waves, fields & nuclear energy. contents oscillations & waves oscillations & waves...

37
Waves, Fields & Nuclear Waves, Fields & Nuclear Energy Energy

Upload: simon-arnold

Post on 25-Dec-2015

235 views

Category:

Documents


3 download

TRANSCRIPT

Page 1: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

Waves, Fields & Nuclear Waves, Fields & Nuclear EnergyEnergy

Page 2: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

ContentsContents

Oscillations & WavesOscillations & Waves CapacitanceCapacitance Gravitational & Electric FieldsGravitational & Electric Fields Magnetic Effects of CurrentsMagnetic Effects of Currents Nuclear ApplicationsNuclear Applications

Page 3: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

Circular MotionCircular Motion Consider an object going round in a circle of radius r:Consider an object going round in a circle of radius r:

- speed is constant- speed is constant

- velocity changes- velocity changes

s = r s = r

- angular velocity- angular velocity

ωω = 2 = 2f = r/vf = r/v

- centripetal acceleration- centripetal acceleration

a = va = v22/r = /r = ωω22rr

- centripetal force- centripetal force

f = ma = mvf = ma = mv22/r = m/r = mωω22rr

Page 4: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

OscillationsOscillations Natural frequencyNatural frequency: an object will swing freely at this : an object will swing freely at this

frequencyfrequency Free oscillationFree oscillation: an object oscillates independently: an object oscillates independently Forced oscillationForced oscillation: a force causes an object to oscillate: a force causes an object to oscillate Resonant frequencyResonant frequency: where maximum amplitude is : where maximum amplitude is

attainedattained

(car suspensions, bridges swaying, bells ringing)(car suspensions, bridges swaying, bells ringing)

DampingDamping: amplitude of oscillations exponentially : amplitude of oscillations exponentially decreasesdecreases

- light damping reduces oscillations slowly- light damping reduces oscillations slowly

- heavy damping reduces oscillations quickly- heavy damping reduces oscillations quickly

- critical damping stops the oscillation within one cycle- critical damping stops the oscillation within one cycle

Page 5: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

SHMSHM

max. a and max. v: originmax. a and max. v: origin V = 0 at –A and +AV = 0 at –A and +A max. PE at –A and +Amax. PE at –A and +A max. KE at originmax. KE at origin

a = - (2a = - (2f )f )22xx a = - a = - ωω22xx v = 2v = 2f f (A(A22 – x – x22)) s = s = A cos 2 A cos 2ftft T = 2T = 2(l/g)(l/g) EEtottot = PE + KE = PE + KE

Page 6: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

SHMSHM

Mass on a springMass on a spring:: FFupup = k(l + x) – mg = k(l + x) – mg a = -kx/m = - (2a = -kx/m = - (2f )f )22x x T = 2T = 2(m/k)(m/k)

Page 7: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

Progressive WavesProgressive Waves

Wave EquationWave Equation::v = fv = fλλ

v = velocity (m/s)v = velocity (m/s)f = frequency (Hz) or (1/s)f = frequency (Hz) or (1/s)λλ = wavelength (m) = wavelength (m) λλ

PolarisationPolarisation::

Page 8: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

Superposition of WavesSuperposition of Waves Superposition can only be applied Superposition can only be applied

to waves of the same kindto waves of the same kind

The diagram shows a green wave The diagram shows a green wave added to a red wave. The result is added to a red wave. The result is the black wave, whose the black wave, whose wavelength and amplitude wavelength and amplitude reflects the sum of the two wavesreflects the sum of the two waves

Page 9: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

Wave BehaviourWave Behaviour InterferenceInterference: When two waves collide, they superimpose: When two waves collide, they superimpose Superposition affects the waveform and interference resultsSuperposition affects the waveform and interference results

Path difference: difference in distance between two sources. Path difference: difference in distance between two sources. It is measured in half wavelengthsIt is measured in half wavelengths

Waves in phase interfere constructively (increased Waves in phase interfere constructively (increased amplitude)amplitude)

Waves out of phase interfere destructively (cancellation)Waves out of phase interfere destructively (cancellation)

Constructive: even number of ½ Constructive: even number of ½ λλss Destructive: odd number of ½ Destructive: odd number of ½ λλss

Page 10: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

Wave BehaviourWave Behaviour Diffraction GratingDiffraction Grating::

- Light is split by travelling through very thin slits - Light is split by travelling through very thin slits called a diffraction gratingcalled a diffraction grating- Light is split because it is composed of different - Light is split because it is composed of different wavelengthswavelengths- Each of these wavelengths diffracts at a different - Each of these wavelengths diffracts at a different angleangle

d sind sin = m = mλλ

d = slit widthd = slit width = angle= anglem = spectrum order number (1m = spectrum order number (1stst: m= 1, 2: m= 1, 2nd:nd: m = 2 etc.) m = 2 etc.)λλ = wavelength = wavelength

NB: “m” is sometimes denoted as “n” insteadNB: “m” is sometimes denoted as “n” instead

Page 11: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

Wave BehaviourWave Behaviour

The more slits, the more defined the diffractionsThe more slits, the more defined the diffractions The more slits, the greater the intensityThe more slits, the greater the intensity The more slits, the greater the angle (easier to The more slits, the greater the angle (easier to

measure!)measure!)

There is a limited number of orders, as sinThere is a limited number of orders, as sin has a has a maximum value of 1maximum value of 1- therefore at maximum, d = m- therefore at maximum, d = mλλ

Page 12: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

CapacitorsCapacitors Capacitors: store charge for a short timeCapacitors: store charge for a short time

- - consists of two metal plates separated by a layer of consists of two metal plates separated by a layer of insulating material insulating material dielectric dielectric

Electrons are pumped onto the –ve plateElectrons are pumped onto the –ve plate Electrons are repelled off the +ve plateElectrons are repelled off the +ve plate A potential difference is formed A potential difference is formed thus a charge thus a charge

Capacitance: charge required to produce 1V of Capacitance: charge required to produce 1V of potential difference in a conductorpotential difference in a conductor

capacitance (F) = charge (C) /voltage (V)capacitance (F) = charge (C) /voltage (V)

CC = = QQ / / VV

Page 13: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

CapacitorsCapacitors Energy in a CapacitorEnergy in a Capacitor: When a capacitor is charged : When a capacitor is charged

up, a certain amount of charge moves through a up, a certain amount of charge moves through a certain voltage. Work is done on the charge to build certain voltage. Work is done on the charge to build up the electric field in the capacitorup the electric field in the capacitor

energy = charge x voltageenergy = charge x voltagecapacitance = charge / voltagecapacitance = charge / voltage

Thus:Thus: E = ½CVE = ½CV22

Discharge of a CapacitorDischarge of a Capacitor: Charge decreases by the : Charge decreases by the same fraction for each time interval, so that if it takes same fraction for each time interval, so that if it takes time, t, for the charge to decay to 50 % of its original time, t, for the charge to decay to 50 % of its original level, the charge after 2t seconds is 25 % of the level, the charge after 2t seconds is 25 % of the originaloriginal

Page 14: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

CapacitorsCapacitors Q = QQ = Q00ee–t/RC–t/RC

V = VV = V00ee–t/RC–t/RC

I = II = I00ee–t/RC–t/RC

RC = time constantRC = time constant

tt½ ½ = 0.693 RC= 0.693 RC

tt½½ = half life = half life

Page 15: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

Gravity FieldsGravity Fields

Newton’s Square Law of Gravitation:Newton’s Square Law of Gravitation:- Every particle of matter in the Universe attracts - Every particle of matter in the Universe attracts every other particle with a gravitational force that is every other particle with a gravitational force that is proportional to the products of the masses and proportional to the products of the masses and inversely proportional to the square of the distance inversely proportional to the square of the distance between thembetween them

Thus:Thus: F = -GMm/rF = -GMm/r22 G = 6.67x10G = 6.67x10--

1111NmNm22kgkg-2-2

a = F/m a = F/m where a = gravity: where a = gravity:g = F/mg = F/m

Thus:Thus: g = -GM/rg = -GM/r22 r = radius from r = radius from centrecentre of of orbit!orbit!

Page 16: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

Gravity FieldsGravity Fields

Heading towards the centre of the Earth…Heading towards the centre of the Earth…

At centre: g = 0 as matter is pulled in all directions At centre: g = 0 as matter is pulled in all directions equallyequally

Page 17: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

Gravity FieldsGravity Fields Gravitational PotentialGravitational Potential::

- Work done on a unit mass in moving it to that point - Work done on a unit mass in moving it to that point from a point remote from all other massesfrom a point remote from all other masses

Always negative, because this involves a closed Always negative, because this involves a closed systemsystem- the zero point of gravitational potential is at infinity- the zero point of gravitational potential is at infinity

VVgg = -GM/r = -GM/r VVgg = gravitational = gravitational potentialpotential

VVg g is the area under the curve on the previous slideis the area under the curve on the previous slide

Potential Energy in space:Potential Energy in space: EEpp = -GMm/r = -GMm/r

Page 18: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

Electric FieldsElectric Fields Electric field: region of force around a point chargeElectric field: region of force around a point charge

F = kQF = kQ11QQ22/r/r22 k =k =

00 = 8.85 = 8.851010-12 -12 CC22NN-1-1mm-2-2 (F/m)(F/m)

Electric Field Strength: force per unit chargeElectric Field Strength: force per unit charge

E = F/QE = F/Q

This is radial for point charges:This is radial for point charges:

Page 19: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

Electric FieldsElectric Fields Electric Field Strength:Electric Field Strength: is inversely proportional to the is inversely proportional to the

square square of the radiusof the radius

- uniform field: E = V/d- uniform field: E = V/d

Electric Potential:Electric Potential: energy per unit chargeenergy per unit charge

Page 20: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

Magnetic FieldsMagnetic Fields

A current (I) has a magnetic field (B) around itA current (I) has a magnetic field (B) around it A wire has a circular magnetic field around itA wire has a circular magnetic field around it

If the current changes direction, so does the fieldIf the current changes direction, so does the field

Page 21: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

Magnetic FieldsMagnetic Fields

Magnets attract magnetic materials using a magnetic Magnets attract magnetic materials using a magnetic fieldfield

The magnetic field surrounds the magnet, and gets The magnetic field surrounds the magnet, and gets weaker as the distance from the magnet increasesweaker as the distance from the magnet increases

Magnets should be called permanent magnetsMagnets should be called permanent magnets

the magnetism is always therethe magnetism is always there

Electricity makes a magnet much strongerElectricity makes a magnet much stronger This can be turned on and offThis can be turned on and off

Page 22: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

Magnetic FieldsMagnetic Fields

Magnets pick up paper clips etc.Magnets pick up paper clips etc.

Electromagnets pick up cars etc.Electromagnets pick up cars etc.

weak

strong

Page 23: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

The magnetic field around a coil electromagnet can be The magnetic field around a coil electromagnet can be increased by:increased by:

- Increasing the current flowing through the wire- Increasing the current flowing through the wire

- Adding loops on the coil (loops are long lengths of - Adding loops on the coil (loops are long lengths of wire)wire)

- Placing an iron or steel core inside the coil- Placing an iron or steel core inside the coil

Basic electromagnetBasic electromagnet

Magnetic FieldsMagnetic Fields

Page 24: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

The Motor EffectThe Motor Effect::

- When two magnets are placed close to each other, - When two magnets are placed close to each other, they the fields affect each other produce a forcethey the fields affect each other produce a force

If a wire carrying a current is placed inside this If a wire carrying a current is placed inside this magnetic field, a force is produced. This is called the magnetic field, a force is produced. This is called the motor effectmotor effect

The direction of the force will depend on the direction The direction of the force will depend on the direction of the magnetic field and the direction of the current in of the magnetic field and the direction of the current in the fieldthe field

Magnetic FieldsMagnetic Fields

Page 25: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

Fleming’s Left Hand RuleFleming’s Left Hand Rule::

- When creating a force, use Fleming’s LH Rule to - When creating a force, use Fleming’s LH Rule to determine in which way the motor will spindetermine in which way the motor will spin

- -

Magnetic FieldsMagnetic Fields

Page 26: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

We can increase the force produced by:We can increase the force produced by:

- increasing the current- increasing the current

- increasing the number of coils- increasing the number of coils

- increasing the magnetic field strength (stronger - increasing the magnetic field strength (stronger magnet)magnet)

Magnetic FieldsMagnetic Fields

Page 27: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

Magnetic FieldsMagnetic Fields

• When a magnet is moved into a coil, an electrical current is induced

• When the magnet stops,the induced current stops

• When the magnet reverses, the electrical current reverses

Page 28: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

Magnetic FieldsMagnetic Fields

Increase the voltage? … 3 ways…

1. Stronger magnet

2. Speed of magnet

3. Number of coils

Page 29: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

Magnetic FieldsMagnetic Fields

To work out the force on a wire: use Fleming’s LH To work out the force on a wire: use Fleming’s LH RuleRule

Force is proportional to:Force is proportional to:- current- current- magnetic field strength- magnetic field strength- length of wire inside magnetic field- length of wire inside magnetic field

F = BIlF = BIl B = magnetic field strength or flux B = magnetic field strength or flux densitydensity

(Tesla)(Tesla)

When a wire is at an angle to the magnetic field… F = When a wire is at an angle to the magnetic field… F = BIl sinBIl sin

Page 30: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

Magnetic FieldsMagnetic Fields To work out the force on a charge: use Fleming’s LH RuleTo work out the force on a charge: use Fleming’s LH Rule

Force is proportional to:Force is proportional to:

- current (flow of charge)- current (flow of charge)

- magnetic field strength- magnetic field strength

- velocity of charged particle- velocity of charged particle

F = BqVF = BqV B = magnetic field strength or flux B = magnetic field strength or flux densitydensity

(Tesla)(Tesla)

When a charge is at an angle to the magnetic field… F = When a charge is at an angle to the magnetic field… F = BqV sinBqV sin

F = mvF = mv22/r /r BqV = mv BqV = mv22/r /r V = Bqr/mV = Bqr/m

Page 31: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

Magnetic FieldsMagnetic Fields Magnetic FluxMagnetic Flux: Product between the magnetic flux : Product between the magnetic flux

density and the area when the field is at right angles to density and the area when the field is at right angles to the areathe area

ФФ = BA = BA

Flux LinkageFlux Linkage: : ФФ multiplied by number of turns on a wire multiplied by number of turns on a wire

ФФ = NBA = NBA

It can be changed by:It can be changed by:- changing the - changing the strength of the magnetic fieldstrength of the magnetic field- move the coil so it enters the field at an angle- move the coil so it enters the field at an angle

Lenz’s Law: direction of an induced current opposes the Lenz’s Law: direction of an induced current opposes the flux change that caused itflux change that caused it

Page 32: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

Mass & EnergyMass & Energy 1 atomic mass unit (u) = 1.661 1 atomic mass unit (u) = 1.661 10- 10-

27 kg27 kg Atomic mass: mass of an atomAtomic mass: mass of an atom Nuclear mass: mass of atom’s Nuclear mass: mass of atom’s

nucleusnucleus

E = mcE = mc22 c = 3x10c = 3x1088m/sm/s (J) = (kgm(J) = (kgm22/s/s22))

1eV = 1.6x101eV = 1.6x10-19-19JJ 1u = 931.3MeV1u = 931.3MeV

Binding Energy per Nucleon: Energy Binding Energy per Nucleon: Energy required to remove a nucleon. Higher required to remove a nucleon. Higher numbers numbers more stable nuclei more stable nuclei

Page 33: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

Mass & EnergyMass & Energy FissionFission: splitting up of a large nucleus which is : splitting up of a large nucleus which is

rarely spontaneousrarely spontaneous

The strong nuclear force acts between The strong nuclear force acts between neighbouring nucleonsneighbouring nucleons

The forces are now weak in this The forces are now weak in this shape/formationshape/formation

Nucleus splits (rarely spontaneously)Nucleus splits (rarely spontaneously)

Induce fission: add thermal neutron whose Induce fission: add thermal neutron whose kinetic energy:kinetic energy:1) isn’t too low (will bounce off nucleus)1) isn’t too low (will bounce off nucleus)2) isn’t too high (will go through nucleus)2) isn’t too high (will go through nucleus)3) is correct to be captured by the attractive 3) is correct to be captured by the attractive force in between nucleonsforce in between nucleons- this can result in a chain reaction- this can result in a chain reaction

Page 34: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

Mass & EnergyMass & Energy FusionFusion: when light nuclei bind together which increases : when light nuclei bind together which increases

the binding energy per nucleon the binding energy per nucleon energy is released energy is released

Each nucleus has to have sufficient energy to:Each nucleus has to have sufficient energy to:

- overcome electrostatic repulsion from the protons- overcome electrostatic repulsion from the protons

- overcome the repulsive strong force which is found - overcome the repulsive strong force which is found outside the region of the strong forceoutside the region of the strong force

High temperatures are required (gas High temperatures are required (gas plasma) plasma)

If it could be made to work, has advantages over If it could be made to work, has advantages over fission: fission:

- greater power per kilogram of fuel used- greater power per kilogram of fuel used

- raw materials are cheap and readily available- raw materials are cheap and readily available

- reaction is not radioactive- reaction is not radioactive

Page 35: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

Nuclear PowerNuclear Power Although the fission products are not easily predictable, Although the fission products are not easily predictable,

three more neutrons are producedthree more neutrons are produced An uncontrolled chain reaction causes a violent explosionAn uncontrolled chain reaction causes a violent explosion Minimum mass before chain reaction occurs: critical massMinimum mass before chain reaction occurs: critical mass

Nuclear power station:Nuclear power station: Reactor is housed in aReactor is housed in a concrete to concrete to

preventprevent radiation from leaking radiation from leaking Expensive to buildExpensive to build Costly to runCostly to run Very clean, no pollutionVery clean, no pollution Need very little fuelNeed very little fuel Produce dangerous wasteProduce dangerous waste Nuclear power Nuclear power France vs. England = 80% vs. 20% France vs. England = 80% vs. 20%

Page 36: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

Nuclear PowerNuclear Power

SafetySafety::

- Strict regulations- Strict regulations

- Serious accidents involving radiation leaks have - Serious accidents involving radiation leaks have occurredoccurred

- Disposal of radioactive waste must be carried out - Disposal of radioactive waste must be carried out carefullycarefully

TransmutationTransmutation::

- Definition: changing the nuclei of elements by - Definition: changing the nuclei of elements by exposing them to particlesexposing them to particles

- Particles have to travel slow enough to be captured - Particles have to travel slow enough to be captured by the nucleusby the nucleus

- used in medicine- used in medicine

Page 37: Waves, Fields & Nuclear Energy. Contents Oscillations & Waves Oscillations & Waves Capacitance Capacitance Gravitational & Electric Fields Gravitational

SummarySummary

Circular MotionCircular Motion OscillationsOscillations SHMSHM Progressive WavesProgressive Waves Superposition of WavesSuperposition of Waves Wave BehaviourWave Behaviour CapacitorsCapacitors Gravity FieldsGravity Fields Electric FieldsElectric Fields Magnetic FieldsMagnetic Fields Mass & EnergyMass & Energy Nuclear PowerNuclear Power