PH5 Mindmap

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  • PH5
    • Capacitance
      • Capacitors
        • Devices that store charge
        • Dielectrics between the plates increase capacitance
          • Dielectrics are insulators between plates
        • PD applied to capacitor causes charge to transfer from power supply to plates
          • Plates carry equal and opposite charge- so the net charge is zero
        • Amount of charge depends on pd applied and capacitance of plate
          • Q=CV
            • Charge = Capacitance x pd between plates
      • Unit of capacitance if Farad (F)
      • Capacitance = (Permittivity of free space x area od plates) / distance between plates
        • Capacitance is proportional to plate area
        • Capacitance is inversley proportional to the sepreration of the plates
      • Energy
        • U=1/2 QV
          • U = 1/2 QV = 1/2 CV^2 = Q^2 / 2C
        • U = internal energy
      • E-Feild
        • Uniform field between capacitor plates
        • E=V/d
      • Combining Capacitors
        • Series
          • Overall capacitance is : 1/Ct = 1/C1 + 1/C2 + ... + 1/Cn
          • Overall capacitance is always less than the smallest capacitor
          • Its like increasing the seperation of the plates
        • Parallel
          • Overall capacitance is: Ct = C1 + C2 + ... + Cn
          • Effectively one big capacitor with a big area
          • Capacitance increases the more there are
      • Discharging a Capacitor
        • Capacitors discharge through a resistor
        • Current in resistor is Q/t
        • Rate at which capacitor loses charge is : Q/t = -current = -V/R = - Q/RC
        • Capacitor loses charge at a rate proportional to the charge on the capacitor
          • When capacitor is fully charged, loses charge quickly
          • As charge decreases, capacitor loses charge at a slower rate
        • Discharging capacitor equation: Q=Q1 x e^(-t/RC)
        • Time constant for discharging capacitor: in one time constant, capacitor loses 63% of its charge
    • B- Fields
      • Wire carrying current in magnetic field
        • Wires carrying a current at an angle to a magnetic field experience  a force
        • Force found by: F=BILsinx
          • B is magnetic flux density (B-field)
          • I is the currrent
          • L is the length of wire in the B-field
          • x is the angle between the wire and the magnetic field
        • For maximum force, sinx=1, so the wire should be at right angles to the magnetic field
          • Then F=BIL
      • Fleming's Left Hand Rule (FLHR)
        • First finger is in the direction of the field (B-field)
        • Second finger is in the direction of the current
        • Thumb points in the direction of the motion
      • Force on charge moving in a magnetic field
        • F=Bqv sinx
          • B is magnetic flux density (B-Field)
          • q is the size of the moving charge
          • v is the velocity of the moving charge
          • x is the angle between the velocity and the B-field
      • Hall Probe
        • Device for measuring B-fields
        • Apply FLHR to find the force on the free electrons
          • Opposite direction is face which becomes positively charged
        • Force on electrons doesn't carry on forever as electrons will be repelled by negative charge of electrons already there
        • Equilibrium reached when magnetic force balances electric repulsion force
          • Bev = Ee
        • Vh = Bvd
          • Hall voltage (Vh) = magnetic flux density (B) x drift velocity (v) x dimensions of hall probe (d)
        • Can use I=nAve and Vh=Bvd to find number of free electrons (n)
        • How to use a hall probe
          • Place probe in the field
          • Orientate probe so front face is at right angles to the B-field
      • Force between two wires carrying a current
        • When two wires carry a current the exert forces on one another
        • Force due to: top wire having a magnetic field, bottom wire is in the field, bottom wire feels force due to F=BILsinx (and same true but with bottom wires magnetic field)
        • Use FLHR to determine the direction of the resultant force
        • By Newton's 3rd law two parallel wires carrying a current in the same direction experience an attractive force
        • Ampere definition; The ampere is the current that flows through two infinite, thin parallel wires, one metre apart in vacuum, producing a force between the wires of exactly 2x10^-7 N per metre of length
      • Ion Beams and Accelerators
        • First particle accelerator just a glass tube, cathode and anode
          • Uniform electric field between cathode and anode which accelerates the electrons with force: F=Eq
        • Electron-volt (eV)
          • Energy transferred when an electron moves between two points with a potential difference of 1 volt between them (1eV = 1.6 x 10^-19 J)
            • For an electron being accelerated, its the KE acquired when accelerated through a pd of 1V
        • You can have a vertical electric field as well as a horizontal one to deflect the electrons further and cause them to also experience a constant force downwards of F=Eq
        • Linear accelerator (Linac)
          • Series of tubes charged either +ve or -ve depending on alternating pd sent to them
          • First tube -ve so proton attracted to it
          • When protons gets inside tube, no force acting on it so pd changes and tube in front is -ve, which attracts it
          • Electric field always accelerates it to the right
          • Pd must be synchronised to proton always inside tube when pd changes
            • Achieved by keeping frequency constant but increasing lengths of tubes and gaps between them as proton moves faster
        • Cyclotron
          • Acceleration provided by electric field
          • As proton is in gap between to Dees (semi-circular plates) it's accelerated across the gap by an electric field
          • Magnetic field keeps proton in circular motion
            • But as speed increases so does radius of circle
              • Proton eventually spirals out and leaves the cyclotron
          • Frequency is constant because B-field is uniform and q and m are both constant in equation: f=(Bq)/(2pim)
            • Frequency stays the same even as velocity increases
        • Synchrotron
          • Speed increase provided by an alternating pd
          • Charged particle performs circular motion due to B-field
          • Acceleration occurs 4 times per orbit, when the particles cross between the differently charged tubes
          • Radius of orbit remains constant, so B-field must increase as particle moves faster and frequency increases as particle moves faster
    • Electromagnetic Induction
      • Magnetic Flux
        • Magnetic flux = AB cosx
          • A is the area, B is the B-field and x is the angle between the B-field and the angle between the normal to the surface and the B-field
        • Unit is the Weber (Wb)
        • B-field is the magnetic flux divided by the area, it's the magnetic flux density
      • Flux Linkage
        • Magnetic flux referring to many loops rather than just one
        • If a coil has N loops and the magnetic flux through each loop is *phi*
          • Total magnetic flux for whole coil is: N*phi*=BAN
        • Unit is Weber-turn
      • Faraday's Law
        • The induced EMF is equal to the rate of change of flux linkage
        • V = (BAN) / t
        • Two ways of inducing EMF from Faraday's Law
          • 1. By varying the B-field
          • 2. By varying the area - through some sort of motion
        • How does a transformer work using Faraday's law?
          • 1. Alternating current in primary coil provides alternating magnetic  field inside it
          • 2. Magnetic field lines follow iron sore to secondary coil
          • 3. Magnetic field inside seconary coil is alternating because the current in the primary is alternating
          • 4. An alternating EMF is induced in the secondary coil because of the changing flux linkage according to Faraday's Law
      • Lenz's Law
        • If an induced current flows due to a change in magnetic flux linkage, then this current will oppose whats causing the current
        • Its the reason why there's a minus sign in Faraday's law
      • Rotating a coil in a magnetic field
        • Coil Position
          • In some positions, the induced EMF is zero because the coil is not cutting any lines of magnetic fliux
            • Or the flux linkage of the coil is a maximum because cosx =1 so rate of change of flux linkage is zero
          • In other positions the induced EMF is a maximum because the coil is cutting lines of magnetic flux at right angles, so cutting lines at the greatest rate
            • Or the flux linkage of the coil is changing at the greatest rate because cosx=0
        • Flux Density
          • Induced EMF proportional t strength of B-field
          • Stronger B-field results in more lines of magnetic flux being cut
            • Or a stronger B-field results in a larger magnetic flux linkage for the coil
        • Coil Area
          • The induced EMF is proportional to the coil area
          • A larger area results in more lines of magnetic flux being cut
            • A larger area results in a larger magnetic flux linkage for the coil
        • Angular Velocity
          • Induced EMF is proportional to the angular velocity
          • As angular velocity increases the rate of cutting of flux increases
            • As angular velocity increases the rate of change of flux linkage increases
      • Alternating current and rms
        • Due to sinusoidal variation of pd the rms pd (Vrms) is: Vrms = (Vo)/ root 2
          • Similar for current, replace V with I
      • The Oscilloscope
        • Oscilloscope trace shows you a sinusoidally varying pd
        • Essentially just a pd against time graph
          • the VOLTS/DIV tells you the height of each square
            • The SEC/DIV tells you the width of each square
        • DC voltage just give horizontal line on the screen
        • Can't find current directly but find voltage then use V=I/R
    • Radioactivity and Radioisotopes
      • Ionising radiation
        • Knock out electrons from atoms or molecules
        • Ionised particles produced are highly reactive and react with molecules nearby
        • In living tissue it can cause cause damage at the cellular level and can damage DNA leading to cancer
        • We are subjected to background radiation all the time and life expectancy isn't that much shorter in places with high background radiation
        • An absorbed dose of 8J per Kg is lethal to humans
        • 3 types of nuclear radiation: Alpha, Beta and Gamma radiation
      • Alpha radiation
        • Fast moving helium nucleas
        • More ionising than beta and gamma radiation
        • Loses energy very quickly because it's so ionising so has low penetration
        • Range of alpha particles is only a few cm in air and absorbed by a sheet of paper
      • Beta radiation
        • Beta particle is a fast moving electron
        • More highly ionising that gamma radiation but less so than alpha radiation
        • Has intermediate penetration power
        • Usually stopped by a few mm of aluminium of a few metres of air
      • Gamma Radiation
        • Gamma radiation is a high energy, low wavelength electromagnetic wave or photon that originates from an excited nucleus
        • It is less ionising than alpha and beta particles
        • More penetrating than alpha and beta particles
        • It is stopped by around 15cm of lead or around a metre of concrete
      • Which radiation?
        • To work out which radiation was emitted from a source, place different materials between the source and the detector
          • Put sheet of paper between source, significant drop in count rate suggests alpha radiation present
          • Put piece of aluminium a few mm thick between source and detector, if further significant drop, suggests beta is present
          • Whatever count rate is left above background radiation is due to gamma radiation. Can double check with gamma absorber though, e.g few cm of lead
          • Looking for significant drop as the absobers can absorb a bit of each of them so must be a significant drop to say for certain
      • Background radiation
        • 5 sources of background rdiation
          • Radon gas: Comes from all natural sources originating from radioactive elements like potassium-40
          • Cosmic rays: Mainly arise from high energy particles arriving at the Earth's atmosphere
          • Man made: Majority comes from having x-ray images taken and a tiny percent from nuclear power and nuclear weapons testing
          • Buildings and ground: Similar to radon gas it originates from radioactive elements like Carbon-14
          • Food and drink: Natural sources that originated from radioactive elements we then eat
      • Theory of radioactivity
        • Radioactivity is an entirely random process and depends purely on the number of radioactive nuclei present
          • So the disintergrations per second is proportional to number of radioactive nuclei present
        • Decay Constant
          • Constant in the decay law and it determines the rate of decay of a particular nucleus
          • The greater  *lambda* the more rapid the rate of decay
          • Probability per second of a nuclus decaying
        • Activity
          • Activity is the number of disintegrations per second
          • Its the rate of decay
          • A = *lambda* N
          • Unit is the Becquerel; one disintegration per second
        • Half-Life
          • Its the time taken for the number of radioactive nuclei to reduce to one half of its initial value
          • Unit is Second, but can also be years due to how long it takes
        • Every time a nucleus disintergrates the number of nuclei decreases which leads to an exponential decay for the number of nuclei
          • As the number of nuclei decreases, so does the activity which also decreases exponentially
      • Radioisotopes
        • An isotope that is radioactive: has the same atomic number but different mass numbers
        • Applications
          • Gamma emitter used to sterilise medical equipment and food
            • Although gamma has low ionising capabilities it can penetrate many  centimetres of metal
            • Can be a large enough dose to kill germs, bacteria and viruses
            • You can sterilise food in tins after the tin has been sealed ensuring the food has a long life and is bacteria free
            • You can sterilise lots of surgical instruments in crates
          • Beta emitter to check thickness of paper
            • A beta source an a detector either side of a sheet of paper and if the count rate increases/ decreases by a significant amount then you know the paper is not the right thickness
    • Nuclear Energy
      • E=mc^2
        • Nuclear energy is based on this equation and benefits from c^2 being verly big
        • This is ther energy produced when some mass is 'lost'
          • To lose mass you can annihalate matter and antimatter
            • Isolated antimatter doesn't exist on Earth so other things have to be done to use nuclear energy
        • First conformation of E=mc^2 cam from Cockroft and Watson's experiment that 'split the atom' for the first time
          • They bombarded a lithium nuclei with protons and obtained two helium nuclei and lots of energy
            • Energy must come from 'lost' mass according to einsteins equation
      • Unified atomic mass unit (u)
        • one twelfth of the mass of an atom of carbon 12
        • 1u = 1.6605x10^(-27)Kg
        • 1u of mass lost gives 931MeV of energy
      • Stable and Unstable nuclei
        • Attractive force between the nucleus and electrons which holds the electrons in place
        • Attractive fore (strong force) which holds the nucleons together in the nucleus
          • 100 times greater than the repulsive force between the positive protons
        • When there's an attractive force, as the particles come closer they lose potential energy
          • This is the energy that can be given out
        • In nuclear reactions, when the nuclei become more stable they give out energy
          • Same happens in  chemical reactions but nuclear reactions give out more energy
        • As the particles come closer together, the total mass decreases- potential energy was a greater mass before the particles were brought together
          • Mass also decreases in exothermic chemical reactions but not by much, in nuclear reactions the change is very big so can easily be measured by a mass spectometer
        • The change in potential energy as the nucleons are brought closer together is called the binding energy
          • Binding energy is the energy that has to be supplied in order to separate a nucleus into its nucleons, or its the energy given out (decrease in PE) when nucleons form a nucleus
      • Binding energy per nucleon vs.nucleon number graph
        • A graph which shows the stability of nuclei and is they are likely to perform fission or fusion
        • A hydrogen nucleus has 0 binding energy because its just a proton and theres nothing else in the nuceus with it
        • Iron is close to the maximum of the curve and is one of the most stable nuclei
          • All the other elements are trying to be as stable as iron
          • This means iron doesn't undergo fission or fusion
        • Smaller nuclei undergo fusion to increase their nucleon number and move towards the more stable part of the graph
        • Heavier nucleons will undergo fission to decrease their nucleon number and move towards stability
      • Fission reactors
        • The fission reaction of Uranium produces three extra neutrons
          • It doesn't undergo fission by itself, it needs to capture a neutron first to turn into a different isotope which spontaneously undergoes fission
          • Can lead to a chain reaction as one neutron produces 3 which each produce 3 and so on and so forth
            • Can easily get out of control and cause a bomb
            • In a nuclear reactor to get a controlled reaction, one product neutron causes one neutron reaction so you have equilibrium
        • Nuclear reactor
          • Control rods
            • They absorb neutrons to decrease the total number of neutrons available for fission
            • Rods start of lowered and are raised until a sustainable chain reaction is reached
            • Material must be a neutron absorber, have a high melting point and other mechanical properties, e.g boron steel
          • Moderator
            • Neutrons produced in fission travelling too fast the moderator slows them down so the probability of fission is increased
            • Material needs to be a poor absorber- neutrons need to be slowed down not taken out
            • Material also needs a light nucleus as neutrons slow down by transferring kinetic energy in collision with moderator nucleus
              • Heavy nuclei cause neutrons to bounce off at same speed
            • Water or graphite are good moderators
          • Coolant
            • Controls temperature of reactor and takes thermal energy away to the steam turbine and generator
            • Coolant is liquid or gas with high heat capacity that doesn't absorb neutrons or become radioactive
              • E.g water or super-heated steam used
          • Waste
            • Radioactive for thousands of years
            • Stable safe place needed to store it

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