Download Waves, Fields & Nuclear Energy

Waves, Fields & Nuclear Energy
Contents
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Oscillations & Waves
Capacitance
Gravitational & Electric Fields
Magnetic Effects of Currents
Nuclear Applications
Circular Motion
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Consider an object going round in a circle of radius r:
- speed is constant
- velocity changes
s=r
- angular velocity
ω = 2f = r/v
- centripetal acceleration
a = v2/r = ω2r
- centripetal force
f = ma = mv2/r = mω2r
Oscillations
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Natural frequency: an object will swing freely at this frequency
Free oscillation: an object oscillates independently
Forced oscillation: a force causes an object to oscillate
Resonant frequency: where maximum amplitude is attained
(car suspensions, bridges swaying, bells ringing)
Damping: amplitude of oscillations exponentially decreases
- light damping reduces oscillations slowly
- heavy damping reduces oscillations quickly
- critical damping stops the oscillation within one cycle
SHM
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max. a and max. v: origin
V = 0 at –A and +A
max. PE at –A and +A
max. KE at origin
a = - (2f )2x
a = - ω2x
 v = 2f (A2 – x2)
 s =  A cos 2ft
 T = 2(l/g)
 Etot = PE + KE
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SHM
Mass on a spring:
 Fup = k(l + x) – mg
 a = -kx/m = - (2f )2x
 T = 2(m/k)
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Progressive Waves
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Wave Equation:
v = fλ
v = velocity (m/s)
f = frequency (Hz) or (1/s)
λ = wavelength (m) λ
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Polarisation:
Superposition of Waves
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Superposition can only be applied to
waves of the same kind
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The diagram shows a green wave
added to a red wave. The result is
the black wave, whose wavelength
and amplitude reflects the sum of
the two waves
Wave Behaviour
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Interference: When two waves collide, they superimpose
Superposition affects the waveform and interference results
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Path difference: difference in distance between two sources. It
is measured in half wavelengths
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Waves in phase interfere constructively (increased amplitude)
Waves out of phase interfere destructively (cancellation)
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Constructive: even number of ½ λs
Destructive: odd number of ½ λs
Wave Behaviour
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Diffraction Grating:
- Light is split by travelling through very thin slits called a
diffraction grating
- Light is split because it is composed of different
wavelengths
- Each of these wavelengths diffracts at a different angle
d sin = mλ
d = slit width
 = angle
m = spectrum order number (1st: m= 1, 2nd: m = 2 etc.)
λ = wavelength
NB: “m” is sometimes denoted as “n” instead
Wave Behaviour
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The more slits, the more defined the diffractions
The more slits, the greater the intensity
The more slits, the greater the angle (easier to measure!)
There is a limited number of orders, as sin has a maximum
value of 1
- therefore at maximum, d = mλ
Capacitors
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Capacitors: store charge for a short time
- consists of two metal plates separated by a layer of
insulating material  dielectric
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Electrons are pumped onto the –ve plate
Electrons are repelled off the +ve plate
A potential difference is formed  thus a charge
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Capacitance: charge required to produce 1V of potential
difference in a conductor
capacitance (F) = charge (C) /voltage (V)
C
= Q
/
V
Capacitors
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Energy in a Capacitor: When a capacitor is charged up, a
certain amount of charge moves through a certain voltage.
Work is done on the charge to build up the electric field in
the capacitor
energy = charge x voltage
capacitance = charge / voltage
Thus: E = ½CV2
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Discharge of a Capacitor: Charge decreases by the same
fraction for each time interval, so that if it takes time, t, for
the charge to decay to 50 % of its original level, the charge
after 2t seconds is 25 % of the original
Capacitors
Q = Q0e–t/RC
 V = V0e–t/RC
 I = I0e–t/RC
RC = time constant
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t½ = 0.693 RC
t½ = half life
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Gravity Fields
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Newton’s Square Law of Gravitation:
- Every particle of matter in the Universe attracts every
other particle with a gravitational force that is proportional
to the products of the masses and inversely proportional to
the square of the distance between them
Thus:
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F = -GMm/r2
G = 6.67x10-11Nm2kg-2
a = F/m  where a = gravity: g = F/m
Thus:
g = -GM/r2
r = radius from centre of orbit!
Gravity Fields
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Heading towards the centre of the Earth…
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At centre: g = 0 as matter is pulled in all directions equally
Gravity Fields
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Gravitational Potential:
- Work done on a unit mass in moving it to that point from a
point remote from all other masses
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Always negative, because this involves a closed system
- the zero point of gravitational potential is at infinity
Vg = -GM/r
Vg = gravitational potential
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Vg is the area under the curve on the previous slide
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Potential Energy in space:
Ep = -GMm/r
Electric Fields
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Electric field: region of force around a point charge
F = kQ1Q2/r2
k=
0 = 8.8510-12 C2N-1m-2 (F/m)
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Electric Field Strength: force per unit charge
E = F/Q
This is radial for point charges:
Electric Fields
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Electric Field Strength: is inversely proportional to the square
of the radius
- uniform field: E = V/d
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Electric Potential: energy per unit charge
Magnetic Fields
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A current (I) has a magnetic field (B) around it
A wire has a circular magnetic field around it
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If the current changes direction, so does the field
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Magnetic Fields
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Magnets attract magnetic materials using a magnetic field
The magnetic field surrounds the magnet, and gets weaker
as the distance from the magnet increases
Magnets should be called permanent magnets
 the magnetism is always there
Electricity makes a magnet much stronger
This can be turned on and off
Magnetic Fields
Magnets pick up paper clips etc.
strong
weak
Electromagnets pick up cars etc.
Magnetic Fields
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The magnetic field around a coil electromagnet can be
increased by:
- Increasing the current flowing through the wire
- Adding loops on the coil (loops are long lengths of wire)
- Placing an iron or steel core inside the coil
Basic electromagnet
Magnetic Fields
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The Motor Effect:
- When two magnets are placed close to each other, they the
fields affect each other produce a force
If a wire carrying a current is placed inside this magnetic field,
a force is produced. This is called the motor effect
The direction of the force will depend on the direction of the
magnetic field and the direction of the current in the field
Magnetic Fields
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Fleming’s Left Hand Rule:
- When creating a force, use Fleming’s LH Rule to determine in
which way the motor will spin
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Magnetic Fields
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We can increase the force produced by:
- increasing the current
- increasing the number of coils
- increasing the magnetic field strength (stronger magnet)
Magnetic 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
Magnetic Fields
Increase the voltage? … 3 ways…
1. Stronger magnet
2. Speed of magnet
3. Number of coils
Magnetic Fields
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To work out the force on a wire: use Fleming’s LH Rule
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Force is proportional to:
- current
- magnetic field strength
- length of wire inside magnetic field
F = BIl
B = magnetic field strength or flux density
(Tesla)
When a wire is at an angle to the magnetic field… F = BIl sin
Magnetic Fields
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To work out the force on a charge: use Fleming’s LH Rule
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Force is proportional to:
- current (flow of charge)
- magnetic field strength
- velocity of charged particle
F = BqV
B = magnetic field strength or flux density
(Tesla)
When a charge is at an angle to the magnetic field… F = BqV sin
F = mv2/r  BqV = mv2/r  V = Bqr/m
Magnetic Fields
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Magnetic Flux: Product between the magnetic flux density and
the area when the field is at right angles to the area
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Ф = BA
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Flux Linkage: Ф multiplied by number of turns on a wire
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Ф = NBA
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It can be changed by:
- changing the strength of the magnetic field
- move the coil so it enters the field at an angle
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Lenz’s Law: direction of an induced current opposes the flux
change that caused it
Mass & Energy
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1 atomic mass unit (u) = 1.661  10-27 kg
Atomic mass: mass of an atom
Nuclear mass: mass of atom’s nucleus
E = mc2
(J) = (kgm2/s2)
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c = 3x108m/s
1eV = 1.6x10-19J
1u = 931.3MeV
Binding Energy per Nucleon: Energy
required to remove a nucleon. Higher
numbers  more stable nuclei
Mass & Energy
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Fission: splitting up of a large nucleus which is
rarely spontaneous
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The strong nuclear force acts between
neighbouring nucleons
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The forces are now weak in this shape/formation
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Nucleus splits (rarely spontaneously)
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Induce fission: add thermal neutron whose kinetic
energy:
1) isn’t too low (will bounce off nucleus)
2) isn’t too high (will go through nucleus)
3) is correct to be captured by the attractive force
in between nucleons
- this can result in a chain reaction
Mass & Energy
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Fusion: when light nuclei bind together which increases the
binding energy per nucleon  energy is released
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Each nucleus has to have sufficient energy to:
- overcome electrostatic repulsion from the protons
- overcome the repulsive strong force which is found outside
the region of the strong force
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High temperatures are required (gas  plasma)
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If it could be made to work, has advantages over fission:
- greater power per kilogram of fuel used
- raw materials are cheap and readily available
- reaction is not radioactive
Nuclear Power
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Although the fission products are not easily predictable,
three more neutrons are produced
An uncontrolled chain reaction causes a violent explosion
Minimum mass before chain reaction occurs: critical mass
Nuclear power station:
 Reactor is housed in a
concrete to prevent
radiation from leaking
 Expensive to build
 Costly to run
 Very clean, no pollution
 Need very little fuel
 Produce dangerous waste
 Nuclear power  France vs. England = 80% vs. 20%
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Nuclear Power
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Safety:
- Strict regulations
- Serious accidents involving radiation leaks have occurred
- Disposal of radioactive waste must be carried out carefully
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Transmutation:
- Definition: changing the nuclei of elements by exposing
them to particles
- Particles have to travel slow enough to be captured by the
nucleus
- used in medicine
Summary
Circular Motion
 Oscillations
 SHM
 Progressive Waves
 Superposition of Waves
 Wave Behaviour
 Capacitors
 Gravity Fields
 Electric Fields
 Magnetic Fields
 Mass & Energy
 Nuclear Power
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