Electric Field Strength, E
The force per unit positive charge = F / Q
Magnitude of the uniform electric field strength between charged parallel plates, E =
V / d (known as Potential Gradient)
Magnetic Flux Density, B
F = BILsin ?
One Tesla, T
the magnetic flux density when a wire of length one metre carrying a current of one Ampere at a right angle to the field experiences a force of one Newton
Force on moving charge in a uniform magnetic field, F =
BQv sin ?
Electric Fields
Are created by electric charges
Electric Field Lines
Go from positive to negative charges, the closer the lines, the stronger the field
Coulomb's Law
Gives the force between two electric charges
E = Q / (4???r�)
Gives the electric field strength of a point charge
A uniform electric field
Causes charged particles to accelerate and move across the field due to the force = Eq
Electric Fields / Grav Fields
In an Electric Field the force acts in the direction of the field for positive charges only, gravitational forces always act in the direction of the field
Magnetic flux density, B
Is defined by B = F/ILsin?
Tesla
The magnetic flux density when a wire of length 1 metre, carrying a current of 1 Ampere at a right angle to the field experiences a force of 1 Newton
F = BILsin?
The force on a wire of length L carrying a current I at an angle ? to the field
F = BQv
The force on a charged particle travelling at right angles to a uniform magnetic field
Magnetic Flux
The product of the magnetic flux density and area at right angles to the flux
Weber
The magnetic flux when a magnetic field of magnetic flux density one Tesla passes at right angles through an area of 1 m�
Magnetic Flux, ? = BAcos?
where ? is the angle between the plane of the area and the projection surface
Magnetic flux linkage for a coil
The magnetic flux through the coil multiplied by the number of turns
Faraday's law of electromagnetic induction
The magnitude of the induced emf is equal to the rate at which magnetic flux is cut
Lenz's law
The direction of an induced current is in a direction that opposes the flux change that causes it
induced emf =
- rate of change of magnetic flux linkage
Turns-ratio equation
Ns / Np = r = Es / Ep
Capacitance
The charge stored per unit potential difference
Farad (F)
One coulomb per volt
Capacitance, C =
Q / V
Energy Stored by a charged capicator, W =
�QV = �CV� = Q / 2C
For Capacitors in Parallel
C = C? + C? + ...
For Capacitors in Series
1 / C = 1 / C? + 1 / C? + ...
Area under a potential difference against charge graph
is equal to energy stored by a capacitor
Time constant of a circuit
The product of the capacitance and resistance
Time Constant =
CR
Nucleon
A nuclear particle, either a proton or neutron
Nucleon number, A
The number of nucleons in any nucleus
Proton number, Z
The number of protons in a nucleus
Isotopes
Two nuclides with the same number of protons but different numbers of neutrons
?? particle
An electron
?? particle
A positron
Leptons
A group of particles including electrons and neutrinos
Activity, A
The rate at which a source emits radioactive particles
Becquerel, Bq
An activity of one particle emitted per second
Decay Constant, ?
Relates activity A to the number of nuclie N by the equation A = ?N
Half-life
The time taken for the activity of a radioactive source to decrease by one half. Also the time taken for the number of radioactive nuclei to decrease by one half
Binding energy
the energy required to separate an atom into its constituent parts
1 Astronomical Unit, AU
1.496 x 10�� m
1 Parsec, pc
3.086 x 10�? m
1 Light Year, ly
9.461 x 10�? m
Hubble's Law
the speed of the recession of a galaxy is directly proportional to its distance from the Earth
Cosmological Principle
on a large scale the universe is uniform. The universe is isotropic (the same in all directions) and homogeneous (of uniform density) as long as a large enough volume is used.
In a nuclear decay reaction
Mass/energy, momentum and charge are conserved
Protons and Neutrons are not fundamental particles
since they contain charged constituents called quarks
Baryons
Group of particles including protons and neutrons
Antiparticle
Opposite in charge to the particle but have the same mass and other properties
Hadrons
Baryons, mesons and their antiparticles. Influenced by the Strong Nuclear Force
Einstein's mass-energy equation
?E = ?mc2
Binding energy per nucleon
The binding energy for an atom divided by the number of nucleons that need to be seperated
Binding energy per nucleon against nucleon number graph
Shows that nuclei with low nucleon number and those with high nucleon number have smaller binding energy per nucleon than those nuclei with a nucleon number around 55
The nature of X-rays
Short wavelength electromagnetic radiation
Energy of an X-ray photon
Emax = hf = eV
X-ray absorption (of a collimated beam)
I = I?e^?�x
Attenuation Coefficient, �
Coefficient for the medium through which the X-rays are passing
Intensity of X-rays produced from a point source
Obeys an inverse square law
Intensity of a parallel (collimated) beam of X-rays
remains constant
The fraction of related intensity
Ir / I? = (Z? - Z?)� / (Z? + Z?)�
Acoustic Impedance, Z =
density of material x speed of sound in material = ?c
Impedance matching
The need to match up similar impedances to get good transmission/reflection values
A gel is required for effective ultrasound imaging techniques
A high proportion of incident ultrasound is reflected when ultrasound passes between two very different materials, so if a gel was not used then most of the ultrasound would be reflected and never enter the body.
? t?/? =
ln 2 = 0.693
A = A?e^-?t and N = N?e^-?t
Where A is the activity and N is the number of undecayed nuclei. (Since A is directly proportional to N)
Radioactive decay of unstable nuclei
is spontaneous and random in nature
?-particles
Helium Nucleus (2 protons + 2 neutrons) Range: few centimetres in air. Penetration: Stopped by paper
?-particles
Electron Range: Several metres in air. Penetration: Stopped by 2-3mm Aluminium sheet
?-rays
Electromagnetic Radiation Range: Very Far in air. Penetration: Stopped by several cm of lead, steel or concrete
Similarities and differences between the decay of radioactive nuclei and decay of charge on a capacitor in a C-R circuit
Both exponential equations but the constants are entered differently: Radioactive decay, decay constant ? is used, whereas for Capacitor Discharge 1 / CR is the constant used.
The use of radioactive isotopes in smoke alarms
Ionisation chamber contains a very small ?-emitter. The source causes ionisation and the battery causes a very small ionisation current through the chamber. If smoke particles enter the chamber, they are charged by the ions, reducing the ionisation curren
The technique of radioactive dating
Carbon Dating: Whilst alive, trees absorb a small amount of Carbon-14. After the tree dies, the Carbon-14 in the wood undergoes radioactive decay, the ratio of Carbon-14 to Carbon-12 decreases with time. The count rate is measured or the amount of Carbon-
Mass-energy equivalence:
1 u = 931 MeV
How to Determine the binding energy of nuclei
?E = ?mc� = relative atomic mass x u x 931
How X-rays are produced
High voltage, vacuum with anode and cathode, electrons from negative cathode are accelerated towards anode. If they have enough energy when they hit the anode then X-rays will be emitted. Energy of X-rays ? 1% of energy of electron beam, most of energy he
X-ray Interaction - Photoelectric Effect
X-rays cause emissions of photoelectrons from a metal, photoelectrons have max KE equal to photon energy of X-rays.
X-ray Interaction - Pair Production
In a beam of high frequency X-rays it is possible for a photon of X-rays to collide with a particle and spontaneously produce a positron and an electron. Min X-ray photon energy = 1.02 MeV
X-ray Interaction - Compton Effect
X-ray photon collides with an electron in an atom, greater the angle of deflection, the more energy the photon will have lost so the wavelength will be longer
Function of a simple a.c. generator
Rectangular coil is rotated in a constant magnetic field. Produces a sine wave shaped alternating current in any connected resistor. Also works with rotating magnets inside fixed coils
When a rotating coil is vertical in a mag field
No emf is generated
When a rotating coil is horizontal in a mag field
generated emf is max
Function of a simple transformer
2 insulated coils wound around an easily magnetised iron core. AC in primary coil causes iron core to become magnetised and re-magnetised. Causes a rapid change in magnetic flux through the secondary coil. By Faraday's Law, induced emf = rate of change of
Step-up and step-down transformers
Are used to change the voltage of electricity from very high values (200 000 V) to mains voltage (230 V)
magnetic field patterns of a long straight current-carrying conductor
Field circling the wire, decreasing in strength, clockwise if current is away from you
magnetic field patterns of a long solenoid (coil of wire)
Field through the coil then out and round. Right to left if current at top is towards you
charged particles moving in a plane perpendicular to a uniform magnetic field
move in circular orbits due to the magnetic force and the centripetal acceleration it causes
Charged particles in both electric and magnetic fields
A velocity selector can be used, where a magnetic field overlaps with an electric field in the opposite direction. A charged particle will undergo a force in both directions (QE for e-fields and BQv for mag-fields) and accelerate in the direction where th
mass spectrometer
A fine beam of ions with the same velocity enter a mag field and travel in a circular path. My measuring the radius the mass can be obtained (F = BQv = mv�/r)
exponential decays
have a constant-ratio property: any given time interval results in the same percentage decrease, the time taken to halve is always the same
x = x? e?^(t/CR)
Equation for capacitor discharge, used for Q, I and V
variation with time of potential difference, charge and current for a capacitor discharging through a resistor
Follows an exponential decay
uses of capacitors
storage of energy in applications such as flash photography, lasers used in nuclear fusion, and as backup power supplies for computers.
properties of ultrasound
High frequency inaudible sound waves (? 2MHz), non-ionising, can distinguish between muscle and blood. High intensity ultrasound can be destructive.
Doppler effect
Change in wavelength caused by the relative motion between a wave source and observer
piezoelectric effect
Alternative method of producing sound: When certain crystals have a pd applied to them, they contract a little. When a high frequency AC pd is applied, the crystals oscillate at the frequency of the signal and produce ultrasound waves. The crystal can als
how ultrasound transducers emit and receive high-frequency sound
A piezoelectric crystal acts as a transmitter and receiver of ultrasound. A curved faceplate is used to shape the ultrasound waves into a narrow beam
principles of ultrasound scanning
Ultrasound waves are reflected at a boundary between mediums, a pulse of ultrasound enters the body, a proportion of the x-ray is reflected at a boundary and the echo is detected
Pulse repetition frequency
Transducer must not be transmitting, whilst waiting for a reflected x-ray to be received. There is a maximum frequency for pulses so that no interference occurs.
A-scan
Produces a graph showing reflected intensity that is detected. Can be used to determined measurements
B-scan
An array of transducers is used to produce an image. Most commonly used for fetal scans
How the Doppler effect can be used to determine the speed of blood
The frequency of the reflected pulse. If blood us flowing towards the source then the reflected wave will have a higher frequency than the transmitted wave
Advantages of MRI
No ionising radiation, high quality image produced, distinguishes between different types of soft tissue, not stopped by bone, no known side effects
Disadvantages of MRI
If metal objects are scanned then they heat up, no other radio waves must enter the equipment, equipment is expensive, slow throughput
Non-invasive techniques in diagnosis
A procedure with no adverse effects for the patient, ie. no ionising radiation
Intensity of a beam of X-rays
Power per unit cross-sectional area