Longman Physics for CXC

GLOSSARY OF PHYSICS TERMS

SECTION A: PHYSICAL MEASUREMENTS AND UNITS

Chapter 2: NUMBERS AND UNITS

Fundamental quantitiesTaken to be mass, length, time, electric current and temperature. The size of their unit is arbitrary (e.g.for mass there is a standard kilogram of matter). All other quantities are then derived from those five.[Page 3]

S.I. unitsStands for Système International, in which the fundamental units are: mass, the kilogram (kg); length,the metre (m); time, the second (s); electric current, the ampere (A) - see Chapter 38; and temperature,the Kelvin (K) - see Chapter 21.[Page 3]

Unit prefixesInclude mega- (M-, a million, x 106); kilo (k-, a thousand, x 103); centi- (c-, one hundredth of, x 10-2);milli- (m-, one thousandth of, x 10-3); and micro- (µ-, one millionth of, x 10-6).[Page 4]

LitreA unit of volume: 1000 cm3. Thus 1 millilitre (1 ml) is the same as 1 cm3.[Page 5]

TonneA unit of mass: 1000 kg.[Page 5]

Standard formIn physics the way we often write numbers that are very large or very small. Thus a distance of 320000 metres would be written 3.2 x 105 m. The first number is made to be between one and ten, then inthis case we say that you must multiply that figure by ten a total of five times (i.e., move the decimalpoint five places to the right).Similarly 3.2 x 10-4 m indicates a distance of only 0.00032 m: this time you divide the 3.2 by ten fourtimes (thus moving the decimal point four places to the left).[Page 5]

Chapter 3: MASS AND VOLUME

DensityGiven the symbol ? (‘rho’). A property of a substance (e.g. water or aluminium or air). The density ofa substance is defined as its mass per unit volume. Thus ? = M/V. The S.I. units will be kg m-3, butwe sometimes use g cm-3.Water has a density of 1000 kg m-3 ( 1 g cm-3).[Page 10]

Relative densityThe relative density of a substance states how its density compares with water. Thus mercury has arelative density of 13.6, meaning that it is 13.6 times as dense as water (and so must have a density of13 600 kg m-3, 13.6 g cm-3). It is just a number, with no units.Relative density is defined as (the density of the substance) / (the density of water).[Page 11]

Chapter 4: TAKING MEASUREMENTS

Random errorsIf you measure a length correctly to (say) the nearest millimetre, your reading may be anything up tohalf a millimetre out. This is because the actual length will not be precisely a whole number ofmillimetres, and it will be pure chance whether your reading is really a bit too high or too low.If you find the density of aluminium by taking measurements on a large number of different-sizedblocks of the metal, working out the average of all your results will tend to cancel out the effect ofthese errors.[Page 14]

Check readingsIn any practical work, you should take AND RECORD check readings whenever you can. If there is abig discrepancy between them, that suggests you have made a mistake in one of the measurements – inwhich case take a further check reading to discover which one to eliminate. If there is acceptableagreement, take as your measurement their average.[Page 14]

Parallax errorsMistakes made in reading instruments if you do not place your eye perpendicular to the point on thescale where the reading occurs. An example where parallax presents a big problem is when you try tomeasure the diameter of a ball with a ruler: because the edge of the ball is closer to you than the ruler,moving your eye will cause the alignment of the edge with the scale to change.[Page 15]

Digital scalesAn instrument with a digital scale displays its reading in the form of a number, as with a digital watch.It has obtained that number by a process of counting.[Page 18]

Chapter 5: COMING TO CONCLUSIONS

Systematic errorsThese are errors in practical work which always make your result too high, or always make it too low.No amount of repeating and averaging will eliminate them. A spring balance with a spring whichstretches too readily will always give readings for weights which are too high, for example, and airresistance always gives a low value for g obtained from objects which are dropping.[Page 21]

Independent variableWhen you investigate the relationship between a pair of quantities, this is the one whose size you arefree to fix at a series of convenient values. Thus if you are finding how the length of a pendulumaffects its time of swing, you would choose a set of different lengths. Such an independent variable isusually plotted along the x-axis of a graph.[Page 24]

Dependent variableIn the example of the previous entry, you have chosen the length of the pendulum: you must then seewhat time of swing that length gives. Here the time is the dependent variable. We usually plot itupwards on the y-axis of our graph.[Page 24]

Best fit lineApplies to graphs in physics which are obtained by plotting experimentally obtained values. We useour judgement to draw the straight line or smooth curve suggested by those points. It need not passthrough any of the points themselves, so long as they are arranged evenly on either side of the line.[Page 22]

Gradient

Also called the slope of a graph. It is the change in one quantity divided by the corresponding changein the other quantity.[Page 25]

SECTION B: MECHANICS

Chapter 6: FORCES

ForceA push or pull. A single force acting on an object will change its motion - speed it up, slow it down orcause it to go in a different direction. A pair of balanced forces acting in opposite directions on anobject will change its size or shape. The unit of force is the Newton (N) - see Chapter 14.[Page 28]

WeightThe weight of a body is the force of attraction between it and the earth, due to gravity. Like allother kinds of force, it is measured in newtons.The strength of the earth’s gravity at its surface is given by g = 10 N kg-1 approximately. The weightW of a mass m (in kilograms) is given by W = mg.[Page 28]

Hooke’s lawThe extension of a spring is proportional to its load. This behaviour applies until the elastic limit ofthe spring has been reached: if loaded beyond that, Hooke’s law no longer correctly predicts theextension and when the load is removed the spring may not return to its original unstretched length.[Page 29]

Chapter 7: TWISTS AND TURNS

FulcrumThis is the name we give to the pivot of a lever system.[Page 32]

MomentThe moment of a force is defined as the force multiplied by the perpendicular distance at which itacts from the fulcrum. Units are Nm (newtons multiplied by metres). In effect it is a measure of theturning effect of the force about the pivot.[Page 32]

Principle of momentsIf a pivoted bar is in a state of balance, all the clockwise moments about the fulcrum addedtogether must exactly equal all the anticlockwise moments.[Page 34]

Equilibrium‘In equilibrium’ means balanced. For a body to be in a state of equilibrium, two conditions must besatisfied: (1) the moments about any pivot must cancel, as stated in the principle of moments; and (2)all the forces in any direction must cancel as well.[Page 37]

Centre of gravityThe centre of gravity of a body is defined as the point at which all the weight of the body may beconsidered to act.[Page 35]

Chapter 8: WORK AND ENERGY

Work

You do work whenever you move a distance exerting a force. Work is defined as the size of the forcebeing exerted multiplied by the distance you move in the direction of that force. Units of work arenewton metres, called joules (J).[Page 40]

EnergyEnergy is needed to perform work. Energy is measured in joules: to do 50 J of work, 50 J of energymust be supplied.[Page 41]

Conservation of energyEnergy cannot be created, nor can it be destroyed; it can only be converted from one form toanother. Thus in the example of the previous entry, the 50 J of energy which must be supplied to dothe work does not just disappear: instead it appears in a different form.[Page 41]

Forms of energyThese include kinetic energy (see below), potential energy (see below), thermal energy, sound,electrical energy, electromagnetic energy (which means light and the other members of that family ofwaves - see Chapter 28), chemical energy and nuclear energy.[Page 41]

Kinetic energyThis is the energy possessed by a body by virtue of its motion. The kinetic energy Ek in joules of abody of mass m kg moving at a speed of v m s-1 is given by Ek = ½.mv2.[Page 42]

Potential energyThis is the energy possessed by a body by virtue of its state or position.Elastic potential energy is stored in a spring which is compressed or stretched: it represents the workdone in deforming the spring, and is energy which will be released as the spring returns to its originallength.Gravitational potential energy is stored in a body which is lifted up: it represents the work done inraising it, and is energy which will be released as the body falls back to ground level. If a mass m kg israised through a height ?h in metres, the extra gravitational potential energy ?Ep in joules it possessesis given by ?Ep = mg. ?h.[Page 43]

Energy sources, renewableRenewable energy sources are those derived directly from the sun - for example: solar power, windpower, wave power. These do not run out because the sun continually creates more energy of that type.[Page 44]

Energy sources, non-renewableThese include oil, natural gas and coal. The chemical energy they contain has come from the sun, butover a time scale which is vast compared to a human life-time. If we use it up, therefore, there is nomore available.[Page 44]

Chapter 9: DOING A JOB OF WORK

MachineIn a physics sense a machine is a device which has an input, where you do a job of work by exerting aforce through a distance. At the output a different sized force is exerted over a different distance, oftenin a different direction. The purpose of most machines is to magnify your applied force (e.g. a pulleysystem). Occasionally, however, the aim is to accept a smaller force which then acts through a largerdistance in a given time (e.g. the bicycle).[Pages 47, 51]

Efficiency

With a machine which is perfectly efficient, if you input 100 J of energy it will all end up doing the jobof work at the output. Efficiency is defined as (useful work done by the machine) divided by (totalenergy put into it) x 100%.[Page 49]

PowerPower is defined as the rate at which work is being done, or the rate at which energy is beingsupplied. The units are joules per second (J s-1), called watts (W).If E represents the energy supplied or the work done (both are measured in joules) in a time t seconds,then the power P developed in watts is given by: P = E / t.[Page 51]

Chapter 10: PRESSURE

PressureThe pressure on a surface is defined as the force per unit area. The units are newtons per squaremetre (N m-2), usually called pascals (Pa).If a total force of F newtons is spread evenly over a surface of area A m2, then the pressure P in pascalsis given by P = F / A.[Page 54]

Pressure within a liquidShows itself as a force which presses normally (i.e., at right angles) against any surface. At a givendepth in a liquid the pressure everywhere is the same. It is caused by the weight of the liquid abovepushing down, so the pressure increases with the depth and with the density of the liquid.[Page 55]

If you descend a depth ?h metres beneath the surface of a liquid whose density is ? kg m-3, the extrapressure ?P in pascals due to the liquid is given by ?P = ?g. ?h.[Page 56]

Chapter 11: MORE ABOUT PRESSURE

Archimedes’ PrincipleIf a body is totally or partially immersed in a fluid, it will experience an upthrust which is equalin magnitude to the weight of the fluid it has displaced.[Page 59]

Chapter 12: TIMINGS AND JOURNEYS

PeriodFor a pendulum this is the time taken for one complete swing. By one swing, we mean that thependulum goes through the centre position to one extreme, goes all the way to the opposite extreme,then gets back to the centre position MOVING IN THE SAME DIRECTION AS AT THE START.See also Section D, chapter 32.[Page 68]

DisplacementDisplacement is a vector quantity (see chapter 13). It is represented by an arrow whose start is at thepoint where a journey begins and whose tip is where that journey ends. Its magnitude may bemeasured in metres.[Page 70]

SpeedRate of change of distance, measured in m s-1. A scalar quantity (see chapter 13).[Page 70]

Average speedThe total distance travelled divided by the total time taken. If the instantaneous value of the speed isnot constant, sometimes it will be greater than the average speed and sometimes less.[Page 70]

VelocityA vector quantity. It is speed in a specified direction. Velocity is rate of change of displacement.[Page 70]

AccelerationIt is the rate at which velocity is changing. Acceleration is (CHANGE in velocity) divided by (timetaken). The units are m s-2.[Page 70]

Displacement-time graphThe slope (gradient) of the graph represents the velocity.[Page 71]

Velocity-time graphThe slope gives the acceleration. The area under the graph indicates the total displacement (the totaldistance travelled if the motion is in a straight line).[Page 72]

Chapter 13: THE WAY FORCES ADD UP

Scalar quantityScalar quantities have magnitude but no direction. They obey addition of the ‘two plus two equalsfour’ type. Examples include mass, volume and energy.[Pages 76, 79]

Vector quantityVector quantities have direction as well as magnitude. They add by the parallelogram law (see below).Examples include force, displacement and velocity.[Pages 76, 79]

Parallelogram lawRepresent each vector by an arrow whose direction is the same as that of the vector, and whose lengthis proportional to the magnitude of the vector. To add the two vectors, draw the arrows pointingoutwards from a common point P. Complete the parallelogram of which the arrows form two sides.Then the diagonal which starts from point P represents the resultant in both direction and magnitude.[Page 79]

ResultantThe single vector obtained when you add two or more vectors.[Page 78]

Newton’s First Law of MotionA body at rest will stay at rest, and a body that is moving will continue to travel at a constantspeed in a straight line, if no resultant force acts on it.[Page 81]

Chapter 14: WHEN A FORCE ACTS

The newtonOne newton is that force which will cause a body of mass 1 kg to accelerate at a rate of 1 m s-2.[Page 84]

Newton’s Second Law of Motion (simple form – for the full statement see Chapter 15)

If a resultant force acts on a body, it will cause that body to accelerate at a rate proportional tothe magnitude of the force. ‘Force = mass x acceleration’. Fres = ma , where a is the acceleration inm s-2 produced on a body of mass m kg by a resultant force of Fres newtons.[Pages 84, 88]

Motion in a circular pathFor a body to move in a circular path, there must be a resultant (unbalanced) force on it which actsinwards, towards the centre of the circle.[Page 89]

Chapter 15: RECOIL AND ROCKETS

Newton’s Third Law of MotionWhenever a force acts on a body, there is a different body which is experiencing a force of exactlythe same size but in the opposite direction. Any ‘Third Law’ pair of forces must satisfy theserequirements: (a) they must act on two different bodies, not both on the same one; and (b) both forcesmust be of the same sort – both gravitational, for example, or both electrical.[Page 92]

Linear momentumYou will usually see this referred to just as ‘momentum’. The linear momentum of a body is itsmass multiplied by its velocity. It is a vector quantity. Its units have no special name, so can beexpressed as kg m s-1.[Page 94]

Newton’s Second Law of Motion (full statement – for its simple form see Chapter 14)If a resultant force acts on a body, it will cause that body’s momentum to change. Themomentum change occurs in the direction of the force, at a rate proportional to the magnitude ofthat force.[Page 95]

Conservation of linear momentumIf two bodies collide or push each other apart, and no forces act except for each one pushing onthe other, then the total momentum of the two bodies cannot change.[Page 96]

SECTION C: THERMAL PHYSICS AND KINETIC THEORY

Chapter 16: HOTTER MEANS BIGGER

Thermal expansionThe increase in volume of a substance as it warms up, which means that its density decreases. Themolecules themselves do not expand – it is their distance apart which gets greater. When the substancecools, thermal contraction occurs.[Page 101]

Bi-metal stripA flat length of metal which has a different metal coated on one of the surfaces. When the temperaturerises the two metals expand by different amounts, which causes the strip to curl with the metal whichexpands the more on the outside of the curve.[Page 103]

InvarA special metal alloy which (around room temperature) hardly expands when heated – useful as one ofthe metals in bi-metal strips.[Page 103]

Chapter 17: MEASURING TEMPERATURES

Lower fixed pointAn agreed standard cold temperature.[Page 105]

Ice pointCommonly taken to be the lower fixed point. The ice point is the temperature at which pure icemelts under a pressure of one atmosphere.[Page 107]

Upper fixed pointAn agreed standard hot temperature.[Page 106]

Steam pointCommonly used as the upper fixed point. The steam point is the temperature at which pure waterwill boil if the pressure on its surface is one standard atmosphere (equivalent to 760 mm ofmercury).[Page 107]

Centigrade scaleA scale of temperature which numbers the ice point 0 and the steam point 100. Temperatures indegrees Celsius (oC) are based on this scale.[Page 106]

Chapter 18: WHAT MATTER IS MADE OF

MoleculeOne of the almost unimaginably tiny separate particles which make up all matter. Occasionally amolecule comprises just a single atom (see below), but more often it is made up of a group of atomsheld together by chemical bonds.[Page 110]

AtomOne of the ninety or so different particles which chemists identify as the chemical elements. Seechapter 52 (Section F) for the structure of an atom.[Page 110]

Kinetic theoryThe idea that matter is made up of lot of tiny molecules all in rapid random movement (gases andliquids) or vibrating about their fixed positions (solids).[Pages 111 to 113]

Brownian motionRandom erratic movements of small solid specks of carbon (i.e., smoke) in still air. These specks arevisible with a microscope as points of light. The motion is caused by them being continually buffetedby the molecules (themselves far too small to be visible) which make up the air.[Page 114]

Chapter 19: WAYS OF COOLING DOWN

EvaporationThe escape of individual molecules from the surface of a liquid. These molecules are then in the gasstate (referred to as a vapour), and enter the space above the liquid. Since it is only the faster-than-average molecules in the liquid which are able to break free, the average speed of the remainingmolecules falls – evaporation causes cooling. Evaporation occurs at all temperatures, but happens at agreater rate if the temperature is higher. See also Boiling (chapter 23).[Page 118]

ConductionThermal conduction is the passage of heat through a material from molecule to molecule, withoutany movement of the material as a whole. Metals are good conductors, but gases are poorconductors (good insulators, so long as convection is prevented from occurring – see below).[Page 118]

ConvectionConvection is the transfer of heat throughout a fluid (that is, a liquid or a gas) by means of bulkmovement of the hot fluid.[Page 120]

Chapter 20: INFRARED RADIATION

Infrared radiationElectromagnetic radiation (see chapter 28, Section D) with a wavelength beyond the red end of thevisible spectrum. It will travel freely through space and through any materials transparent to it, but iseither reflected off the surface of or absorbed by other materials. When infrared radiation is absorbed,its energy is usually changed into thermal energy.[Page 122]

Effect of the surfaceA black surface absorbs most of the incident radiation, whereas a white or shiny surface reflects most.The best surfaces for emitting radiation are those which are also best at absorbing it – good absorbersare also good emitters. As a surface gets hotter, the amount of radiation emitted increases rapidly andits wavelength gets shorter (until eventually it emits in the visible range, as it becomes first red hot thenwhite hot).[Page 123]

Thermal equilibriumA body with a black surface out in the sun will absorb infrared radiation and warm up; as it does so itloses thermal energy to the surroundings, mainly by convection and conduction. When its temperaturebecomes constant because it is losing energy as rapidly as it is gaining it, the body is said to be inthermal equilibrium.[Page 124]

Glass-house effectAlso called the greenhouse effect. There is a layer of carbon dioxide gas and other pollutants in theupper atmosphere, caused largely by our burning of oil and coal. This layer is transparent to theincoming radiation from the Sun, but is not transparent to the Earth’s much longer-wavelength infraredradiation which it emits in an outward direction. The effect is predicted to be global warming.[Page 125]

Chapter 21: HOW GASES BEHAVE

Boyle’s LawFor a fixed mass of gas at constant temperature, the product of the pressure and the volume is aconstant. Under those conditions, p2V2 = p1V1.[Page 127]

Absolute zeroThe lowest possible temperature – that at which the motion of molecules may be considered to haveceased. About -273oC.[Page 131]

KelvinA scale of temperature which keeps the size of the degree the same as on the celsius scale but whichhas its zero at absolute zero. Temperatures on this scale are said to be in kelvin (K), not degreeskelvin. T (in K) = 273 + ? (in oC).[Page 131]

Charles’s LawFor a fixed mass of gas kept at a constant pressure, the volume it will occupy is proportional toits temperature in kelvin. V2/T2 = V1/T1 so long as T is in kelvin.[Page 132]

The Pressure LawFor a fixed mass of gas held at a constant volume, the pressure it exerts will be proportional to itstemperature in kelvin. P2/T2 = p1/T1 so long as T is in kelvin.[Page 133]

The complete gas equation P2V2/T2 = p1V1/T1.The equation describes a fixed mass of gas, so long as T is in kelvin.[Page 134]

Chapter 22: WARMING THINGS UP

CaloricAn old idea which imagined heat to be a self-repelling fluid. In 1798 Rumford (who was engaged indrilling the barrels of cannons), noticing that the heat produced by the process never seemed to run out,suggested that the heat must be something the drill was putting in rather than a fluid which was beingsqueezed out of the metal. Around 1850 Joule showed that a given quantity of mechanical workalways converted to the same amount of heat, which led to the idea that heat was a form of energy.[Page 137]

Specific heat capacityA property of a material, defined as the number of joules of heat energy required to raise thetemperature of 1 kg of a substance by 1 K. It is represented by the symbol ‘c’, and has the units J kg-

1 K-1. EH = mc.??.[Page 139]

Heat capacityA property of a particular body, defined as the number of joules of heat energy needed for each 1 Kwe wish to raise the temperature of that body. It is represented by the symbol ‘C’, and has the unitsJ K-1. EH = C.?? . For a body of mass m made from a material whose specific heat capacity is c, theheat capacity is given by C = mc.[Page 140]

Chapter 23: MELTING AND BOILING

BoilingBoiling occurs when a liquid changes to a gas. It happens within the bulk of the liquid once aparticular temperature (dependent on the pressure on the liquid’s surface) is reached. Bubbles of gas(created from the liquid, and sometimes referred to as vapour) form within the liquid, rise to thesurface and escape. See also Evaporation (chapter 19).[Page 144]

Latent heatEnergy supplied to a substance which causes it to change state (solid to liquid, or liquid to gas) but notto increase in temperature.[Page 143]

Specific latent heat of fusionA property of a material, defined as the thermal energy required to change 1 kg of a solid at itsmelting point into 1 kg of liquid at the same temperature. It is represented by the symbol ‘lf’ , andhas the units J kg-1 . EH = m lf .[Page 144]

Specific latent heat of vaporization

A property of a material, defined as the thermal energy required to change 1 kg of a liquid at itsboiling point into 1 kg of gas at the same temperature. It is represented by the symbol ‘lv’, and hasthe units J kg-1. EH = m lv.[Page 144]

SECTION D: RAY OPTICS AND WAVES

Chapter 24: GOING IN STRAIGHT LINES

Eclipse of MoonOccurs when the Earth gets in the way of the light travelling from the Sun toward the Moon, thuscasting the Earth’s shadow on the Moon.[Page 152]

Eclipse of SunOccurs when the Moon gets in the way of the light travelling from the Sun toward the Earth. Thisresults in the Moon’s shadow passing over the Earth, so the Moon cuts off people’s view of the Sun.[Page 153]

Chapter 25: REFLECTION OF LIGHT

NormalThe normal to a surface is a line drawn at 90o to that surface. When light is incident on a surface, weusually measure its angle to the normal, and not to the surface itself.[Page 156]

Laws of reflection(1) The angle of reflection is equal to the angle of incidence; and (2) the reflected ray lies in theplane which contains the incident ray and the normal.[Page 157]

Object and imageIn optics the object is the thing that is really there, while the image is the thing that we see.[Page 158]

Plane mirror.One whose reflecting surface is flat rather than curved.[Page 157]

Image formed by a plane mirrorThe position of the image can be summed up like this: (1) The image is as far behind the mirror asthe object is in front; and (2) the line joining object and image cuts the mirror surface at rightangles.[Page 160]

Lateral inversionThis term describes the left-right reversal experienced by the image in a plane mirror.[Page 160]

Chapter 26: REFRACTION OF LIGHT

RefractionThe change in the direction of travel of a light beam which occurs as the light crosses theboundary between one transparent medium and another. All types of waves show the effect. It iscaused by an abrupt change in speed as they move from one medium to the other.[Page 162]

Lateral displacement

The sideways shift of a beam of light after it has passed through a rectangular glass block at an angle.[Page 165]

Snell’s LawWhenever light crosses a boundary between two transparent media, the sines of the angles(measured to the normal) on each side of the boundary bear a constant ratio to each other.[Page 167]

Refractive indexA property of a transparent material, given the symbol ‘n’. It is a number, greater than one, such thatthe bigger the number the greater the refraction produced. The definition of refractive index (seechapter 32) can be expressed in the form:n = sin ?1 / sin ?2 at a boundary between the medium and a vacuum. For most purposes we considerlight crossing a boundary between the material and air, which behaves almost the same as a vacuum.[Page 167]

Optical densityAn optically dense medium is one with a large refractive index. It has nothing to do with the idea ofdensity as described in Section A (chapter 3).[Page 168]

Chapter 27: TRANSPARENT SURFACES

Total internal reflectionThis is when none of the light crosses the boundary between one transparent medium and another;instead it is all reflected back as if from a mirror. Total internal reflection will occur if (1) lighttravelling in a medium such as water or glass comes to a surface with a less optically densemedium (usually air); and (2) it hits the inside of this surface at an angle of incidence greaterthan the critical angle.[Page 171]

Critical angleThe particular angle of incidence for which light emerges along the surface (i.e., at an angle ofrefraction of 90o). For a medium of refractive index n, the critical angle at a boundary with a vacuum(or air) can be worked out from sin c = 1 / n.[Page 171]

Chapter 28: DEVIATION AND DISPERSION

DeviationApplied to the passage of light through a triangular prism, deviation is the angle between the directionof the light as it reaches the prism and its direction once it leaves the prism.[Page 177]

DispersionDispersion is the splitting up of white light into its constituent colours.[Page 177]

Electromagnetic radiationA family of waves of which visible light forms one small part. They are all transverse waves (seechapter 32) and all travel through a vacuum at the speed of light. Going from the long wavelength (lowfrequency) end of the spectrum through to the short wavelength (high frequency) end, the members ofthe family include: radio waves, microwaves, infrared radiation (see Section C, chapter 20), red light,blue light, ultraviolet radiation, X-rays and gamma rays (see Section F, chapter 53).[Page 179]

Chapter 29: HOW LENSES BEHAVE

Converging lens

A lens which will refract a parallel beam of light inwards to a focus. Also called a convex lens fromits shape.[Page 182]

Diverging lensA lens which will refract a parallel beam of light so it spreads outwards. Also called a concave lensfrom its shape[Page 182]

Principal axisThis is a line drawn through the centre of a lens, perpendicular (i.e., at 90o) to it.[Page 182]

Principal focusSometimes just called the focus of the lens. It relates to what the lens will do to a beam of parallel lightincident along the principal axis: for a converging lens it is the point at which this light is brought to afocus; for a diverging lens it is the point where the emerging light seems to be spreading out from.[Page 182]

Focal lengthThe distance from the centre of a lens to its (principal) focus. A strong lens will have a short focallength.[Page 182]

Focal planeThis is represented by the surface of a screen placed at a distance back from a lens equal to its focallength, and arranged so it lies at right angles to the principal axis.[Page 182]

MagnificationMagnification is defined as the height of the image divided by the height of the object. It may alsobe predicted by (distance from lens to image) divided by (distance from lens to object).[Pages 183, 191]

Real imageA real image is one through which the light has actually passed, so it can be cast on a screen. Thisis the sort of image produced by a converging lens whenever the object lies outside the focus of thelens – in a camera or a slide projector, for example.[Page 186]

Virtual imageA virtual image is one from which the light only appears to have come, so it cannot be cast on ascreen. This is the sort of image produced by a converging lens being used as a magnifying glass, by adiverging lens always, and by a plane mirror.[Page 186]

Chapter 30: MORE ABOUT LENSES

Path of light through a converging lensThere are two special directions of travel of the incident light whose direction we can predict as itleaves the lens. These are (1) light entering the lens parallel to its principal axis, which will berefracted through the focus of the lens; and (2) light passing through the centre of the lens at any angle,which will carry on undeviated.[Page 190]

CameraThe object must be more than twice the focal length away from the converging lens. The image is real,upside down and smaller than the object, and lies just beyond the focus.[Page 191]

Slide projectorThe object must lie just beyond the focus of the converging lens, and less than twice the focal lengthfrom it. The image is real, upside down and magnified, and lies at a large distance from the lens.[Page 191]

Magnifying glassThe object must lie within the focus of the converging lens. The image is virtual, the right way up andmagnified, and lies further back from the lens than the object.[Page 191]

Chapter 31: THE EYE AND VISION

RetinaThe screen at the back of the eye, packed with light-sensitive cells connected to the brain.[Page 194]

CorneaThe curved transparent part of the eyeball, through which the light enters. The cornea does most of thefocussing of the light, but the lens of the eye does the ‘fine-tuning’ to ensure that a focussed real imageis cast on the retina.[Page 194]

IrisA coloured ring just inside the cornea which opens or closes to control the amount of light entering theeye. The black opening in its centre is called the pupil.[Page 194]

AccommodationAccommodation is the eye’s ability to focus on objects at different distances. It achieves this bymaking the lens become stronger to view near objects by causing it to bulge into a fatter more roundedshape.[Page 195]

Near pointThe eye’s near point is the distance of the closest object which it can clearly focus on. It correspondsto the greatest extent to which the lens can be fattened.[Page 196]

Chapter 32: THE LANGUAGE OF WAVES

WavelengthThe distance from one crest to the next one. It is often given the symbol ? (‘lambda’) and is usuallymeasured in metres.[Page 198]

AmplitudeIt is the height of a crest or the depth of a trough MEASURED FROM THE CENTRE LINE. It is ameasure of the amount of energy being conveyed each second by the wave. For light waves itrepresents the brightness, for radio waves the signal strength and for sound waves the loudness.[Page 198]

PeriodThe period of a wave (symbol T) is the time it takes to perform one complete oscillation. It is usuallymeasured in seconds. (See Section B, chapter 12).[Page 199]

FrequencyThe frequency (‘f’) of a wave is the number of crests which pass a given point every second. For anoscillator it is the number of oscillations each second. The units are s-1 called hertz (Hz). Frequencyand period are related, since f = 1 / T.

[Page 199]

SpeedThe speed of a wave is the distance which an individual crest travels in one second. Speed (in m s-1)equals frequency (in Hz) times wavelength (in metres). V = f ?.[Page 199]

Transverse waveA transverse wave is one in which each particle of the medium vibrates at right angles to thedirection in which the wave is travelling. Electromagnetic waves such as light and radio waves areexamples of transverse waves.[Page 200]

Longitudinal waveA longitudinal wave is one in which each particle of the medium vibrates back and forth in thedirection in which the wave is travelling. Sound waves with their compressions and rarefactionsare a good example of longitudinal waves.[Page 201]

CHAPTER 33: SIMPLE WAVE BEHAVIOUR

WavefrontWavefronts are drawn to show how a wave behaves. You may think of them as the crests of the wave,each spaced one wavelength apart.[Page 203]

Change in wavelength across a boundaryAs the wave enters a medium in which it travels more slowly, the wavefronts get closer together. If vstands for speed and ? for wavelength, then ?2 / ?1 = v2 / v1.[Page 206]

Refractive indexAn alternative but equivalent definition of the refractive index n of a medium (see chapter 26) is theratio between the speed of light in a vacuum and its speed in the medium. n = c / v. Thus aslight crosses the boundary between two media, sin ?1 / sin ?2 = v1 / v2.[Page 207]

Chapter 34: SOUND WAVES

PitchThe pitch of a musical note is determined by its frequency – a high frequency means a high pitch. Anote an octave higher will have double the frequency.[Page 211]

Frequency range of human earRoughly 20 Hz to 20 kHz (20,000 Hz).[Page 211]

Chapter 35: DIFFRACTION

DiffractionThis is a property of all waves. Diffraction is the way waves spread out round the edge of anobstacle into the ‘shadow zone’ behind it. It shows up most when the obstacle is no more than a fewwavelengths across. The extremely short wavelength of visible light means that ordinary objects willcast sharp shadows.[Pages 215, 216]

Waves passing through a gapIf the gap is only a wavelength or so across, diffraction is total: the wavefronts emerge with asemicircular shape. If the gap is very many wavelengths across, there is very little diffraction.

[Page 219]

Chapter 36: INTERFERENCE EFFECTS

SuperpositionThe principle of superposition states that at any moment, the combined effect of two overlappingtrains of waves may be obtained simply by adding the two separate displacements.[Page 223]

Constructive interferenceThis is the effect which occurs when two sets of waves arrive at a point exactly in steph (in phase).Crest combines with crest, and a little later trough combines with trough. This results in a single waveof much greater amplitude (brighter light, louder sound).[Page 223]

Destructive interferenceThis happens if the two sets of waves arrive exactly out of phase. A crest from one cancels out a troughfrom the other. This keeps happening to give darkness or silence.[Page 223]

Young’s slitsThis is an arrangement to give two sources of light only a few wavelengths apart so an interferencepattern of alternate bright and dark fringes may be viewed. A common way of achieving this set-up isto have two narrow slits very close together in front of a single light source.[Page 228]

SECTION E: ELECTRICITY AND MAGNETISM

Chapter 37: STATIC ELECTRICITY

Electric chargeThere are two sorts of charge which we call positive and negative. Like charges repel; unlike charges(that is, a positive one and a negative one) attract each other. An uncharged body still contains charges– but it must have an equal number of each sort. The unit we use to measure a quantity of charge is thecoulomb, C.[Pages 235, 237]]

Electric fieldAn electric field is a region where an electric charge will experience a force of electrical origin.The arrows on an electric field plot indicate the direction of the force a POSITIVE charge willexperience. Where the lines are closest together, there the field is strongest.[Page 237]

Chapter 38: ELECTRIC CURRENT

Electric currentAn electric current is a flow of charge. The unit in which we measure the rate of flow of charge is theampere, A. A current of 1 ampere indicates that charge is flowing past a point at a rate of 1 coulombevery second. Thus 1 A = 1 C s-1.When a current I (in amperes) is flowing, the quantity of charge Q (in coulombs) which passes in atime t (in seconds) is given by Q = I t.[Page 241]

ElectronA particle with a negative charge which is present in all atoms. See Section F, chapter 52. The chargecarried by a single electron, which we denote by e, is the fundamental unit of electric charge – 1.6 x 10-

19 C. A metal is characterised by having electrons within it which are not attached to any one atom(conduction electrons), and these are the charges which are free to flow through a wire which iscarrying a current.

[Page 243]

IonThis is the name we give to an atom which carries an overall charge (e.g. one of its outside electrons ismissing: since that atom is then one negative charge short, it will have a single unbalanced positivecharge).[Page 243]

Conventional currentConventional current indicates the direction in which positive charge would flow round a circuit – i.e.away from the positive terminal of the battery round the circuit towards the negative terminal. In fact,what are actually moving through a wire are negative electrons the opposite way.[Page 243]

Chapter 39: ELECTRICAL CIRCUITS

Series circuitA circuit in which the charge has to flow through each component in turn. The current has the samevalue all the way round a series circuit.[Page 245]

Parallel circuitThis is a circuit which splits up and so offers alternative routes for the charge to flow. Where thecircuit divides, the currents in each branch added together equal the current approaching the point.[Page 246]

Chapter 40: RESISTANCE

ResistanceThe unit we use to measure resistance is the ohm, symbol ‘O’. For a battery of voltage V, the greaterthe resistance of the circuit the smaller will be the current. The current I in amperes may be predictedby I = V / R , where R is the resistance in ohms. For a formal statement of Ohm’s Law, see chapter45.[Page 249]

Resistors in seriesFor a series circuit, the total resistance is the sum of the resistances of each separate component. R =R1 + R2.[Page 250]

Resistors in parallelIf R1 and R2 are two resistors connected in parallel, they behave like a single resistance R whose valueis given by: 1 / R = 1 / R1 + 1 / R2.[Page 252]

Chapter 41: BATTERIES

CellThe name we give to a single component which converts chemical energy into electrical energy,consisting of two different metals (or one metal plus carbon) in an electrolyte (e.g. ammonium chloridesolution or dilute sulphuric acid).[Page 255]

Primary cellThis is one which must be discarded once the chemicals within it have been used up, e.g. the dry cell.[Page 256]

Secondary cell

A cell which produces its electrical energy by means of a chemical reaction which is reversible. It cantherefore be recharged by forcing a current ‘backwards’ through it. An example is the lead / acid cell,six of which make up a 12 V car battery.[Page 256]

BatteryA circuit component consisting of a single cell, or of more than one cell connected in series. Itprovides an electromotive force (e.m.f.), measured in volts.[Page 245]

Chapter 42: MAGNETS

Magnetic polesThese are of two opposite kinds, and are located at each end of a bar magnet. One is the north-seekingpole (the north, N for short), which points to magnetic north if the bar magnet is free to turn. The otheris the south-seeking pole. Like poles repel, unlike poles attract.[Page 258]

Magnetic materialsThese are ones which are capable of being magnetized (i.e., of being turned into a magnet). Examplesinclude a few metals (iron, cobalt and nickel), a few alloys (e.g. steel, mu-metal) and a few othercompounds (e.g. a naturally occurring oxide of iron and a material called Magnadur). Iron is easy tomagnetize, but rapidly loses it magnetism; steel is less ready to magnetize, but then stays magnetized.[Pages 261, 268]

Test for a magnetThe only sure test is repulsion by another known magnet.[Page 259]

Magnetic fieldA magnetic field is a region in which a magnetic force may be exerted. The field is plotted as a setof magnetic lines of force (sometimes called magnetic flux lines) which indicate the direction a smallcompass would set at any point: the lines are marked with an arrow which shows the direction in whichthe north end of the compass would point. Where the field is strongest the lines are closest together.[Page 262]

Chapter 43: CURRENTS AFFECT MAGNETS

Magnetic field due to a current. An electric current flowing through a long straight wire will affect amagnet. The field pattern comprises circular lines of force whose centre is at the wire. To predict whichway the arrows run on those lines, take your right hand and hold the wire with your thumb going in thedirection of the conventional current: the way your fingers then wrap round the wire is the way thefield lines go.[Page 265]

SolenoidA length of wire wound into a long coil for the purpose of producing a magnetic field when a currentflows round it. Inside the solenoid the magnetic field is strong and uniform, but outside it the field islike that of a bar magnet. Placing a soft iron core into the solenoid makes it act as a far strongermagnet – this arrangement is called an electromagnet. To predict which end of the solenoid will actlike the north of a bar magnet, imagine grasping the solenoid with your right hand, your fingers goinground the same way as the conventional current: your outstretched thumb then points to the ‘N’ end ofthe solenoid.[Page 266]

RelayA relay is a switch which is pulled closed not by hand but by an electromagnet.[Page 268]

Chapter 44: ELECTRIC MOTORS

Fleming’s Left hand RuleUsed to predict the direction of the movement produced by the motor effect. Hold the thumb andfirst two fingers of your left hand at right angles to each other. If the First finger points alongthe magnetic Field and the seCond finger shows the Conventional Current, then the Thumbpoints in the direction of the Thrust.[Page 272]

Chapter 45: POTENTIAL DIFFERENCE

Potential difference (p.d.)This is the voltage drop between two points, usually between the two ends of a resistor or other circuitcomponent. It is measured in volts. There is no voltage drop down a conducting lead. The voltagedrops across each resistor in series add up to the voltage of the battery. If resistors are connected inparallel, they each have the same voltage drop across them.[Pages 281, 285]For a formal definition of potential difference, see chapter 46.

Ohm’s LawFor a metal wire at a constant temperature, the current which flows through it is proportional tothe potential difference (the voltage drop) between its ends.[Page 283]

Chapter 46: THE VOLT – AN ENERGY UNIT

VoltA volt is a measure of the quantity of electrical potential energy stored in a charge. One volt meansone joule of energy per coulomb of charge: 1 V is the same as 1 J C-1.[Page 287]

Potential differenceThere is a potential difference of 1 volt between two points in a circuit if 1 joule of electricalenergy is released whenever 1 coulomb of charge passes from one point to the other. The energyE in joules released when a total charge Q in coulombs ‘falls’ through a p.d. V in volts is given by E =Q V.[Page 288]

Power of a heaterIf a heater has a p.d. V volts across it and in consequence a current I amperes flows through it, then itgenerates thermal energy at a rate of P watts given by P = V I . Thus the energy E in joules itproduces over a time t seconds is given by E = V I t.[Page 290]

Chapter 47: THE DYNAMO EFFECT

The dynamo effectAlso known as electromagnetic induction. It is a voltage which is generated when a conductor cutsthrough lines of magnetic flux.[Page 294]

Faraday’s LawThe size of the e.m.f. in volts is proportional to the rate at which the conductor is cutting throughthe lines of magnetic flux.[Page 294]

Lenz’s LawThe direction of an induced current is such as to oppose the change that is causing it. Thus togenerate electrical energy, work in some form must be done.[Page 295]

Fleming’s Right Hand RuleIf an induced current is being generated by moving a conductor through a magnetic field, this Ruleprovides an alternative way to predict the direction of the induced current. The fingers stand for thesame things as in the Left Hand Rule (chapter 44) but this time the right hand must be used.[Page 296]

Chapter 48: REAL DYNAMOS

DiodeA diode is a circuit component which will allow current to pass freely through it in one direction, butwill not conduct in the other direction.[Page 301]

RectificationThis is the conversion of an alternating current (see chapter 50) into a direct current. A diode placed inseries in the circuit will allow the current to flow forwards through it in one half of the cycle, but willnot allow the current to flow back again in the other half-cycle. The result is a direct current which isnot smooth as it would be from a battery, but instead consists of a sequence of pulses all in the samedirection.[Page 302]

Chapter 49: TRANSFORMERS

TransformerA device which takes an alternating voltage and either steps it up to a higher voltage or steps it down toa lower alternating voltage. It is made from a primary (or input) winding and a secondary (or output)winding, usually linked by a soft iron core.[Page 304]

Turns ratioVout / Vin = No. of turns on the secondary (Ns) / No. of turns on the primary (Np).[Page 305]

Eddy currentsUnfortunately the iron core conducts electricity in addition to having the necessary magneticproperties. The changing magnetic fields could cause unwanted eddy currents to swirl around in theiron core, resulting in it heating up and wasting energy. These currents are minimised by using alaminated iron core – one made from a large number of separate flat sheets of iron.[Page 304]

PowerWith an efficient transformer, the energy delivered at the secondary each second is the same as thatsupplied to the primary – i.e, Vout x Iout = Vin x Iin . Thus the input can give a smaller current at ahigher voltage, or vice versa.[306-307]

Chapter 50: HOUSEHOLD ELECTRICITY

Live terminalIn one cycle of an alternating supply, the live terminal swings alternately very positive and half a cyclelater very negative compared to earth. 110 V or 220 V are a kind of average: at the peak values the liveterminal swings between ± 155 V or ± 310 V respectively. The live wire in a plug is colouredBROWN.[Page 310]

Neutral terminal

Sometimes called the return. The neutral terminal stays at about earth voltage all the time, andprovides the route for the live terminal to send a current out then draw it back again in each cycle. Theneutral wire in a plug is coloured BLUE.[Page 310]

FuseA device to switch the power off if the current flowing is too great for the wiring (thus riskingoverheating and an electrical fire). It is made from a wire of low melting point which will melt and sobreak the circuit. It must be placed in the live line. Nowadays fuses are sometimes replaced by circuitbreakers which use an electromagnet to do the same job.[Page 311]

EarthThe earth connection is an extra third pin which may be provided in a mains socket, which is connectedto earth by a very low-resistance route. An appliance with a metal case (e.g. kettle) should have itscasing connected to earth (via the GREEN and YELLOW wire in it lead). If a fault should develop sothe live wire comes in contact with the casing, a large current would go from the live line down to earthby this route, thus melting the fuse so as to switch off and make it safe.[Page 312]

Electricity billsThese bill you for the energy supplied, measured not in joules but in kilowatt hours (kWh). Akilowatt hour is the amount of energy required to keep a 1 kW appliance running for 1 hour.Energy used (in kWh) is obtained by multiplying the total power (in kW) by the time for which theyare running (in hours).[Page 315]

Chapter 51: LOGIC GATES

Logic gateA device which has one or more inputs and a single output. The state at the output (0 or 1) isdetermined by the states of each of the inputs. The device is operated by voltages, not currents. Theinputs draw virtually no current, while the output can deliver only a tiny current which is capable ofoperating just a very sensitive device (e.g. a L.E.D. – see below – or the coil of a small relay).[Page 318]

Truth tableA description of what a given gate does. Logic 0 means that no voltage is present. Logic 1 indicatesthat a voltage (typically 5 V) is applied to that input or is present at the output.[Page 318]

NOT gateA gate with a single input. If that input is made 0, the output is a 1. If that input is made 1, the outputis a 0.[Page 320]

AND gateIt has two inputs. It may be simulated by two switches in series. Its truth table is:-

INPUT A INPUT B OUTPUT 0 0 0 0 1 0 1 0 0 1 1 1[Page 318]

NAND gateIt has two inputs. It is essentially an AND gate followed by a NOT gate. Its truth table is:-

INPUT A INPUT B OUTPUT 0 0 1 0 1 1

1 0 1 1 1 0[Page 320]

OR gateIt has two inputs. It may be simulated by two switches in parallel. Its truth table is:-

INPUT A INPUT B OUTPUT 0 0 0 0 1 1 1 0 1 1 1 1[Page 320]

NOR gateIt has two inputs. It is essentially an OR gate followed by a NOT gate. Its truth table is:-

INPUT A INPUT B OUTPUT 0 0 1 0 1 0 1 0 0 1 1 0[Page 320]

L.E.D.Short for light-emitting diode. A tiny current in the forward direction (small enough for a logic gateto be able to deliver) will make it glow. Like all diodes, if it is connected the wrong way round nocurrent will pass so it will not light up.[Page 319]

ThermistorA resistor whose value decreases as the temperature rises. (All semiconductor resistors have thisproperty, but a thermistor is specially designed to make use of it). It enables a logic gate to respond tochanging temperatures.[Page 323]

L.D.R.Short for light-dependent resistor. When light falls on its surface, its resistance drops. It enables alogic gate to respond to changing brightness.[Page 323]

SECTION F: THE PHYSICS OF THE ATOM

Chapter 52: THE STRUCTURE OF AN ATOM

NucleusThe central part of an atom, containing all its positive charge and virtually all its mass. It is made fromtwo sorts of particles – the proton which carries a single positive charge (+e) and the neutron with asimilar mass to the proton but with no charge.[Page 331]

Neutral atomMost of the atom is empty space. The nucleus is at its centre. In ‘distant’ orbit round the nucleus areelectrons – particles with a mass far smaller than that of the protons and neutrons, but each carrying asingle negative charge (-e). In the neutral atom the number of these electrons must equal the number ofprotons in the nucleus.[Page 332]

Atomic number, ZAlso called the proton number. The atomic number of an nucleus is the number of protons itcontains. The number of protons determines the number of electrons in orbit in a neutral atom, and it

is the electrons which determine its chemical behaviour – so all atoms with the same number of protonsare the same chemical element.[Page 333]

IsotopeIsotopes are atoms of the same element which have the same number of protons in their nucleusbut a different number of neutrons. They therefore differ in mass.[Page 332]

Radio-isotopeAn isotope which is radioactive – see chapter 53.[Page 333]

Mass number, AAlso called the nucleon number (nucleon is a term which includes both protons and neutrons). Themass number of a nucleus is the total number of protons and neutrons in it counted together. For anucleus with Z protons and N neutrons, A = Z + N.[Page 333]

Chapter 53: RADIOACTIVE EMISSIONS

RadioactiveRadioactive describes isotopes which are liable to release energy spontaneously and randomly byemitting a particle from their nucleus, sometimes accompanied by a pulse of electromagnetic radiation.[Page 336]

Alpha (a) particleAn alpha particle is a cluster of two protons and two neutrons, carrying a charge +2e and identical tothe nucleus of a helium atom. When an alpha particle is emitted, the mass number of the remainingnucleus drops by four and its proton number drops by two. Alpha particles are the least penetratingtype of radiation, but they cause heavy ionization.[Pages 337, 341, 349]

Beta (ß) particleA beta particle is a single electron EMITTED FROM A NUCLEUS. It occurs when a neutron decaysinto a proton (which stays in the nucleus) and an electron (which is emitted). When a beta particle isemitted, the mass number of the remaining nucleus is unchanged but its proton number rises by one.Beta particles carry a charge of –e and are of far smaller mass than alpha particles: they are morepenetrating, but cause less ionization.[Pages 338, 342, 350]

Gamma (?) radiationGamma radiation is extremely short wavelength electromagnetic radiation, of the same family asordinary visible light. It is sometimes released from a nucleus which has just emitted an alpha or abeta particle. It carries no charge, is the most penetrating of the three types but causes the leastionization.[Page 338, 342]

IonizationIonization in this context refers to the damaging of any atoms which lie in the path of the radioactiveemissions. The damage is the breaking off of one of the atom’s outermost electrons, leaving twocharged particles – the damaged atom which now has an unbalanced positive charge, and the freenegatively-charged electron.[Page 337]

Chapter 54: HOW A NUCLEUS DECAYS

Background count

Ever-present radiation (e.g. from naturally radioactive rocks, from the Sun and from man-madecauses). To arrive at a value for the count rate due to a radioactive source, the average backgroundcount should be subtracted to give the corrected count rate.[Page 344]

Half life (t½)The half life is the average time required for half of the nuclei in a sample of a particularradioactive element to decay to a different element. This will therefore be the time for the count rateto drop to a half its original value, which is the usual way to measure it.[Page 347]

ActivityThe activity of a radioactive source is the total number of particles it emits every second. Only afraction of these particles will be picked up by the detector, so the measured count rate will be less.[Page 349]

Chapter 55: NUCLEAR ENERGY

Energy has massThe mass m in kg of E joules of energy is given by E = m c2 . The constant c is a speed: the speed atwhich light travels through a vacuum (3.0 x 108 m s-1). This applies to all types of energy but is onlynoticeable with nuclei, which are capable of releasing a large quantity of energy relative to their tinymass.[Page 352]

Nuclear fissionNuclear fission occur when a heavy nucleus splits up into two medium-sized ones, with some massbeing lost in the process and a corresponding quantity of energy being released. One particular isotopeof uranium (U-235) and plutonium are capable of releasing energy rapidly by a chain reaction - whenone nucleus splits up, it triggers another one to do the same, and so on.[Page 353]

Nuclear fusionNuclear fusion occurs if two light nuclei are made to join together, with a release of energy in theprocess. This can happen only if the two nuclei are approaching one another fast enough to preventtheir mutual electrical repulsion from bringing them to rest before they join, and these speeds areassociated with temperatures in excess of a million degrees.[Page 355]

END