#### 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 = ½Q^{2}/C and W = ½CV^{2} - 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 = x
_{0}e^{ –t/CR}and x = x_{0}(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/4πε
_{0}r^{2}for the force between two point charges - electric field strength E = Q/4 πε
_{0}r^{2}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= ε
_{0}A/d; C= εA/d; ε = ε_{r}ε_{0} - 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/4πε
_{0}r^{2}at a distance r from a point charge; changes in electric potential - capacitance C = 4πε
_{0}R 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/4πε
_{0}r 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; n
_{s}/n_{p}= V_{s}/V_{p}= I_{p}/I_{s}for an ideal transformer - techniques and procedures used to investigate transformers

## A Level Maths Home Study Kit

(3 Reviews) £24.99#### 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
_{z}^{A}X 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 = r
_{o}A^{⅓}where r_{o}is a constant and A is the nucleon number - mean densities of atoms and nuclei.

## A Level Maths Home Study Kit

(3 Reviews) £24.99#### 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 - (β
^{–}) decay in terms of a quark model; d → u + e^{–}+ ν - (β
^{+}) 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; λt
_{½}= ln(2) - techniques and procedures used to determine the half-life of an isotope such as protactinium
- the equations A = A
_{o}e^{–λt}and N = N_{o}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 = Δmc
^{2} - 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 = Δmc
^{2}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 = I
_{o}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.