Waves, Fields & Nuclear Energy

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  - angular velocity ω = 2f = r/v - centripetal acceleration a = v2/r = ω2r - centripetal force f = ma = mv2/r = mω2r

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 • Wave Equation: v = fλ v = velocity (m/s) f = frequency (Hz) or (1/s) λ = wavelength (m) λ • Polarisation:

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 • 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 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 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: 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

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

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 • 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 Fields • Heading towards the centre of the Earth… • At centre: g = 0 as matter is pulled in all directions equally

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 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 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 • 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 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 Fields Magnets pick up paper clips etc. Electromagnets pick up cars etc. strong weak

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 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 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 Fields • 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… • Stronger magnet • 2. Speed of magnet • 3. Number of coils

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 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 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 • 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 & 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 & 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 • 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 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 • Circular Motion • Oscillations • SHM • Progressive Waves • Superposition of Waves • Wave Behaviour • Capacitors • Gravity Fields • Electric Fields • Magnetic Fields • Mass & Energy • Nuclear Power

Waves, Fields & Nuclear Energy