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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


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


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


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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