Physics H556, from September 2015, examined in 2017

Module 6: Physics A level, Particles and medical physics revision

Capacitors, electric field, electromagnetism, nuclear physics, particle physics and medical imaging.



6.1 Capacitors

Capacitors, use in electrical circuits as a source of electrical energy. The mathematics of exponential decay.

You will cover:

  • capacitance; C = Q/V; the unit farad
  • charging and discharging of a capacitor or capacitor plates with reference to the flow of electrons
  • total capacitance of two or more capacitors in series; 1/C = 1/C1 + 1/C2 ....
  • total capacitance of two or more capacitors in parallel; C = C1 + C2 + ...
  • analysis of circuits containing capacitors, including resistors
  • investigation of capacitors in both series and parallel combinations using ammeters and voltmeters
Energy

You will cover:

  • p.d. - charge graph for a capacitor; energy stored is area under graph
  • energy stored by capacitor;
    W = ½QV,  W = ½Q2/C and W = ½CV2
  • uses of capacitors as storage of energy.
Charging and discharging capacitors

You will cover:

  • Charging and discharging capacitors a resistor
  • techniques and procedures to investigate the charge and the discharge of a capacitor using both meters and data-loggers
  • time constant of a capacitor-resistor circuit; τ = CR
  • equations of the form x = x0 e –t/CR and x = x0(I – e –t/CR) for capacitor-resistor circuits
  • using lnx-t graphs can be used to determine CR.
  • graphical methods and spreadsheet modelling of the equation ΔQ/Δt = –Q/CR for a discharging capacitor
  • exponential decay graph; constant-ratio property of such a graph.
6.2 Electric fields

Coulomb's law, uniform electric fields, electric potential and energy.

Point and spherical charges

You will cover:

  • electric fields are due to charges
  • modelling a uniformly charged sphere as a point charge at its centre
  • electric field lines to map electric fields
  • electric field strength; E = F/Q
Coulomb's law

You will cover:

  • Coulomb's law; F = Qq/4πε0r2 for the force between two point charges
  • electric field strength E = Q/4 πε0r2 for a point charge
  • similarities and differences between the gravitational field of a point mass and the electric field of a point charge
  • the concept of electric fields as being one of a number of forms of field giving rise to a force.
Uniform electric field

You will cover:

  • uniform electric field strength; E = V/d
  • parallel plate capacitor; permittivity; C= ε0A/d; C= εA/d; ε = εr ε0
  • motion of charged particles in a uniform electric field.
Electric potential and energy

You will cover:

  • bringing unit charge from infinity to the point; electric potential is zero at infinity
  • electric potential V = Q/4πε0r2 at a distance r from a point charge; changes in electric potential
  • capacitance C = 4πε0R for an isolated sphere
  • Derivation expected from equation for electric potential and Q = VC.
  • force-distance graph for a point or spherical charge; work done is area under graph
  • electric potential energy E = Vq = Qq/4πε0r at a distance r from a point charge Q
6.3 Electromagnetism

Magnetic fields, motion of charged particles in magnetic fields, Lenz's law and Faraday's law.

Magnetic fields

You will cover:

  • magnetic fields are due to moving charges or permanent magnets
  • magnetic field lines to map magnetic fields
  • magnetic field patterns for a long straight currentcarrying conductor, a flat coil and a long solenoid
  • Fleming's left-hand rule
  • force on a current-carrying conductor; F = BIL sin θ
  • determine the uniform magnetic flux density between the poles of a magnet using a current-carrying wire and digital balance
  • magnetic flux density; the unit tesla.
Motion of charged particles

You will cover:

  • angles to a uniform magnetic field; F = BQv
  • charged particles moving in a uniform magnetic field; circular orbits of charged particles in a uniform magnetic field
  • charged particles moving in a region occupied by both electric and magnetic fields; velocity selector
Electromagnetism

You will cover:

  • magnetic flux Φ; the unit weber; Φ = BAcosθ
  • magnetic flux linkage
  • Faraday's law of electromagnetic induction and Lenz's law
  • e.m.f. = - rate of change of magnetic flux linkage; ε = – Δ(NΦ)/ Δt
  • techniques and procedures used to investigate magnetic flux using search coils
  • simple a.c. generator
  • simple laminated iron-cored transformer; ns/np = Vs/Vp = Ip/Is for an ideal transformer
  • techniques and procedures used to investigate transformers
6.4 Nuclear and particle physics

Atom, nucleus, fundamental particles, radioactivity, fission and fusion and nuclear power

The nuclear atom

You will cover:

  • a small charged nucleus
  • simple nuclear model of the atom; protons, neutrons and electrons
  • relative sizes of atom and nucleus
  • proton number; nucleon number; isotopes; notation zAX for the representation of nuclei
  • strong nuclear force; short-range nature of the force; attractive to about 3 fm and repulsive below about 0.5 fm 1 fm = 10–15
  • radius of nuclei; R = roA where ro is a constant and A is the nucleon number
  • mean densities of atoms and nuclei.
Fundamental particles

You will cover:

  • particles and antiparticles; electron-positron, proton-antiproton, neutron-antineutron and neutrino-antineutrino
  • particle and its corresponding antiparticle have same mass; electron and positron have opposite charge; proton and antiproton have opposite charge
  • classification of hadrons; proton and neutron as examples of hadrons; all hadrons are subject to the strong nuclear force
  • classification of leptons; electron and neutrino as examples of leptons; all leptons are subject to the weak nuclear force
  • simple quark model of hadrons in terms of up (u), down (d) and strange (s) quarks and their respective anti-quarks
  • quark model of the proton (uud) and the neutron (udd)
  • charges of the up (u), down (d), strange (s), anti-up u̅ , anti-down d̅ and the anti-strange s̅ quarks as fractions of the elementary charge e
  • beta-minus (β) decay; beta-plus (β+) decay
  • ) decay in terms of a quark model; d → u + e- + ν
  • +) decay in terms of a quark model; u → d + e- + ν̅
  • balancing of quark transformation equations in terms of charge
  • decay of particles in terms of the quark model.
Radioactivity

You will cover:

  • radioactive decay; spontaneous and random nature of decay
  • α-particles, β-particles and γ-rays; nature, penetration and range of these radiations
  • techniques and procedures used to investigate the absorption of α--particles, β-particles and γ--rays by appropriate materials
  • nuclear decay equations for alpha, beta-minus and beta-plus decays; balancing nuclear transformation equations
  • activity of a source; decay constant λ of an isotope; A = λN
  • half-life of an isotope; λt½ = ln(2)
  • techniques and procedures used to determine the half-life of an isotope such as protactinium
  • the equations A = Ao e–λt and N = No e–λt where A is the activity and N is the number of undecayed nuclei
  • simulation of radioactive decay using dice
  • graphical methods and spreadsheet modelling of the equation ΔN/Δt = –λNfor radioactive decay
  • radioactive dating, e.g. carbon-dating
Nuclear fission and fusion

You will cover:

  • Einstein's mass-energy equation; ΔE = Δmc2
  • energy released (or absorbed) in simple nuclear reactions
  • creation and annihilation of particle-antiparticle pairs
  • mass defect; binding energy; binding energy per nucleon
  • binding energy per nucleon against nucleon number curve; energy changes in reactions
  • binding energy of nuclei using ΔE = Δmc2 and masses of nuclei
  • induced nuclear fission; chain reaction
  • basic structure of a fission reactor; components - fuel rods, control rods and moderator
  • environmental impact of nuclear waste
  • nuclear fusion; fusion reactions and temperature
  • balancing nuclear transformation equations
6.5 Medical imaging

Non-invasive techniques: X-rays, CAT scans, PET scans and ultrasound scans.

Using X-rays

You will cover:

  • basic structure of an X-ray tube; components - heater (cathode), anode, target metal and high voltage supply
  • production of X-ray photons from an X-ray tube
  • X-ray attenuation mechanisms; simple scatter, photoelectric effect, Compton effect and pair production
  • attenuation of X-rays; I = Io e–μx , where μ is the attenuation (absorption) coefficient
  • X-ray imaging with contrast media; barium and iodine
  • computerised axial tomography (CAT) scanning; components - rotating X-tube producing a thin fan-shaped X-ray beam, ring of detectors, computer software and display
  • advantages of a CAT scan over an X-ray image
Diagnostic methods in medicine

You will cover:

  • medical tracers; technetium-99m and fluorine-18
  • gamma camera; components - collimator, scintillator, photomultiplier tubes, computer and display; formation of image
  • diagnosis using gamma camera
  • positron emission tomography (PET) scanner; annihilation of positron-electron pairs; formation of image
  • diagnosis using PET scanning
Using ultrasound

You will cover:

  • ultrasound; longitudinal wave with frequency greater than 20 kHz
  • piezoelectric effect; ultrasound transducer as a device that emits and receives ultrasound
  • ultrasound A-scan and B-scan
  • acoustic impedance of a medium; Z = ρc
  • reflection of ultrasound at a boundary
    z impedance
  • impedance (acoustic) matching; special gel used in ultrasound scanning
  • Doppler effect in ultrasound; speed of blood in the patient;
    Δf/f = 2vCosθ/c for determining the speed v of blood.

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