PH5 Mindmap

• Created by: Jasmine W
• Created on: 29-05-16 15:22
• 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
• 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
• 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
• 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
• 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 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 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
• 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
• 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
• 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