IGCSE Physics

Length and volume

Use a ruler 直尺 to measure length. Read the scale with your eye straight in front of the mark to avoid a reading error.

Use a measuring cylinder 量筒 to measure the volume of a liquid. Read the scale at the bottom of the curved surface (the meniscus 弯月面), with your eye level with it.

Measuring small amounts

A single small length or a short time is hard to measure well. The trick is to measure many and divide 测多个再相除:

• To find the thickness of one page, measure 100 pages and divide by 100.
• To find the time for one swing of a pendulum 摆, measure the time for 20 swings and divide by 20. One full swing is called the period 周期.

This makes the uncertainty 不确定度 (the size of the error) much smaller.

Scalars and vectors

A scalar 标量 has size (magnitude 大小) only. A vector 矢量 has size and direction.

• Scalars: distance, speed, time, mass 质量, energy 能量, temperature 温度.
• Vectors: force 力, weight 重力, velocity 速度, acceleration 加速度, momentum 动量.

To add two vectors at right angles (90°), draw them as two sides of a rectangle. The resultant 合矢量 is the diagonal. Find its size with Pythagoras and its direction with trigonometry.

Speed and velocity

Speed 速率 is the distance travelled per unit time.

Velocity is speed in a stated direction. So velocity is a vector but speed is a scalar.

Acceleration

Acceleration is the change in velocity per unit time.

Here $\Delta v$ means "the change in velocity". A deceleration 减速 (slowing down) is a negative acceleration.

Worked example. A car speeds up from $8\ \text{m/s}$ to $20\ \text{m/s}$ in $4.0\ \text{s}$. Find its acceleration.

Motion graphs

A distance–time graph 距离-时间图 shows how far an object has gone:

• A flat (horizontal) line means the object is at rest 静止.
• A straight slope means constant speed. The gradient 斜率 (steepness) is the speed.
• A curve that gets steeper means the object is speeding up.

A speed–time graph 速度-时间图 shows how fast an object is going:

• A flat line means constant speed.
• A straight slope means constant acceleration. The gradient is the acceleration.
• The area under the line 线下面积 is the distance travelled.

Falling objects

Near the Earth, all objects speed up as they fall at the same rate. This is the acceleration of free fall 自由落体加速度, $g \approx 9.8\ \text{m/s}^2$.

When an object falls through air, air resistance 空气阻力 (a drag force) acts upward. As it speeds up, air resistance grows. When air resistance equals the weight, the resultant force is zero and the object stops speeding up. It then falls at a steady terminal velocity 收尾速度.

Mass is the amount of matter 物质 in an object. It is measured in kilograms (kg) and does not change when you move the object.

Weight is the force of gravity on a mass. It is measured in newtons (N). Weight can change: it is smaller on the Moon because the Moon's gravity is weaker.

Gravitational field strength 重力场强度 is the force per unit mass:

This $g$ has the same value as the acceleration of free fall ($\approx 9.8\ \text{N/kg}$). You can compare masses with a balance 天平.

Density is the mass per unit volume.

The symbol $\rho$ is the Greek letter "rho". The unit is $\text{kg/m}^3$ or $\text{g/cm}^3$.

To find density: measure the mass with a balance, find the volume, then divide.

• Regular solid 规则固体 (like a box): measure the sides and calculate the volume.
• Irregular solid 不规则固体 (a strange shape): lower it into water in a measuring cylinder. The rise in water level is its volume. This is the displacement method 排水法.

An object floats 漂浮 if its density is less than the density of the liquid. It sinks if its density is greater.

Worked example. A stone of mass $54\ \text{g}$ is lowered into a measuring cylinder. The water level rises from $20\ \text{cm}^3$ to $40\ \text{cm}^3$. Find the density of the stone.

The volume of the stone is the rise in water level, $40 - 20 = 20\ \text{cm}^3$, so

A force is a push or a pull. A force can change the shape 形状, the speed, or the direction of an object.

Stretching (Hooke's law)

When you hang a load on a spring, it stretches. The stretch is called the extension 伸长量.

On a load–extension graph 载荷-伸长图 the line is straight at first: extension is proportional to load. The point where the line stops being straight is the limit of proportionality 比例极限.

The spring constant 弹簧常数 is the force per unit extension:

A large $k$ means a stiff spring.

Resultant force and Newton's laws

Add forces on a straight line to get the resultant force 合力 (forces one way are positive, the other way negative).

• If the resultant force is zero, the object stays at rest or keeps moving in a straight line at constant speed. (Newton's first law.)
• If the resultant force is not zero, the object accelerates in the direction of the force:

Worked example. A $1200\ \text{kg}$ car has a $3000\ \text{N}$ driving force and $600\ \text{N}$ of friction. Find its acceleration.

First find the resultant force: $3000 - 600 = 2400\ \text{N}$. Then

Friction

Friction 摩擦力 is the force between two surfaces that touch. It tries to stop motion and makes things heat up. Drag (friction in a liquid or gas, like air resistance) also slows objects down.

Moments — the turning effect

The moment 力矩 of a force is its turning effect about a pivot 支点.

The unit is the newton metre (N m).

Principle of moments 力矩原理: when an object is balanced (in equilibrium 平衡),

An object is in equilibrium when there is no resultant force and no resultant moment.

Worked example. A $30\ \text{N}$ weight sits $0.20\ \text{m}$ to the left of a pivot. How far to the right must a $20\ \text{N}$ weight sit to balance the beam?

Balanced, so anticlockwise moment $=$ clockwise moment:

Centre of gravity

The centre of gravity 重心 is the single point where all the weight of an object seems to act.

For a flat shape (lamina 薄片), hang it from a pin and let it settle; draw a vertical line down from the pin using a plumb line. Repeat from another point. The centre of gravity is where the lines cross.

An object is more stable 稳定 when its centre of gravity is low and its base is wide. It tips over when the centre of gravity passes outside the base.

Momentum is mass times velocity. It is a vector.

Impulse 冲量 is the force times the time it acts, and it equals the change in momentum:

So the resultant force is the change in momentum per unit time:

Conservation of momentum 动量守恒: when objects collide and no outside force acts, the total momentum before equals the total momentum after.

(Here $u$ is a velocity before and $v$ is a velocity after.)

Worked example. A $2.0\ \text{kg}$ trolley moving at $3.0\ \text{m/s}$ hits a stationary $1.0\ \text{kg}$ trolley and they stick together. Find their common velocity afterwards.

Total momentum is conserved, so

Energy stores

Energy can be stored 储存 in different ways: kinetic 动能, gravitational potential 重力势能, chemical 化学能, elastic (strain) 弹性势能, nuclear 核能, electrostatic 静电能, and internal (thermal) 内能.

Energy is transferred 转移 between stores by forces (mechanical work), by electric currents, by heating, and by waves (such as light and sound).

Kinetic and potential energy

Kinetic energy is the energy of a moving object:

The change in gravitational potential energy when an object goes up or down by a height $\Delta h$:

Conservation of energy

The principle of conservation of energy 能量守恒定律 says energy is never made or destroyed; it only moves between stores. A falling object turns gravitational potential energy into kinetic energy. A Sankey diagram 桑基图 shows how the input energy splits into useful energy and wasted 浪费 energy.

Worked example. A $0.50\ \text{kg}$ ball is dropped from a height of $1.8\ \text{m}$. Ignoring air resistance, find its speed just before it lands. (Take $g = 10\ \text{m/s}^2$.)

All the gravitational potential energy becomes kinetic energy, so $\tfrac{1}{2}mv^2 = mg\,\Delta h$. The mass cancels, leaving $v^2 = 2g\,\Delta h$:

Because the mass cancels, every object dropped from this height would land at the same speed.

Work

Work done 做功 equals the energy transferred. When a force moves an object:

The unit of work and energy is the joule 焦耳 (J).

Power

Power 功率 is the work done (or energy transferred) per unit time.

The unit is the watt 瓦特 (W). $1\ \text{W} = 1\ \text{J/s}$.

Efficiency

Efficiency 效率 tells you how much of the input energy becomes useful energy.

Efficiency is always less than 100% because some energy is always wasted (usually as heat).

Worked example. A motor is supplied with $200\ \text{J}$ of electrical energy and lifts a load, giving it $150\ \text{J}$ of gravitational potential energy. Find its efficiency.

Energy resources

We generate electricity from many energy resources. Most spin a turbine that drives a generator – often by boiling water to make steam (fossil fuels, nuclear fuel, geothermal, biofuels), or directly by moving water or air (hydroelectric, waves, tides, wind). Solar cells make electricity from sunlight directly; solar panels heat water.

Most of these trace back to the Sun (fossil fuels are ancient stored sunlight; wind and waves come from solar heating) – the exceptions are geothermal, nuclear, and tidal energy. The Sun itself is powered by nuclear fusion 核聚变, joining hydrogen nuclei into helium.

Pressure is the force per unit area.

The unit is the pascal 帕斯卡 (Pa). $1\ \text{Pa} = 1\ \text{N/m}^2$.

A small area gives a large pressure (a sharp knife cuts well). A large area gives a small pressure (snowshoes stop you sinking).

Pressure in a liquid

In a liquid, pressure increases with depth 深度 and with the liquid's density:

This is why a dam is built thicker at the bottom, where the water pressure is greatest. Pressure in a liquid acts in all directions.

Worked example. Find the extra pressure at a depth of $2.0\ \text{m}$ in water (density $1000\ \text{kg/m}^3$, $g = 10\ \text{N/kg}$).

• On a distance–time graph the gradient is the speed; on a speed–time graph the gradient is the acceleration and the area under the line is the distance travelled. Never read one graph as if it were the other.
• Mass (kg) is the amount of matter and is the same everywhere; weight (N) is the force of gravity, $W = mg$. On the Moon your mass is unchanged but your weight is smaller.
• Speed is a scalar; velocity is a vector. Something moving at steady speed around a curve is still accelerating, because its direction keeps changing.
• In Hooke's law, load is proportional to extension only up to the limit of proportionality. Use the extension (stretched length − original length), never the whole length.
• Momentum $p = mv$ is conserved in a collision. Give each velocity a $+$ or $-$ sign for its direction before you add them.
• Convert units first (cm → m, g → kg). Use $p = F/A$ for a solid pressing on a surface, but $p = \rho g h$ for the pressure inside a liquid — they are different formulas.

Matter exists in three states: solid 固体, liquid 液体 and gas 气体.

The changes of state are: melting (solid → liquid), boiling/evaporating (liquid → gas), condensation 凝结 (gas → liquid) and solidification 凝固 (liquid → solid).

All matter is made of tiny particles 粒子 that are always moving. This is the kinetic particle model.

• In a solid the particles only vibrate 振动 about fixed positions.
• In a liquid they are still close but can slide past each other.
• In a gas they are far apart and move quickly in random directions.

Temperature and particle energy

When you heat a substance, its particles move faster, so they have more kinetic energy 动能. Temperature 温度 is a measure of the average kinetic energy of the particles.

The lowest possible temperature is absolute zero 绝对零度, $-273\,{}^{\circ}\text{C}$. At this point the particles have the least possible energy.

Gas pressure

Gas particles hit the walls of their container. Each hit is a tiny push. The pressure 压强 of the gas is the total force of these hits per unit area.

• Heating a gas (at constant volume) makes particles move faster and hit harder and more often, so the pressure rises.
• Squeezing a gas into a smaller volume (at constant temperature) means more hits per second on each unit of area, so the pressure rises.

For a fixed mass of gas at constant temperature:

So if the volume halves, the pressure doubles.

Worked example. A gas has a volume of $200\ \text{cm}^3$ at a pressure of $100\ \text{kPa}$. It is squeezed to $50\ \text{cm}^3$ at constant temperature. Find the new pressure.

Since $pV$ stays constant, $p_1 V_1 = p_2 V_2$:

Brownian motion

If you look at smoke in air under a microscope, you see tiny specks moving in a jerky, random way. This is Brownian motion 布朗运动. The specks are pushed by fast, invisible air particles hitting them. It is strong evidence for the kinetic particle model.

The kelvin scale

Scientists often use the kelvin 开尔文 (K) temperature scale, which starts at absolute zero. To convert:

So $0\,{}^{\circ}\text{C} = 273\ \text{K}$.

Worked example. Convert $25\,{}^{\circ}\text{C}$ to kelvin, and $200\ \text{K}$ to degrees Celsius.

When matter is heated, its particles move more and take up more space, so the material expands. Gases expand the most, then liquids, then solids.

Everyday examples: gaps are left between railway lines; bridges sit on rollers; a tight metal lid loosens when heated.

The internal energy 内能 of an object is the total energy of all its particles. Heating an object raises its internal energy and usually its temperature.

The specific heat capacity 比热容 is the energy needed to raise the temperature of 1 kg of a material by 1 °C.

A material with a high specific heat capacity (like water) needs a lot of energy to warm up and cools down slowly.

Worked example. How much energy is needed to heat $2.0\ \text{kg}$ of water from $20\,{}^{\circ}\text{C}$ to $70\,{}^{\circ}\text{C}$? The specific heat capacity of water is $4200\ \text{J/(kg}\,{}^{\circ}\text{C)}$.

Rearranging $c = \frac{\Delta E}{m\,\Delta\theta}$ gives $\Delta E = mc\,\Delta\theta$, with $\Delta\theta = 70 - 20 = 50\,{}^{\circ}\text{C}$:

Melting 熔化 and boiling 沸腾 need energy, but the temperature stays the same while the state changes. This energy breaks the forces between particles. For water at normal air pressure, melting is at $0\,{}^{\circ}\text{C}$ and boiling at $100\,{}^{\circ}\text{C}$.

Evaporation 蒸发 is when a liquid changes to a gas at its surface, below the boiling point. The fastest particles escape from the surface. Because the fastest (most energetic) particles leave, the average energy of those left behind falls, so the liquid cools down 冷却.

Evaporation is faster when the temperature is higher, the surface area is larger, and there is more air movement over the surface.

Thermal energy moves from hotter places to colder places in three ways.

Conduction

Conduction 热传导 is the transfer of thermal energy through a material without the material moving. Heated particles vibrate more and pass the energy to their neighbours. In metals, free (delocalised) electrons 自由电子 carry energy quickly, so metals are good thermal conductors 热导体.

Materials that conduct badly (like air, wood and plastic) are thermal insulators 热绝缘体.

Convection

Convection 对流 happens in liquids and gases. When a fluid is heated it expands, becomes less dense, and rises. Cooler, denser fluid sinks to take its place. This circle of moving fluid is a convection current.

Convection cannot happen in a solid because the particles cannot move from place to place.

Radiation

Thermal radiation 热辐射 is energy carried by infrared 红外线 waves. All objects emit it, and it needs no material to travel through — it can cross empty space (this is how energy reaches us from the Sun).

A surface that is dull 暗淡 and black is a good emitter 发射体 and a good absorber 吸收体 of infrared. A surface that is shiny and white is a poor emitter and a good reflector 反射体.

An object stays at a constant temperature when it emits energy at the same rate as it absorbs energy. The rate of emission is greater when the surface is hotter and larger.

• In the kinetic particle model, heating a gas makes its particles move faster and hit the walls harder and more often, so the pressure rises. The particles themselves do not get bigger.
• Evaporation happens only at the surface and at any temperature; boiling happens throughout the liquid at one fixed temperature. Evaporation cools the liquid left behind, because the fastest particles escape.
• During melting and boiling the temperature stays constant even though energy is still being supplied — that energy breaks the forces between particles.
• For specific heat capacity use $\Delta E = mc\,\Delta\theta$, where $\Delta\theta$ is the change in temperature, not the final temperature.
• Dull black surfaces are the best emitters and absorbers of infrared; shiny, light surfaces are the best reflectors. Convection needs a fluid to flow, so it cannot happen in a solid.

A wave 波 carries energy 能量 from place to place without carrying matter. For example, a water wave makes a floating cork bob up and down, but the cork does not travel along with the wave.

Describing a wave

• wavefront 波前: a line joining points on a wave that move together (for example, the top of one ripple)
• wavelength 波长 ($\lambda$): the distance between two neighbouring wavefronts (one full wave)
• frequency 频率 ($f$): the number of waves passing a point each second, measured in hertz (Hz)
• crest 波峰 (top) and trough 波谷 (bottom)
• amplitude 振幅: the largest distance a point moves from its rest position
• wave speed 波速 ($v$): how fast a wavefront travels

These are linked by the wave equation:

Worked example. A sound wave travels at $340\ \text{m/s}$ and has a frequency of $170\ \text{Hz}$. Find its wavelength.

Rearranging $v = f\lambda$ gives $\lambda = \dfrac{v}{f}$:

Two types of wave

• In a transverse wave 横波 the particles vibrate at right angles (90°) to the direction the wave travels (its propagation 传播). Light and water waves are transverse.
• In a longitudinal wave 纵波 the particles vibrate along the same direction as the wave travels. Sound is longitudinal.

Wave behaviour

All waves can show three behaviours, which you can see in a ripple tank 波纹水槽:

• reflection 反射: the wave bounces off a surface.
• refraction 折射: the wave changes speed (and usually direction) when it enters a different material or depth.
• diffraction 衍射: the wave spreads out after passing through a gap or around an edge. The spreading is greatest when the gap is about the same size as the wavelength.

Reflection

When light hits a mirror, it reflects. We measure angles from the normal 法线 (a line at 90° to the surface).

The law of reflection: the angle of incidence 入射角 equals the angle of reflection 反射角.

A plane mirror 平面镜 forms an image that is the same size as the object, the same distance behind the mirror, and virtual (it cannot be caught on a screen).

Refraction

When light passes from one material into another, it changes speed and bends. The angle in the second material is the angle of refraction 折射角.

The refractive index 折射率 $n$ compares the speed of light in the two materials:

Worked example. A ray of light passes from air into glass. The angle of incidence is 60° and the angle of refraction is 35°. Find the refractive index of the glass. (Take $\sin i = 0.87$ and $\sin r = 0.57$.)

When light tries to leave glass or water and the angle is too large, it cannot get out and instead reflects completely. This is total internal reflection 全反射. It happens when the angle inside is bigger than the critical angle 临界角 $c$:

This effect is used in optical fibres 光纤, thin glass threads that carry light signals for telephones and the internet.

Lenses

A converging lens 凸透镜 (fat in the middle) bends parallel rays inwards to a point called the principal focus 焦点. The distance from the lens to this point is the focal length 焦距. A diverging lens 凹透镜 (thin in the middle) spreads rays out.

A converging lens can form a real image 实像 (rays really meet; can be shown on a screen) or, when the object is very close, a virtual image 虚像 (rays only seem to come from it). Used close to the eye, a converging lens is a magnifying glass 放大镜.

Dispersion

A glass prism 棱镜 splits white light into the colours of the spectrum 光谱. This splitting is called dispersion 色散.

The order of colours is red, orange, yellow, green, blue, indigo, violet. Red light has the longest wavelength and the lowest frequency; violet is the opposite. Light of a single frequency (one pure colour) is monochromatic 单色.

The electromagnetic spectrum is a family of waves that all travel at the same high speed in a vacuum 真空, $3.0 \times 10^8\ \text{m/s}$. In order from longest wavelength (lowest frequency) to shortest:

As you go from radio waves to gamma rays, the frequency rises, the wavelength falls, and the energy (and danger) rises.

Digital and analogue signals

Radio waves and microwaves carry information as signals, and a signal is either analogue 模拟 or digital 数字. An analogue signal varies continuously and can take any value; a digital signal is a stream of just two values, on or off (1 or 0).

Modern communication prefers digital signalling for two reasons the exam asks for:

• a higher rate of data transmission;
• a greater range: a weak digital signal can be regenerated back to a clean 1/0 exactly, because only two levels have to be told apart, so noise picked up along the way is removed. An analogue signal cannot be cleaned up this way, so its noise builds up.

Sound is made by a vibrating object. It is a longitudinal wave: the air is squeezed into a compression 压缩 (particles close together) and stretched into a rarefaction 稀疏 (particles far apart).

• Sound needs a medium 介质 (a material) to travel through, so it cannot travel through a vacuum.
• Humans can hear frequencies from about $20\ \text{Hz}$ to $20\,000\ \text{Hz}$.
• Sound travels much slower than light (about $340\ \text{m/s}$ in air), and faster in liquids and solids than in gases.
• A larger amplitude makes a louder sound (greater loudness 响度); a higher frequency makes a higher pitch 音调. So a dolphin's rapid clicks are high-pitched, and a hard drum-hit (big vibration) is loud.

A reflected sound is an echo 回声. You can find the speed of sound by timing an echo over a known distance.

Worked example. A student stands 85 m from a large wall and claps once. The echo returns 0.50 s later. Find the speed of sound.

The sound travels to the wall and back, a distance of $2 \times 85 = 170\ \text{m}$, in $0.50\ \text{s}$:

Ultrasound 超声波 is sound above $20\,000\ \text{Hz}$ – too high for humans to hear. Its uses rely on reflection: sonar measures water depth, medical scanning images a baby or soft tissue, and non-destructive testing finds cracks inside metal without cutting it open. Like an echo, an ultrasound pulse travels there and back, so halve the total distance to reach the object.

Worked example. A sonar pulse returns from the seabed $0.10\ \text{s}$ after it is sent; sound travels at $1500\ \text{m/s}$ in water. The pulse covers $s = v\times t = 1500\times0.10 = 150\ \text{m}$ there and back, so the sea is $150/2 = 75\ \text{m}$ deep.

• Learn $v = f\lambda$ and be ready to rearrange it. Measure all angles of incidence, reflection and refraction from the normal (the line at 90° to the surface), never from the surface itself.
• Transverse waves vibrate across the direction of travel (light, water); longitudinal waves vibrate along it (sound). Sound needs a medium, so it cannot cross a vacuum; light can.
• Total internal reflection happens only when light travels from a denser material to a less dense one and the angle inside is bigger than the critical angle.
• Know the electromagnetic spectrum in order — radio, microwave, infrared, visible, ultraviolet, X-ray, gamma. All travel at the same speed in a vacuum; frequency and energy rise from radio to gamma.
• Going into a denser material (air → glass) light slows down and bends towards the normal; leaving it (glass → air) light speeds up and bends away.

A magnet 磁体 can attract some metals. Every magnet has two ends, called poles 磁极: a north pole 北极 (N pole) and a south pole 南极 (S pole).

The rule for two poles is like the rule for charges:

• Poles that are the same (N and N, or S and S) repel 排斥 (push apart).
• Poles that are different (N and S) attract 吸引 (pull together).

A magnet attracts a magnetic material 磁性材料, such as iron, steel, cobalt and nickel. Other materials (copper, plastic, wood) are non-magnetic and feel no force.

Induced magnetism

Put a piece of iron near or touching a magnet, and the iron becomes a magnet itself. This is induced magnetism 感应磁性. The end of the iron nearest the magnet gains the opposite pole, so the two then attract.

Temporary and permanent magnets

• Soft iron 软铁 is easy to magnetise 磁化 but loses its magnetism quickly. It is used for a temporary magnet 临时磁体.
• Steel 钢 is harder to magnetise but keeps its magnetism. It is used for a permanent magnet 永磁体.

So an unmagnetised 未磁化 piece of soft iron is the best core for an electromagnet, while steel is best for a bar magnet.

Magnetic fields

A magnetic field 磁场 is a region 区域 where a magnetic pole feels a force. We draw it with magnetic field lines 磁场线:

• The lines come out of the N pole and go into the S pole.
• The field direction at a point is the direction of the force on the N pole of a small test magnet placed there.
• Where the lines are close together the field is strong; where they are far apart the field is weak.

You can show the pattern by sprinkling iron filings 铁屑 on paper over a magnet, or by moving a small plotting compass 指南针 around it (the needle points along the field).

Uses of magnets

• Permanent magnets: fridge door catches, compass needles, loudspeakers.
• Electromagnets 电磁铁 (magnetic only while a current flows): cranes that lift scrap iron, electric bells, relays. An electromagnet can be switched on and off and made stronger, which a permanent magnet cannot.

Magnetic forces happen because the fields of the two magnets push and pull on each other.

There are two kinds of electric charge 电荷: positive charge 正电荷 and negative charge 负电荷. The rule is like the rule for poles — same charges repel, different charges attract.

Charging by friction

When you rub two different materials together, electrons 电子 (tiny negative particles) move from one to the other. This is charging by friction 摩擦起电.

• The material that gains electrons becomes negative.
• The material that loses electrons becomes positive.

Only the negative electrons move; the positive charge stays in place. For example, a plastic rod rubbed with a cloth becomes negative because electrons move from the cloth onto the rod, leaving the cloth positive.

Conductors and insulators

• A conductor 导体 (copper and other metals) lets charge flow through it easily, because it has free electrons that can move.
• An insulator 绝缘体 (plastic, rubber, glass) does not let charge flow, because its electrons cannot move freely.

To test a material, join it in a circuit with a lamp and a battery: the lamp lights only for a conductor.

Electric fields and ions

Charge is measured in coulombs 库仑 (C). An electric field 电场 is a region where an electric charge feels a force. Its direction at a point is the direction of the force on a positive charge. Simple field patterns (the arrows show the direction):

• around a point charge 点电荷: straight lines, pointing away from a positive charge and towards a negative charge;
• around a charged ball (sphere): the same, spreading out evenly all around;
• between two parallel plates with opposite charges: straight, evenly spaced lines from the positive plate to the negative plate.

An atom is normally neutral. If it loses electrons it becomes a positive ion 离子; if it gains electrons it becomes a negative ion.

An electric current 电流 is a flow of electric charge. It is measured in amperes 安培 (A) with an ammeter 电流表, joined in series in the circuit.

Current is the charge that passes a point each second:

Here $I$ is current (A), $Q$ is charge (C) and $t$ is time (s). Rearranged, $Q = It$.

Worked example. A current of $3.0\ \text{A}$ flows through a lamp for $20\ \text{s}$. How much charge passes through it?

In a metal the current is a flow of free electrons 自由电子. There are two "directions" to know:

• Conventional current 常规电流 is taken to flow from + to − round the outside of the cell.
• The free electrons really drift the other way, from − to +.

A direct current 直流电 (d.c.) always flows one way, as from a battery. An alternating current 交流电 (a.c.) keeps swapping direction many times each second, as from the mains supply 市电.

A cell gives energy 能量 to the charges that move through it. Two quantities describe this, and both are measured in volts 伏特 (V).

• The electromotive force 电动势 (e.m.f.) of a source is the electrical work it does to drive unit charge all the way round a complete circuit 电路.
• The potential difference 电势差 (p.d.) across a component is the work done by unit charge as it passes through that component.

A voltmeter 电压表 measures e.m.f. or p.d. It is joined in parallel (across the component).

Both are work done per unit charge:

where $W$ is the energy transferred (J) and $Q$ is the charge (C). For example, if a cell does $120\ \text{J}$ of work moving $60\ \text{C}$ of charge round a circuit, its e.m.f. is $120 / 60 = 2\ \text{V}$.

Resistance 电阻 measures how hard it is for current to flow. A bigger resistance gives a smaller current. It is measured in ohms 欧姆 (Ω).

To find the resistance of a component, join an ammeter in series (to read $I$) and a voltmeter across it (to read $V$), then divide.

Worked example. A $12\ \text{V}$ battery drives a current of $0.50\ \text{A}$ through a lamp. Find the lamp's resistance.

For a metal wire at constant temperature:

• a longer wire has a bigger resistance — resistance is directly proportional 成正比 to length, $R \propto l$;
• a thicker wire has a smaller resistance — resistance is inversely proportional 成反比 to cross-sectional area 横截面积, $R \propto \dfrac{1}{A}$.

So doubling the length doubles the resistance; doubling the area halves it. (Area depends on the diameter squared, so a small change in diameter changes the resistance a lot.)

Current–voltage graphs show how three components behave:

A circuit transfers energy from a source (a cell or the mains) to the components, and then into the surroundings (often as heat, light or sound).

Electrical power 电功率 is the energy transferred each second, measured in watts 瓦特 (W):

The electrical energy 电能 transferred in a time $t$, measured in joules 焦耳 (J), is:

Worked example. A $12\ \text{V}$ motor draws a current of $2.0\ \text{A}$. Find its power, and the energy it transfers in $30\ \text{s}$.

The kilowatt-hour

Home electricity bills use a bigger energy unit, the kilowatt-hour 千瓦时 (kWh). One kilowatt-hour is the energy used by a $1\ \text{kW}$ appliance 电器 in $1$ hour.

For example, a $2\ \text{kW}$ heater 加热器 used for $3$ hours uses $2 \times 3 = 6\ \text{kWh}$. If one kWh costs $20$ cents, the cost is $6 \times 20 = 120$ cents.

Circuit components

You should know these components and how they behave:

Series and parallel

In a series 串联 circuit the parts form one single loop:

• the current is the same at every point;
• the supply p.d. is shared between the components;
• cells in series add their e.m.f.s (when they point the same way);
• resistors in series add up: $R_{\text{total}} = R_1 + R_2 + \dots$

In a parallel 并联 circuit the parts are on separate branches:

• each branch gets the full supply p.d.;
• the current splits, so the current from the source is bigger than the current in any one branch;
• the total resistance 总电阻 is less than the smallest single resistance.

Lamps in a home are wired in parallel: each gets the full voltage, and if one fails the others stay on.

For calculations (with the rules above):

• at a junction 节点, the total current flowing in equals the total current flowing out;
• in series, the supply p.d. equals the sum of the p.d.s across the components;
• in parallel, the p.d. across each branch is the same;
• two resistors in parallel combine as

Worked example. A $6\ \Omega$ resistor and a $3\ \Omega$ resistor are connected in parallel. Find their combined resistance.

Notice the combined resistance ($2\ \Omega$) is smaller than the smaller of the two resistors.

Potential dividers

Two resistors in series share the supply voltage. This is a potential divider 分压器. For the same current, a bigger resistance has a bigger p.d. across it, so the bigger resistor takes the bigger share:

A variable potential divider (or a variable resistor) lets you change the output voltage smoothly, for example from $0\ \text{V}$ up to the full supply. If you use a thermistor or an LDR as one of the resistors, the output voltage changes with temperature or light — handy for switching a heater or a lamp on and off automatically.

A home is fed by the mains. The mains is dangerous if it is used wrongly.

Hazards

These are hazards 危险 (dangers) with mains electricity:

• damaged insulation 绝缘层 — bare wires can give a shock or start a fire;
• overheating 过热 cables — too much current makes a cable hot, which can start a fire;
• damp 潮湿 conditions — water lets current pass into a person, raising the risk of a shock;
• overloading 过载 — plugging too many appliances into one socket 插座 draws too much current.

Live, neutral and earth

A mains cable has three wires:

• the live wire 火线 carries the high voltage;
• the neutral wire 零线 completes the circuit at about zero voltage;
• the earth wire 地线 is a safety wire joined to the ground.

A switch (and a fuse) must be fitted in the live wire. Then, when the switch is off, the appliance is cut off from the high voltage and is safe to touch.

Fuses, trip switches and earthing

A fuse is a thin wire that melts if the current gets too big, breaking the circuit before the cable overheats. Choose a fuse rating 额定值 just above the normal working current — for example a $13\ \text{A}$ fuse for an appliance that normally uses about $10\ \text{A}$.

A trip switch 跳闸开关 (circuit breaker) does the same job but acts faster and can be reset instead of replaced.

The metal casing 外壳 of an appliance must be made safe in one of two ways:

• earthed 接地: the casing is joined to the earth wire. If a live wire touches the casing, a large current flows to earth and blows the fuse.
• double-insulated 双重绝缘: the casing is plastic, so it can never become live. Such an appliance needs no earth wire; its fuse still protects the cable.

The magnetic effect of a current

A current in a wire makes a magnetic field around it.

• Around a straight wire the field lines are circles around the wire; the field is stronger close to the wire. Reverse the current and the field reverses.
• A solenoid 螺线管 (a long coil 线圈 of wire) makes a field just like a bar magnet, with a N pole at one end and a S pole at the other. The field inside is strong and even.

You can show both patterns with iron filings or a plotting compass. The field gets stronger if you increase the current, add more turns, or place a soft-iron core inside.

The magnetic effect is used in a relay and in a loudspeaker: in a loudspeaker 扬声器 a changing current in a coil makes the coil push and pull a paper cone, which moves the air and makes sound.

Electromagnetic induction

When a wire moves across a magnetic field, or the field through a coil changes, an e.m.f. is induced in the wire. If the wire is part of a complete circuit, this e.m.f. drives a current. This is electromagnetic induction 电磁感应.

To show it: move a magnet in and out of a coil joined to a sensitive meter, and watch the needle flick. The induced e.m.f. is bigger when you use a stronger magnet, move faster, or use more turns on the coil. The induced e.m.f. always acts to oppose the change that causes it.

The a.c. generator

An a.c. generator 交流发电机 turns movement into electricity. A coil is spun in a magnetic field (or a magnet is spun near a coil). As it turns, the field through the coil keeps changing, so an alternating e.m.f. is induced.

• Slip rings 滑环 and carbon brushes 电刷 carry the current out to the circuit while the coil keeps turning.
• The e.m.f. is largest when the coil is flat (moving fastest across the field) and zero when the coil is upright (moving along the field). So the e.m.f.–time graph is a wave: peak, zero, opposite peak, zero, for each turn.

Force on a current-carrying conductor

When a current-carrying wire lies in a magnetic field, the field of the wire and the field of the magnet push on each other, so the wire feels a force. This is the motor effect.

• Reverse the current, or reverse the field, and the force reverses.
• Make the current bigger or the field stronger, and the force is bigger.

The force, the field and the current are at right angles to one another. You can find the force direction with the left-hand rule: thumb = force (motion), first finger = field (N to S), second finger = current.

A moving stream of charged particles is a current, so a magnetic field pushes it sideways too — it deflects 偏转 the beam. (Remember electrons flow opposite to the conventional current.)

The d.c. motor

A coil carrying a current in a magnetic field feels a turning effect 转动效应, because the forces on its two sides act in opposite directions. This is a d.c. motor 直流电动机. The turning effect is bigger with more turns on the coil, a bigger current, or a stronger field.

A split-ring commutator 换向器 swaps the current direction in the coil every half-turn. This keeps the coil turning the same way instead of stopping after half a turn.

The transformer

A transformer changes the size of an a.c. voltage. It has two coils wound on a soft-iron core 软铁芯:

• the primary coil 原线圈 takes in the a.c. voltage;
• the secondary coil 副线圈 gives out the changed voltage.

The a.c. in the primary makes a changing magnetic field in the core. The core carries this field to the secondary, where it induces an a.c. e.m.f. The voltages and the numbers of turns are linked by:

Worked example. A transformer has $1200$ turns on the primary coil and $100$ turns on the secondary coil. The primary is connected to a $240\ \text{V}$ a.c. supply. Find the secondary voltage.

Fewer turns on the secondary, so this is a step-down transformer.

If the secondary has more turns it is a step-up 升压 transformer (voltage rises); fewer turns make a step-down 降压 transformer (voltage falls). For example, a transformer changing $240\ \text{V}$ to $12\ \text{V}$ is a step-down type, and the primary has $20$ times as many turns as the secondary.

If a transformer is 100% efficient, the power in equals the power out:

So a step-up transformer raises the voltage but lowers the current.

Why we use high voltage to send power

Electricity is sent across the country by high-voltage transmission 高压输电. The power lost as heat in the cables is

where $R$ is the resistance of the cables. A step-up transformer raises the voltage and so lowers the current for the same power ($P = IV$). A smaller current means much less power wasted in the cables. A step-down transformer then lowers the voltage again to a safe value before it reaches homes.

• Current is the same everywhere in a series circuit; in a parallel circuit it splits between the branches. Voltage (p.d.) is shared out in series, but is the same across every parallel branch.
• Adding resistors in series increases the total resistance ($R_1 + R_2$); adding them in parallel makes the total less than the smallest single resistor.
• An ammeter goes in series and has very low resistance; a voltmeter goes in parallel across a component and has very high resistance.
• In a transformer $\dfrac{V_p}{V_s} = \dfrac{N_p}{N_s}$: more turns on the secondary steps the voltage up, fewer steps it down. Transformers only work on a.c.
• Power is sent across country at high voltage so the current — and the heat wasted in the cables, $P = I^2R$ — is small.
• Fit the switch and the fuse in the live wire, and choose a fuse rating just above the appliance's normal working current.

An atom 原子 is made of a tiny central nucleus 原子核 with electrons 电子 moving around it (in orbit 轨道, like planets around the Sun).

• The nucleus has a positive charge 电荷.
• The electrons have a negative charge.
• The atom as a whole is neutral, because the positive and negative charges are equal.

Almost all the mass 质量 is in the nucleus, but the nucleus is very small compared with the whole atom. So an atom is mostly empty space.

Ions

An atom is neutral, but it can gain or lose electrons to become an ion 离子.

• Lose one or more electrons → a positive ion (now there are more protons than electrons).
• Gain one or more electrons → a negative ion.

The alpha-scattering experiment

This experiment gave the evidence for the nuclear model. Alpha particles α粒子 (small, fast, positive) were fired at a very thin gold foil 金箔, and the scattering 散射 (the way they bounced off) was watched.

The results and what they tell us:

• Almost all the alpha particles went straight through. → The atom is mostly empty space.
• A few were deflected 偏转 (bent) through small angles. → The nucleus has a positive charge, which pushes the positive alpha particles away.
• A very few bounced almost straight back. → The nucleus is very small and very heavy, and holds most of the mass of the atom.

The nucleus is made of two kinds of particle, together called nucleons 核子:

• protons 质子, which have a relative 相对 charge of $+1$;
• neutrons 中子, which have a relative charge of $0$ (they are neutral).

An electron has a relative charge of $-1$. A proton and a neutron each have a relative mass of about $1$; an electron is almost massless in comparison.

Two numbers describe a nucleus:

• the proton number 质子数 $Z$ (also called the atomic number) — the number of protons;
• the nucleon number 核子数 $A$ (also called the mass number) — the number of protons plus neutrons.

So the number of neutrons is $A - Z$.

We write a nucleus in nuclide 核素 notation:

where X is the chemical symbol. For example, $^{197}_{\ 79}\text{Au}$ has $79$ protons and $197 - 79 = 118$ neutrons. The relative charge of the whole nucleus is just $+Z$ (here $+79$), and its relative mass is about $A$.

Isotopes

Isotopes 同位素 are atoms of the same element (the same $Z$) but with different numbers of neutrons (different $A$). They behave the same in chemistry but differently in the nucleus. For example, $^{12}_{\ 6}\text{C}$ and $^{14}_{\ 6}\text{C}$ are both carbon.

Nuclear fission and fusion

In nuclear fission 核裂变, a heavy nucleus absorbs a neutron and then splits into two smaller nuclei, giving out two or three neutrons and a lot of energy 能量:

The top numbers (nucleon numbers) balance on both sides, and so do the bottom numbers (proton numbers). You can use this to find a missing number — for example, how many neutrons are released.

In nuclear fusion 核聚变, two light nuclei join to make a heavier one, also giving out energy. This is how the Sun makes its energy, joining hydrogen 氢 nuclei to make helium 氦. The reaction below — two heavy forms of hydrogen (deuterium and tritium) joining into helium — is the one used in fusion reactors on Earth:

In both fission and fusion, a small amount of mass is lost and turned into energy.

A nucleus that is unstable 不稳定 will sooner or later break down and give out radiation 辐射. This is radioactive 放射性 decay 衰变. A nucleus may be unstable because it has too many neutrons, or because it is too heavy.

Decay is spontaneous 自发 (it happens on its own, and you cannot speed it up or slow it down) and random 随机 (you cannot say which nucleus will decay next, or exactly when).

Background radiation

Some radiation is around us all the time. This is background radiation 背景辐射. Its main sources are:

• radon 氡 gas in the air (usually the biggest source);
• rocks and buildings;
• food and drink;
• cosmic rays 宇宙射线 from space.

Measuring radiation

Radiation can be measured with a detector 探测器 joined to a counter 计数器. The count rate 计数率 is the number of counts each second (or each minute).

To find the true count rate from a source, first measure the background count rate on its own, then subtract it. The answer is the corrected 修正 count rate:

Worked example. A detector placed next to a source reads $250$ counts/min. With the source taken away, the background count rate is $30$ counts/min. Find the corrected count rate.

The radiation can be one of three types. Each type is ionising 电离, which means it can knock electrons off atoms in its path.

So an alpha particle is the most ionising but the least penetrating 穿透 (it is easily absorbed 吸收). A beta particle β粒子 is in the middle. Gamma radiation γ射线 is the least ionising but the most penetrating.

We can explain the ionising effects from charge and kinetic energy 动能: an alpha particle has a large charge ($+2$) and is slow and heavy, so it pulls strongly on the electrons it passes and ionises a lot. A beta particle has a smaller charge and moves faster, so it ionises less.

Deflection in fields

Because alpha and beta particles are charged, they are deflected by an electric field 电场 and by a magnetic field 磁场. They bend in opposite directions, because their charges have opposite signs, and the lighter beta particle bends more. Gamma rays have no charge, so they are not deflected at all.

When a nucleus decays, the nucleon and proton numbers must balance on both sides.

Alpha decay — the nucleus loses 2 protons and 2 neutrons, so $A$ falls by $4$ and $Z$ falls by $2$. It becomes a different element:

Worked example. A radium nucleus $^{226}_{\ 88}\text{Ra}$ emits an alpha particle. Find the nucleon number and proton number of the new nucleus.

Alpha decay lowers $A$ by $4$ and $Z$ by $2$:

So the new nucleus (radon) has nucleon number $222$ and proton number $86$.

Beta decay — inside the nucleus a neutron changes into a proton plus an electron:

The fast electron leaves as the beta particle. So $A$ stays the same but $Z$ rises by $1$, giving a different element:

Gamma emission — the nucleus loses only energy, so $A$ and $Z$ do not change. Alpha and beta decay leave the nucleus more stable 稳定; gamma is often given out at the same time to carry away spare energy.

Because decay is random, we cannot follow one nucleus. Instead we describe a large sample 样品 using its half-life.

The half-life 半衰期 of an isotope is the time taken for half the unstable nuclei in a sample to decay. After each half-life, the count rate (or the number of unstable nuclei left) falls to half.

For example, if a source has a count rate of $800$ counts/min and a half-life of $3$ hours:

After $6$ hours (two half-lives) the count rate has halved twice: $800 \to 400 \to 200$. You can read a half-life off a decay graph by finding the time for the count rate to drop from any value to half of it.

Worked example. The activity of a source falls from $800$ counts/min to $100$ counts/min. Its half-life is $5$ days. How long did this take?

Count the halvings: $800 \to 400 \to 200 \to 100$ is three half-lives, so the time is $3 \times 5 = 15\ \text{days}$.

The isotope chosen for a job depends on its type of radiation and its half-life:

• smoke alarms 烟雾报警器 use an alpha source (alpha is easily blocked, so it is safe outside the alarm, and a long half-life means it lasts for years);
• using radiation on food, or on equipment, kills bacteria 细菌 and germs — this needs penetrating gamma rays to sterilise 消毒 the sealed item;
• measuring and controlling the thickness of paper or metal sheets uses a beta source (the amount that passes through changes with the thickness);
• gamma rays are used to find and to treat cancer 癌症 inside the body, because they can pass out of (or into) the body.

Ionising radiation harms living cells 细胞. It can cause cell death, mutations 突变 (changes to the genes) and cancer.

When working with radioactive sources, keep the dose 剂量 (the amount of radiation received) low by:

• reducing the exposure 照射 time — spend as little time near the source as possible;
• increasing the distance between you and the source;
• using shielding 屏蔽, such as lead, between the source and your body.

Radioactive sources should be handled with tongs (not bare hands), kept pointing away from people, and stored in a lead-lined box.

• The nucleon number (top) is protons + neutrons; the proton number (bottom) is protons only. Number of neutrons = nucleon number − proton number.
• Isotopes have the same proton number but different nucleon numbers — the same element with a different number of neutrons.
• Rank the radiations two ways: alpha is the most ionising but least penetrating (stopped by paper); gamma is the least ionising but most penetrating (needs thick lead). Beta is in between (stopped by a few mm of aluminium).
• In every decay equation the top numbers must balance and the bottom numbers must balance. Alpha decay: $A-4$, $Z-2$. Beta decay: $A$ unchanged, $Z+1$.
• Always subtract the background count rate before using a source's readings. After $n$ half-lives the count rate has halved $n$ times — count the halvings rather than guessing from the total time.

The Earth spins (rotates 自转) on its axis 轴 once in about $24$ hours. The axis is tilted 倾斜 (not straight up). This spin gives us day and night, and makes the Sun 太阳 appear to move across the sky each day.

The Earth also moves around the Sun in an orbit 轨道, once in about $365$ days (one year). Because the axis is tilted, different parts of the Earth lean towards the Sun at different times of the year. This gives the seasons 季节: it is summer in the half of the Earth that leans towards the Sun.

The Moon 月球 orbits the Earth once in about one month. As it goes round, we see different amounts of its lit side, which gives the phases 月相 of the Moon (new moon, half moon, full moon).

So, from shortest to longest: one day (Earth's spin) < one month (Moon's orbit) < one year (Earth's orbit).

For an object going round a circle, the distance for one full orbit is the circumference 周长 $2\pi r$, where $r$ is the radius of the orbit. The orbital speed 轨道速率 is this distance divided by the period 周期 $T$ (the time for one orbit):

The same equation works for planets, moons and satellites.

Worked example. A space station orbits the Earth at a radius of $r = 7000\ \text{km}$ and takes $T = 5800\ \text{s}$ for one orbit. Find its orbital speed.

First convert the radius to metres: $7000\ \text{km} = 7.0 \times 10^6\ \text{m}$. Then

The Solar System 太阳系 has one star, the Sun, at its centre. Around it move the eight planets 行星. In order from the Sun they are: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune.

• The four planets nearest the Sun are small and rocky 岩石.
• The four planets furthest from the Sun are large and gaseous 气态 — they are made mostly of gas 气体, with no solid surface to stand on.
• The two nearer giants, Jupiter and Saturn, are gas giants 气态巨行星. The two outer giants, Uranus and Neptune, are ice giants 冰巨行星: they hold much more ice, so they are not true gas giants.