p c m c2 2 20

2 2 ( )