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Waves, Fields & Nuclear Energy. Contents. Oscillations & Waves Capacitance Gravitational & Electric Fields Magnetic Effects of Currents Nuclear Applications. Circular Motion. Consider an object going round in a circle of radius r: - speed is constant - velocity changes s = r 

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contents
Contents
  • Oscillations & Waves
  • Capacitance
  • Gravitational & Electric Fields
  • Magnetic Effects of Currents
  • Nuclear Applications
circular motion
Circular Motion
  • 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
Oscillations
  • 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

slide5
SHM
  • 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
slide6
SHM
  • Mass on a spring:
  • Fup = k(l + x) – mg
  • a = -kx/m = - (2f )2x
  • T = 2(m/k)
progressive waves
Progressive Waves
  • Wave Equation:

v = fλ

v = velocity (m/s)

f = frequency (Hz) or (1/s)

λ = wavelength (m) λ

  • Polarisation:
superposition of waves
Superposition of Waves
  • Superposition can only be applied to waves of the same kind
  • 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
Wave Behaviour
  • Interference: When two waves collide, they superimpose
  • Superposition affects the waveform and interference results
  • Path difference: difference in distance between two sources. It is measured in half wavelengths
  • Waves in phase interfere constructively (increased amplitude)
  • Waves out of phase interfere destructively (cancellation)
  • Constructive: even number of ½ λs
  • Destructive: odd number of ½ λs
wave behaviour1
Wave Behaviour
  • 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 behaviour2
Wave Behaviour
  • 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
Capacitors
  • Capacitors: store charge for a short time

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

  • Electrons are pumped onto the –ve plate
  • Electrons are repelled off the +ve plate
  • A potential difference is formed  thus a charge
  • Capacitance: charge required to produce 1V of potential difference in a conductor

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

C = Q / V

capacitors1
Capacitors
  • 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

  • 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
capacitors2
Capacitors
  • Q = Q0e–t/RC
  • V = V0e–t/RC
  • I = I0e–t/RC

RC = time constant

  • t½ = 0.693 RC

t½ = half life

gravity fields
Gravity Fields
  • 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: 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 fields1
Gravity Fields
  • Heading towards the centre of the Earth…
  • At centre: g = 0 as matter is pulled in all directions equally
gravity fields2
Gravity Fields
  • Gravitational Potential:

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

  • Always negative, because this involves a closed system

- the zero point of gravitational potential is at infinity

Vg = -GM/r Vg = gravitational potential

  • Vg is the area under the curve on the previous slide
  • Potential Energy in space: Ep = -GMm/r
electric fields
Electric Fields
  • Electric field: region of force around a point charge

F = kQ1Q2/r2 k =

0 = 8.8510-12 C2N-1m-2 (F/m)

  • Electric Field Strength: force per unit charge

E = F/Q

This is radial for point charges:

electric fields1
Electric Fields
  • Electric Field Strength: is inversely proportional to the square of the radius

- uniform field: E = V/d

  • Electric Potential: energy per unit charge
magnetic fields
Magnetic Fields
  • A current (I) has a magnetic field (B) around it
  • A wire has a circular magnetic field around it
  • If the current changes direction, so does the field
magnetic fields1
Magnetic Fields
  • 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 fields2
Magnetic Fields

Magnets pick up paper clips etc.

Electromagnets pick up cars etc.

strong

weak

magnetic fields3
Magnetic Fields
  • 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 fields4
Magnetic Fields
  • 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 fields5
Magnetic Fields
  • Fleming’s Left Hand Rule:

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

-

magnetic fields6
Magnetic Fields
  • We can increase the force produced by:

- increasing the current

- increasing the number of coils

- increasing the magnetic field strength (stronger magnet)

magnetic fields7
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
slide28

Magnetic Fields

  • Increase the voltage? … 3 ways…
  • Stronger magnet
  • 2. Speed of magnet
  • 3. Number of coils
magnetic fields8
Magnetic Fields
  • To work out the force on a wire: use Fleming’s LH Rule
  • 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 fields9
Magnetic Fields
  • To work out the force on a charge: use Fleming’s LH Rule
  • 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 fields10
Magnetic Fields
  • Magnetic Flux: Product between the magnetic flux density and the area when the field is at right angles to the area
  • Ф = BA
  • Flux Linkage: Ф multiplied by number of turns on a wire
  • Ф = NBA
  • It can be changed by:

- changing the strength of the magnetic field

- move the coil so it enters the field at an angle

  • Lenz’s Law: direction of an induced current opposes the flux change that caused it
mass energy
Mass & Energy
  • 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 c = 3x108m/s

(J) = (kgm2/s2)

  • 1eV = 1.6x10-19J
  • 1u = 931.3MeV
  • Binding Energy per Nucleon: Energy required to remove a nucleon. Higher numbers  more stable nuclei
mass energy1
Mass & Energy
  • Fission: splitting up of a large nucleus which is rarely spontaneous
  • The strong nuclear force acts between neighbouring nucleons
  • The forces are now weak in this shape/formation
  • Nucleus splits (rarely spontaneously)
  • 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 energy2
Mass & Energy
  • Fusion: when light nuclei bind together which increases the binding energy per nucleon  energy is released
  • 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

  • High temperatures are required (gas  plasma)
  • 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
Nuclear Power
  • 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%
nuclear power1
Nuclear Power
  • Safety:

- Strict regulations

- Serious accidents involving radiation leaks have occurred

- Disposal of radioactive waste must be carried out carefully

  • 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
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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