 # A Level Physics M6 Particles and Medical Physics Detailed Spec

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:

1. ultrasound; longitudinal wave with frequency greater than 20 kHz

2. piezoelectric effect; ultrasound transducer as a device that emits and receives ultrasound

3. ultrasound A-scan and B-scan

4. acoustic impedance of a medium; Z = ρc

5. reflection of ultrasound at a boundary

6. impedance (acoustic) matching; special gel used in ultrasound scanning

7. Doppler effect in ultrasound; speed of blood in the patient;

8. Δf/f = 2vCosθ/c for determining the speed v of blood.