Chapter 8 - Electric Fields - Key Points1 of 24

An electric field is created by electric charges, and can be represented by electric field lines. The strength of the field is the force acting per unit positive charge at a point in the field. E = F/Q. In a uniform field (e.g. between two charged parallel plates), the force on a charge is the same at all points. The magnitude of the electric field strength is given by: E = V/d. Coulomb’s Law states that “two point charges exert an electrical force on each other that is proportional to the product of their charges and inversely proportional to the square of the distance between them. Coulomb’s Law gives the force between two point charges or two spherical charges. The distance must be from centre to centre. The equation for Coulomb’s Law is F = Qq/4πε0r2. A point charge Q gives rise to a radial field. The electric field strength is given by the equation E = q/4πε0r2. The force between point charges and the electric field strength due to a point charge both obey the inverse square law with distance.

Chapter 9 - Magnetic Fields - Key Points3 of 24

Moving charges produce a magnetic field, this is electromagnetism. A current carrying conductor has concentric magnetic field lines. The magnetic field pattern for a solenoid resembles that of a bar magnet.· Magnetic flux density B is defined by the following equation: B = F/IL, where F is the force experienced by a current carrying conductor, I is the current in the conductor and L is the length of the conductor in the uniform magnetic field. The unit of magnetic flux density is the tesla (T). 1T = 1 NA-1m-1. The magnetic flux density is 1T when a wire carrying a current of 1A placed at right angles to the magnetic field experiences a force of 1N per metre of its length. The magnetic force on a current-carrying conductor is given by F = BIL or F = BIL sin Θ. The magnetic force on a moving charged particle is given by the equation F = BQv. For an electron the equation is F = Bev.·A charged particle entering at right angles to a uniform magnetic field describes a circular path because the magnetic force is perpendicular to the velocity. The equation for an electron travelling in a uniform magnetic field is mv2/r = Bev. The velocity of an undeflected charged particle in a region where electric and magnetic fields are at right angles is given by the equation v = E/B.

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Chapter 10 - Electromagnetic Induction - Key PointsIn a magnetic field of magnetic flux density B, the magnetic flux passing through an area A is given by Φ = BA cos Θ. The magnetic flux linking a coil of N turns is the magnetic flux linkage, NΦ = NBA cos θ. Flux and flux linkage are measured in webers (Wb). One weber is equal to one tesla metre-square. 1Wb = 1Tm2. When a conductor moves so that it cuts across a magnetic field, an e.m.f. is induced across its ends. When the magnetic flux linking a coil changes, an e.m.f. is induced in the coil. Faraday’s law states that the magnitude of the induced e.m.f. is equal to the rate of change of magnetic flux linkage. E = ΔNΦ/Δt or E = ΔNBA cos θ/Δt. Lenz’s law states that the induced current or e.m.f. is in a direction so as to produce effects which oppose the change that is producing it. In an a.c. generator, an e.m.f. is induced because the rotating coil changes the magnetic flux linking the coil. For a transformer, Vs/Vp = Ns/Np. If it is 100% efficient, then Vp Ip = Vs Is.

Chapter 11 - Capacitors - Key Points7 of 24

Capacitors are constructed from two metal sheets (“plates”) separated by an insulating material. They store charge. For a capacitor, the charge stored is directly proportional to the p.d. between the plates: Q = VC. Capacitance is the charge stored per unit of p.d. and is measured in farads. A farad is a coulomb per volt. 1F = 1CV-1. Capacitors store energy. The energy W stored at p.d. V is: W = ½ QV = ½ CV2 = ½ Q2/C. For capacitors connected in parallel and in series the combined capacitances are as follows: Parallel: Ctotal = C1 + C2 + C3 +… Series: 1/Ctotal = 1/C1 + 1/C2 + 1/C3 +… When a capacitor is discharged through a resistor, the charge, current and p.d. show an exponential decrease with time, which can be represented by equations of the form: x = x0 e-t/CR. An exponential decay graph has a constant-ratio property. The time constant is defined as the time it takes for the current, charge or p.d. to fall to 1/e of its initial value, which is about 37% of its initial value. Time constant τ = CR and is measured in seconds (s).

Chapter 12 - Atomic Structure - Key Points9 of 24

The alpha-particle scattering experiment provides evidence for the existence of a small, massive and

positively charged nucleus at the centre of the atom. Most of the mass of an atom is concentrated in its

nucleus. The nucleus consists of protons and neutrons, and is surrounded by a cloud of electrons. The

number of protons and neutrons in the nucleus of an atom is called its nucleon number, A. The number

of protons in the nucleus of an atom is called its proton number (or atomic number) Z. Isotopes are nuclei

of the same element with a different number of neutrons but the same number of protons. Different

isotopes (or nuclides, if referring to the nucleus only) can be represented by the notation AZ X, where X

is the chemical symbol for the elements.The strong nuclear force acts between nucleons, it is attractive

and very short range. The electrostatic force acts between protons in the nucleus and is balanced by the

strong force, the gravitational force between nucleons is very small. Hadrons (e.g. the neutron) are

particles that consist of quarks and hence are affected by the strong nuclear force. Leptons (e.g. the

electron) are particles that are unaffected by the strong nuclear force. All hadrons consist of quarks (up,

down, strange, charm, bottom and top) and their antiquarks. Quarks are now thought to be fundamental

particles. In all hadron interactions, the quantities of charge Q, baryon number B, strangeness S, charm,

bottomness and topness are all conserved.

Chapter 13 - Nuclear Physics - Key Points11 of 24

Nuclear reactions can be represented by balanced nuclear equations. In any such reaction, the following quantities are conserved: Proton number Z, Nucleon number A, ‘mass-energy’. In an induced nuclear fission, a heavy nucleus (e.g. Uranium-235) absorbs a neutron and splits into lighter fragments and two or more fast neutrons. In nuclear fusion, light nuclei (e.g. 21H) join to form a more massive one. In stars, high temperatures and pressure are needed to achieve this. Atomic and nuclear masses are often expressed using the unified atomic mass unit u, where 1u = 1.66 x 1027kg. Einstein’s mass-energy equation ΔE = Δmc2 relates mass charges to energy charges. The mass defect is equal to the difference between the mass of the separate nucleons and the nucleus. The binding energy of a nucleus is the minimum energy required to break up the nucleus into separate nucleons. The binding energy per nucleon indicates the relative stability of different nuclides. The variation of binding energy per nucleon shows that energy is released when light nuclei undergo fusion and when heavier nuclei undergo fission, because these processes increase the binding energy per nucleon and hence result in more stable nuclides. Fissile materials are used as fuel in nuclear power stations and in nuclear bombs. The core of a nuclear reactor contains fuel rods, control rods and a moderator. Waste materials from nuclear reactors are highly radioactive and pose a threat to the environment.

Chapter 14 - Radioactivity - Key Points13 of 24

There are three types of ionising radiation produced by radioactive substances: a-particles, β-particles

and γ-rays. The most strongly ionising, and hence the least penetrating, is a-radiation. The least strongly

ionising is γ-radiation. Because of their different charges, masses and speeds, they can be identified by

the effect of an electric or magnetic field. The weak interaction between quarks is responsible for β-

decay. There are two types of β-decay, β- and β+. In β- decay, an electron is emitted along with an

antineutrino v-bar. A down quark in the nucleus changes into an up quark. d = u + 0-1 e + v-bar. In β+

decay, a positron is emitted along with a neutrino v. An up quark in the nucleus changes into a down

quark. u = d + 01 e + v. Electrons, positrons and neutrinos are all leptons. Nuclear decay is a

spontaneous and random process. This unpredictability means that count rates tend to fluctuate, and we

have to measure average quantities. The half life t1/2 of a radioisotope is the mean time taken for half of

the active nuclei in a sample to decay. The decay constant λ is the probability that an individual nucleus

will decay per unit time interval. The decay constant and half-life are related by the equation: λt1/2 = ln 2

or λt1/2 = 0.693. We can represent the exponential decrease of a quantity by an equation of the form x =

x0e-λt, where x can be activity A, count rate R or number of undecayed nuclei N.

Chapter 15 - X-Rays - Key Points15 of 24

X-rays are short-wavelength, high frequency electromagnetic radiation, produced when electrons are decelerated. There are three main mechanisms by which X-rays are absorbed as they pass through matter the photoelectric effect, Compton scattering and pair production. The intensity of an X-ray beam is the power transmitted per unit cross-sectional area. The intensity of a collimated X-ray beam decreases exponentially according to the equation I = Ioe-μx, where μ is

the attenuation coefficient of the medium. μ has units m-1 (or cm-1 or mm-1). X-ray images can be improved using image intensifiers and contrast media (such as barium or iodine). A computer axial tomography scanner (CAT scanner) produces three-dimensional X-ray images of a patient.

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Chapter 16 - Diagnostic Methods in Medicine - KeyPoints

Medical tracers such as technetium-99m are used to diagnose the function of organs. A gamma camera detects gamma radiation coming from the medical tracer in the body and deduces its position. The main components of a gamma camera are: collimator, scintillator crystal, photomultiplier tubes and computer. In PET scanning, a β+ emitter is used as a tracer; γ-rays produced as the positrons annihilate with electrons are used to determine the position of the tracer. In MRI scanning, spinning, precessing protons are forced to resonate using radio frequency pulses. RF radiation from relaxing protons is used to obtain diagnostic information about internal organs, particularly soft tissues. The main components of an MRI scanner are: superconducting magnet, RF transmitter coil, RF receiver coil, set of gradient coils and computer.

Chapter 17 - Using Ultrasound in Medicine - KeyPoints

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Ultrasound is a longitudinal mechanical wave with a frequency greater than 20kHz. Ultrasound transducers use the piezoelectric effect to generate and detect ultrasound waves. The acoustic impedance Z of a material depends on its density ρ and the speed c of sound: Z = ρc. The fraction of the intensity of an ultrasound wave reflected at a boundary is given by: Ir/I0 = (Z2 - Z1)2/(Z2 + Z1)2 or Ir/I0 = ((Z2 – Z1)/( Z2 + Z1)2). To transfer a high proportion of the intensity of an ultrasound pulse into the patient’s body, an impedance-matching gel must be used with acoustic impedance almost the same as that of the skin. In ultrasound scanning, an A-scan uses a single pulse to determine the depth and nature of reflecting surfaces. A B-scan builds up a two-dimensional image from multiple A-scans. In the Doppler effect, the wavelength and frequency of a wave are altered on reflection by a moving surface. The frequency of a wave decreases for a receding source and increases for an approaching source. The Doppler effect can be used to determine the speed of blood in arteries.

Chapter 18 - The Nature of the Universe21 of 24

The cosmological principle suggests that the Universe is uniform, there are no “special places” in the universe. This principle is based on a universe that is homogeneous and isotropic and in which the laws of physics are universal. The universe contains matter in the form of stars, clustered into galaxies, and electromagnetic radiation. The solar system consists of the Sun and all the objects (planets, comets etc.) held in its gravitational field. Stars form when clouds of interstellar gas and dust contract under the pull of their own gravity. The Sun will evolve to become a red giant and then a planetary nebula and a white dwarf. A more massive star will become a super red giant and then a supernova and either a neutron star or a black hole, depending on its initial mass. Astronomical distances may be measured in astronomical units (AU), light years (ly) or parsecs (pc). 1 AU = 1.5 x 1011m, 1 ly = 9.5 x 1015m, 1 pc = 3.1 x 1016m. Olber’s paradox : For an infinite, uniform and static universe, the night sky should be bright because of light received in all directions from stars. (The paradox is resolved because the universe is neither static nor infinite.) Redshift is related to speed of recession by the Doppler equation: Δλ/λ = v/c. Hubble’s law: speed of recession of a galaxy α distance of galaxy. An equation for Hubble’s law is: v = H0x. The age of the Universe is related to the Hubble constant H0 by the equation: Age = 1/H0. The SI unit for the Hubble constant is s-1.

Chapter 19 - The Evolution of the Universe - KeyPoints

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The standard (hot Big Bang) model of the universe suggests the universe has a finite age. Since the Big Bang, the universe has expanded and cooled, so that matter and radiation have gradually separated and matter has coalesced. Evidence for the Big Bang comes from the cosmic microwave background radiation whose current temperature is about 2.7K. The universe may be open, flat or closed, depending on its density relative to the critical density. The critical density is given by the equation: ρ0 = 3H02 / 8πG. The density of the universe is close to (and may be exactly equal to) the critical value, so that our universe may be flat.