PH5 Mindmap
- Created by: Jasmine W
- Created on: 29-05-16 15:22
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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
- Q=CV
- 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
- U=1/2 QV
- 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
- Series
- 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
- Capacitors
- 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
- F=Bqv sinx
- 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
- 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)
- 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
- But as speed increases so does radius of circle
- 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
- First particle accelerator just a glass tube, cathode and anode
- Wire carrying current in magnetic field
- 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 = AB cosx
- 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
- In some positions, the induced EMF is zero because the coil is not cutting any lines of magnetic fliux
- 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
- Coil Position
- 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
- Due to sinusoidal variation of pd the rms pd (Vrms) is: Vrms = (Vo)/ root 2
- 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
- the VOLTS/DIV tells you the height 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
- Magnetic Flux
- 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
- To work out which radiation was emitted from a source, place different materials between the source and the detector
- 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
- 5 sources of background rdiation
- 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
- Radioactivity is an entirely random process and depends purely on the number of radioactive nuclei present
- 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
- Gamma emitter used to sterilise medical equipment and food
- Ionising radiation
- 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
- To lose mass you can annihalate matter and antimatter
- 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
- They bombarded a lithium nuclei with protons and obtained two helium nuclei and lots of energy
- 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
- Control rods
- The fission reaction of Uranium produces three extra neutrons
- E=mc^2
- Capacitance
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