The induced EMF of moving conductor in magnetic field

A conductor initial in magnetic field doesn’t have induced

current because no change in magnetic flux. However, when it

starts moving magnetic flux increase significantly, then doesn’t

change and then slightly decrease until 0.

𝜺=𝑩𝒍𝒗

𝜀: induced emf (V)

B: magnetic field

strength (T)

l: length of conductor

v: velocity of

conductor

Faraday’s Law of induction

Doesn’t matter whether the coil or magnet are changed if it

is a change in magnetic flux there is induced EMF.

Farday states if the flux through “N” number of loops of a coil

changes from 𝜙𝑖𝑛𝑡𝑖𝑎𝑙 to 𝜙𝑓𝑖𝑛𝑎𝑙then induced EMF/current.

𝜺=−𝑵𝚫𝝓

𝚫𝒕 =−𝑵𝝓𝒇𝒊𝒏𝒂𝒍−𝝓𝒊𝒏𝒕𝒊𝒂𝒍

𝒕𝒇𝒊𝒏𝒂𝒍−𝒕𝒊𝒏𝒊𝒕𝒂𝒍

If the ends of a coil are connected to circuit, then a current will

flow:

𝐼=𝜀

𝑡

N: number of loops/turns

Lenz’s Law

1. Don’t confuse induced current and induced current action.

2. When induced current action (magnet) try to move in/move

out a coil or solenoid. Initially coil or solenoid don’t have

induced current but because of induced current action this

will generate induced current in coil or solenoid. The

direction of this induced current will oppose direction of

induced current action

Tips: negative sign indicate anticlockwise direction of

induced current.

1. Δ𝜙=−;𝜙𝑓𝑖𝑛𝑎𝑙 <𝜙𝑖𝑛𝑡𝑖𝑎𝑙: clockwise: 𝜀=+

2. Δ𝜙=+;𝜙𝑓𝑖𝑛𝑎𝑙 >𝜙𝑖𝑛𝑡𝑖𝑎𝑙: anticlockwise

𝜀=−

The direction of induced current by changing area

1. For a magnetic field get into a page

When S.A B:out of page Anticlockwise

When S.A B: into the page Clockwise

2. For a magnetic field go out page

When S.A B: into the page Clockwise

When S.A B: out of page Anticlockwise

AC Generator/Alternator

• Main different is slip ring: allow the coil rotating without

tangling. Produce AC voltages which can be either positive

or negative

• NOTE: GRAPH of EMF is NEGATIVE DERIVATIVE of

magnetic flux

DC generator

For Dc generator

because of

commutator reverse

direction of current

every half turn. So no

negative area

Peak, Peak-Peak&RMS

Root mean square voltage is the

equivalent steady voltage DC supply

which provide the same power

𝑉𝑟𝑚𝑠 =𝑣𝑝𝑒𝑎𝑘

√2

𝐼𝑟𝑚𝑠 =𝐼𝑝𝑒𝑎𝑘

√2

𝑉𝑝𝑒𝑎𝑘−𝑝𝑒𝑎𝑘 =2𝑉𝑝𝑒𝑎𝑘

𝑃𝑟𝑚𝑠 =𝐼𝑟𝑚𝑠𝑉𝑟𝑚𝑠 =1

2𝑣𝑝𝑒𝑎𝑘𝐼𝑝𝑒𝑎𝑘

𝑃𝑝𝑒𝑎𝑘 =2𝐼𝑟𝑚𝑠𝑉𝑟𝑚𝑠

Factors:

speedvoltage f  period

speedvoltagefperiod

Transformers

Application of electromagnetic

induction, metal core increase

efficiently. Size is independent. Only

work for AC voltages.

𝑁𝑝

𝑁𝑠=𝑉𝑝

𝑉𝑠=𝐼𝑠

𝐼𝑝

𝑁𝑠>𝑁𝑝=Step up

𝑁𝑠<𝑁𝑝=Step down

Factors

𝑁𝑝 by X factor

𝑉𝑝 will  by X factor

𝐼𝑝will  by X factor

Transmission Loss

𝐼 𝑤𝑖𝑟𝑒𝑠 =𝑃𝑖𝑛

𝑉𝑖𝑛

𝑉 𝑙𝑜𝑠𝑠 =𝐼 𝑤𝑖𝑟𝑒𝑠𝑅 𝑤𝑖𝑟𝑒𝑠

𝑉 𝑜𝑢𝑡 =𝑉𝑖𝑛− 𝑉 𝑙𝑜𝑠𝑠

𝑃𝐿𝑜𝑠𝑠 =𝐼𝑤𝑖𝑟𝑒𝑠2𝑅 𝑤𝑖𝑟𝑒𝑠

𝑃 𝑜𝑢𝑡 =𝑃𝑖𝑛− 𝑃 𝑙𝑜𝑠𝑠

𝑃 𝑜𝑢𝑡 =𝑉𝑜𝑢𝑡 −𝐼

Transformer allow same power

to transmitted at higher voltage,

higher voltage lower current,

lower current means lower

power losses in transmissions.

Waves

Transverse wave: oscillations are

perpendicular to wave direction(light)

Longitudinal wave: oscillations are parallel to

the wave direction (sound)

Graphs:

Doppler efect

Doppler effect is produced when

the source of a wave moves with

respect to the observed causing an

apparent shift in frequency for the

observer

Relative motion Toward

frequency  

Relative motion away

frequency  

Reflection of waves

Superposition of waves

Resonance

When an object creates an external force and

vibrates another object at a frequency that

exactly matches one of the natural

frequencies. This object then absorbs energy

and have twice of amplitude

Standing Waves

ONE CLOSED END&ONE OPEN END

(Start: Node; End: Antinode)

𝝀𝒏=𝟒𝒍

𝟐𝒂−𝟏= 𝟒𝒍

𝒏

𝒇𝒏=𝒏𝒗

𝟒𝒍=(𝟐𝒂−𝟏)𝒗

𝟒𝒍 =𝒏𝒇𝟏

n: number of harmonic (odd number only)

a: number of antinodes

l: length of string

TWO CLOSED ENDS

(Start&end: Nodes)

𝝀𝒃=𝟐𝒍

𝒃

𝒇𝒃=𝒃𝒗

𝟐𝒍=𝒃𝒇𝟏

b: number of antinodes and number of

harmonics

TWO OPEN ENDS

(Start&end: antinode)

𝝀𝒄=𝟐𝒍

𝒄

𝒇𝒄=𝒄𝒗

𝟐𝒍=𝒄𝒇𝟏

c: number of nodes

𝑓1 : frequency of first harmonic

Diffraction of Wave

Number of diffractions =𝝀

𝑤 ; 𝝀

𝑤≥1:

significant diffraction

Light as Wave

Light is transverse wave or electromagnetic wave. In

this model, magnetic field travel parallel to wave

direction and electric field travel perpendicular to

wave direction. Electric field travel perpendicular to

magnetic field.

Power doesn’t affect by transformer

Electromagnetic Wave

In vacuum, all magnetic wave travel at “c”

Coherent&Incoherent

Incoherent: doesn’t contain same frequency

and doesn’t not have wavelengths that are in

phase with one another (LED)

Coherent: Waves are in step or in phase

(LAZER)

Interference

Constructive (bright band/antinodal

/maxima/ 2waves inphase

𝒑.𝒅=𝒏𝝀

Destructive (Dark band/nodal/minima/2

waves outphase )

𝒑.𝒅=(𝒏+𝟏

𝟐)𝝀

Fringe separation

∆𝑥=𝑛𝜆𝐿

𝑑

∆𝑥: distance between any two bright

band or dark band. These are equal

L: distance from slits to screen

d: slit separation

n: number of bright band

if it is a dark band then (

𝒏+𝟏

𝟐)

Single slit diffraction of light

dsin𝜃=𝑛𝜆=𝑑𝑦

𝐿

d: slit separation

L: distance from slits to screen

Y: distance from centre to minimum

point or n.

Smaller d greater intensity fridge

separation increase appear further

on screen

Refraction of light

When light change medium, speed will

change due to wavelength change,

Frequency doesn’t change. It will cause

refraction. 𝑛=𝑐

𝑣

𝑛1𝑣1=𝑛2𝑣2

n: refractive index

v: speed of light in medium

Snell’s Law

n1: refractive index of medium coming from

n2: refractive index of medium going to

Dispersion

White light is combination of different colours of light.

Different colour of light has different wavelength and

travel refract differently.

Lower frequency: less refract

Higher frequency: more refract

Polarisation

Occur to transverse wave. Allowed wave to vibrate in

one direction. Light show electric field perpendicular

to magnetic field Vertical filter: block magnetic

field horizontal filter:block electric field

Ratio

𝑛2

𝑛1=sin𝜃1

sin𝜃2=𝜆1

𝜆2= 𝑣1

𝑣2

Photoelectric effect

IMPORTANT OBSERVATION

1. Existence of threshold frequency: for each metal

used at cathode there is unique frequency call

threshold frequency if frequency of light is used <

threshold frequency no photoelectrons is

emitted or released from cathode

2. Emission is instantaneous: No delay between light

shining on the cathode&photoelectrons being

produced/ It doesn’t depend on intensity of light

IMPORTANT RELATIONSHIP

1. Intensity of light independent Stopping voltage (K.E

max)

2. Intensity of light Photocurrent

3. Frequency of light was used  stopping voltage (K.E

max)

4. Frequency of light was used independent

photocurrent

FLAW OF WAVE MODEL

1.Energy of the wave is dependent on amplitude, if

sufficiently intense light is used, the electrons would

absorb enough energy to escape no threshold

frequency

2.Time delay should observe, particular at low

intensities, as energy is gradually transferred to the

metal by the light waves

3. Intensity of light should be proportional to K.E max

Work function ∅=ℎ𝑓𝑜

∅1

𝑠𝑡𝑜𝑝𝑝𝑖𝑛𝑔 𝑣𝑜𝑙𝑡𝑎𝑔𝑒

This is the amount of energy required to

eject a photoelectron

If energy of photon less than this value

no photoelectron is emitted ℎ𝑓<ℎ𝑓𝑜

K.E MAX 𝐾.𝐸𝑚𝑎𝑥 =ℎ𝑓−ℎ𝑓𝑜

K.E max is stopping voltage

𝐾. 𝐸 𝑚𝑎𝑥1

𝜆

Light as Particle (Photon)

𝐸𝑝ℎ𝑜𝑡𝑜𝑛 =ℎ𝑓=𝑝𝑐=ℎ𝑐

𝜆

𝑝=𝐸𝑝ℎ𝑜𝑡𝑜𝑛

𝑐=ℎ

𝜆

𝜆=𝑐

𝑓,𝑓=𝑐

𝜆

Particles behave as Wave

𝐸𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 =𝑝2

2𝑚=ℎ2

2𝑚𝜆2=1

2𝑚𝑣2

𝜆=ℎ

𝑝=ℎ

𝑚𝑣=ℎ

√2𝑚𝐸

Only moving particle behave as wave

Electron diffraction pattern

IF photon and beam of electron pass through

a crystal sample

produce same wavelength

produce same momentum

same fringe spacing

Energy of electron different from energy of

photon

Single Photon/Young’s Double slit

When the light source so weak (intensity is

too low) we can conclude only one photon

was passing through a slit

after long tome light&dark bands patter

appear

evidence for Wave-particle duality

Einstein&Photonelectric effect

Light travelled in discrete packets of energy

and defined intensity as number of

photon(N)

𝑁= 𝑒𝑛𝑒𝑟𝑔𝑦 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡 𝑏𝑒𝑎𝑚

𝑒𝑛𝑒𝑟𝑔𝑦 𝑜𝑓 𝑝ℎ𝑜𝑡𝑜𝑛 (ℎ𝑓)

Adsorption&Emission

∆𝐄=𝐡𝐟=𝐡𝐜

𝛌

Energy level

Eemission=Eintial-Efinal

Eg from energy level n=3 to ground state

It will be 2 possible ways: n=3 to n=2 and n=2 to n=1.

Eabsorption=Efinal-Eintial

Electrons exist in discrete energy levels, for emission, when

electron moves to lower level it release a photon with energy

exactly equal to the difference between energy levels of

atom. For absorption, when a photon/light go to an atom, an

electron will absorb an energy from photon, this energy

equal to energy levels between ground state and higher

state.

Emission spectra dark and some colour/Absorption spectra: colour and

some dark

Uncertainty principle&Single slit

diffraction

-Uncertainty in position is inversely proportional

to uncertainty in momentum

-Increasing the slit width, increase the positional

uncertainty, decreases the uncertainty of the

momentum of the particles decrease in the

extent of diffraction on the screen (Less

diffraction).

Standing waves of electron

According to de Broglie’s model of atom.

Electrons are modelled as standing waves

around the nucleus. Their wavelengths are

restricted to discrete values fit as only certain

wavelengths will support standing waves.

(Wavelength must be whole number to keep it

orbiting in stable 2πr=n 𝛌 Discrete wavelengths

mean discrete momenta and thus discrete

energy levels which we see as quantised energy

states.

The reason for whole number of wavelengths is

to avoid destructive interference with itself

Practical

Independent: controlled by experimenter (x-axis)

Dependent: outcome of independent(y-axis)

Hypothesis: suggested explanation and be tested

Error: different between measured and actual value

Uncertainty: maximum different from average value of

repeated measurement

Systematic error: affect the accuracy (incorrect use of

equipment, bias) can be reduce by using calibrating

equipment (more decimal place or significant figure)

Random error: affect the reliability (measure time) can

be reduce by repeated experiment.

Average EMF

𝜺=−𝑵𝝓𝒎𝒂𝒙

𝟎.𝟐𝟓𝑷

Negative derivative of sin(x) is -

cos(x) and negative derivative of

cos(x) is sin(x)

𝑛1>𝑛2

1eV=1V

eV –> J : x1.6x10^-19

J eV: :1.6x10^-19

VCE unit 3 and 4 physics cheat sheet

Physics- Unit 4

VCE

High School - Australia

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