Electromagnetic waves form a fundamental concept in physics, encompassing a broad spectrum that includes radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. Understanding that all electromagnetic waves are transverse in nature and propagate at a constant speed in free space is crucial for students studying the "Electromagnetic Spectrum" chapter under the "Waves" unit in AS & A Level Physics (9702). This knowledge not only underpins various technological applications but also provides a foundation for exploring advanced physical phenomena.

Key Concepts

Definition of Electromagnetic Waves

Electromagnetic waves are oscillations of electric and magnetic fields that propagate through space. Unlike mechanical waves, they do not require a medium to travel, enabling them to move through the vacuum of space. These waves are characterized by their wavelength, frequency, and speed, which are interrelated through the equation:

$$ c = \lambda \cdot f $$

where $c$ is the speed of light in free space ($3 \times 10^8 \, m/s$), $\lambda$ is the wavelength, and $f$ is the frequency.

Transverse Nature of Electromagnetic Waves

Electromagnetic waves are inherently transverse, meaning that the oscillations of the electric ($\vec{E}$) and magnetic ($\vec{B}$) fields are perpendicular to the direction of wave propagation. Additionally, these fields are perpendicular to each other, forming a right-handed coordinate system. This transverse configuration is essential for the wave's ability to carry energy and momentum across space.

The transverse nature can be visualized using the right-hand rule: if the thumb points in the direction of wave propagation, the index finger represents the electric field, and the middle finger indicates the magnetic field.

Speed of Electromagnetic Waves in Free Space

All electromagnetic waves travel at the same speed in free space, denoted by $c$, which is approximately $3 \times 10^8 \, m/s$. This constant speed arises from the intrinsic properties of the vacuum, specifically the permittivity ($\epsilon_0$) and permeability ($\mu_0$) of free space, as described by the equation:

$$ c = \frac{1}{\sqrt{\epsilon_0 \mu_0}} $$

This universality implies that regardless of the wave's frequency or wavelength, its speed remains unchanged in a vacuum. This principle is foundational in the theory of relativity and underpins the synchronization of various physical phenomena.

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all possible electromagnetic waves, classified based on their wavelength and frequency. From longest to shortest wavelength, the spectrum includes:

Radio Waves
Microwaves
Infrared
Visible Light
Ultraviolet
X-Rays
Gamma Rays

Each category has distinct properties and applications, such as radio waves for communication, microwaves for cooking and radar, infrared for thermal imaging, visible light for vision, ultraviolet for sterilization, X-rays for medical imaging, and gamma rays for cancer treatment.

Wave Equations and Mathematical Descriptions

The behavior of electromagnetic waves is governed by Maxwell's equations, which describe how electric and magnetic fields are generated and altered by each other and by charges and currents. In free space, these equations simplify to:

$$ \nabla \cdot \vec{E} = 0 $$ $$ \nabla \cdot \vec{B} = 0 $$ $$ \nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t} $$ $$ \nabla \times \vec{B} = \mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t} $$

Solutions to these equations reveal that electromagnetic waves are transverse and propagate at the speed $c$. The wave equations for the electric and magnetic fields in free space are:

$$ \nabla^2 \vec{E} = \mu_0 \epsilon_0 \frac{\partial^2 \vec{E}}{\partial t^2} $$ $$ \nabla^2 \vec{B} = \mu_0 \epsilon_0 \frac{\partial^2 \vec{B}}{\partial t^2} $$

Energy and Momentum in Electromagnetic Waves

Electromagnetic waves carry energy and momentum, which are fundamental to their interactions with matter. The energy density ($u$) and Poynting vector ($\vec{S}$) describe the energy per unit volume and the energy flux, respectively:

$$ u = \frac{1}{2} (\epsilon_0 E^2 + \frac{B^2}{\mu_0}) $$ $$ \vec{S} = \vec{E} \times \vec{B} $$

The Poynting vector indicates the direction of energy propagation and is parallel to the direction of wave travel, reaffirming the transverse nature of electromagnetic waves.

Polarization of Electromagnetic Waves

Polarization refers to the orientation of the electric field vector in an electromagnetic wave. Since $\vec{E}$ oscillates perpendicular to the direction of propagation, electromagnetic waves can exhibit various polarization states, including linear, circular, and elliptical polarization. Polarization has significant applications in areas such as optics, telecommunications, and display technologies.

Propagation in Different Media

While electromagnetic waves travel at speed $c$ in free space, their speed can vary when propagating through different media due to interactions with the material's atoms and molecules. The speed of light in a medium is given by:

$$ v = \frac{c}{n} $$

where $n$ is the refractive index of the medium. However, the statement under discussion pertains specifically to free space, where $n = 1$ and thus $v = c$ for all electromagnetic waves.

Applications of Transverse Electromagnetic Waves

Understanding that electromagnetic waves are transverse and travel uniformly at $c$ in free space underpins numerous technological advancements. Examples include:

Communication Systems: Radio and microwave transmissions rely on the transverse nature of EM waves for signal propagation.
Optical Technologies: Fiber optics utilize the properties of light waves to transmit data over long distances with minimal loss.
Medical Imaging: X-rays and gamma rays are employed in diagnostic procedures due to their ability to penetrate various materials.
Astronomy: The study of electromagnetic radiation from celestial objects provides insights into the universe's structure and composition.

Advanced Concepts

Maxwell's Equations and Wave Solutions

Maxwell's equations are the cornerstone of classical electromagnetism, detailing how electric and magnetic fields interact and propagate as waves. In free space, these equations predict that changes in electric fields generate magnetic fields and vice versa, leading to the self-sustaining propagation of electromagnetic waves. The derivation of wave equations from Maxwell's equations demonstrates that electromagnetic waves are inherently transverse and travel at speed $c$.

Starting with Faraday's law of induction:

$$ \nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t} $$

and Ampère's law (with Maxwell's addition):

$$ \nabla \times \vec{B} = \mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t} $$

Taking the curl of both sides and substituting, we arrive at the wave equations:

$$ \nabla^2 \vec{E} = \mu_0 \epsilon_0 \frac{\partial^2 \vec{E}}{\partial t^2} $$ $$ \nabla^2 \vec{B} = \mu_0 \epsilon_0 \frac{\partial^2 \vec{B}}{\partial t^2} $$>

These equations confirm that both electric and magnetic fields satisfy the conditions of a transverse wave propagating at speed $c$.

Doppler Effect for Electromagnetic Waves

The Doppler effect describes the change in frequency and wavelength of a wave in relation to an observer moving relative to the source. For electromagnetic waves, the Doppler shift is significant in astrophysics for determining the velocity of stars and galaxies relative to Earth. The shift in wavelength ($\Delta \lambda$) due to the Doppler effect is given by:

$$ \frac{\Delta \lambda}{\lambda} = \frac{v}{c} $$>

where $v$ is the relative velocity. This effect adheres to the principles governing transverse electromagnetic waves moving at speed $c$ in free space.

Relativistic Implications of Constant Speed

The invariance of the speed of light in free space is a pivotal postulate in Einstein's theory of relativity. It leads to profound implications such as time dilation and length contraction, fundamentally altering our understanding of space and time. The fact that all electromagnetic waves travel at the same speed $c$ in a vacuum reinforces the concept that the speed of light is a universal constant, regardless of the observer's frame of reference.

Quantum Electrodynamics (QED) Perspective

While classical electromagnetism treats electromagnetic waves as continuous fields, Quantum Electrodynamics (QED) describes them as discrete particles called photons. Despite this quantum description, the macroscopic properties—such as being transverse and traveling at speed $c$ in free space—remain consistent with classical predictions. QED provides a deeper understanding of electromagnetic interactions at atomic and subatomic levels, bridging classical and quantum physics.

Interference and Diffraction of Transverse Waves

Electromagnetic waves exhibit wave behaviors like interference and diffraction, characteristic of transverse waves. Constructive and destructive interference patterns arise from the superposition of electric and magnetic fields, affecting the intensity and distribution of electromagnetic radiation. These phenomena are fundamental in technologies such as holography, diffraction gratings, and wireless communications.

Electromagnetic Wave Polarization and Its Applications

Beyond basic polarization, advanced studies explore elliptical and circular polarization states, which are pivotal in various applications. Circularly polarized waves, for instance, are essential in satellite communications and 3D display technologies. Understanding these polarization states enhances the design and functionality of optical systems and communication protocols.

Nonlinear Optics and Transverse Wave Propagation

In nonlinear optics, the interaction of intense electromagnetic waves with materials leads to phenomena like harmonic generation and self-focusing. These effects rely on the transverse nature of the waves and their interactions with the medium's electric and magnetic fields. Nonlinear optical processes are crucial in developing advanced laser technologies and photonic devices.

Electromagnetic Waveguides and Transmission Lines

Waveguides and transmission lines are structures designed to direct electromagnetic waves efficiently. The transverse nature ensures that modes of propagation can be controlled and guided with minimal loss. Applications range from fiber optic cables in telecommunications to microwave transmission lines in radar systems.

Plasmonics and Surface Electromagnetic Waves

Plasmonics studies the interaction between electromagnetic waves and free electrons in conductors, leading to surface electromagnetic waves known as plasmons. These waves are confined to the surface of materials and have applications in nanotechnology, sensors, and enhancing photovoltaic devices. The transverse characteristics of plasmons are critical for their behavior and applications.

Metamaterials and Electromagnetic Wave Manipulation

Metamaterials are engineered structures with properties not found in natural materials, allowing unprecedented control over electromagnetic wave propagation. By manipulating the transverse electric and magnetic fields, metamaterials can achieve negative refraction, cloaking, and superlensing. These advancements hinge on the fundamental understanding of transverse electromagnetic waves.

Astrophysical Implications of Electromagnetic Wave Propagation

In astrophysics, the propagation of transverse electromagnetic waves across vast interstellar distances provides insights into cosmic phenomena. Observations of electromagnetic radiation from stars, galaxies, and cosmic microwave background radiation aid in understanding the universe's composition, structure, and evolution. The consistent speed of these waves in the vacuum of space is essential for accurate measurements and interpretations.

Advanced Mathematical Treatments of Wave Dynamics

Higher-level studies involve solving Maxwell's equations under various boundary conditions to predict wave behavior in complex scenarios. Techniques such as Fourier analysis and vector calculus are employed to analyze wave propagation, reflection, refraction, and dispersion. Mastery of these mathematical tools is essential for tackling advanced problems in electromagnetism.

Experimental Techniques for Studying Transverse Waves

Experimental investigations of electromagnetic waves utilize instruments like oscilloscopes, interferometers, and spectrometers to observe and measure wave properties. Advanced techniques enable the visualization of wavefronts, polarization states, and interference patterns, providing empirical validation of theoretical concepts related to transverse wave behavior and uniform propagation speed.

Comparison Table

Aspect	Electromagnetic Waves	Mechanical Waves
Nature	Transverse	Transverse and Longitudinal
Medium Requirement	No medium required (can travel in a vacuum)	Requires a medium (solid, liquid, or gas)
Speed in Free Space	Constant (~3 × 10⁸ m/s)	Dependent on medium properties
Examples	Light, radio waves, X-rays	Sound waves, seismic waves
Energy Transmission	Mechanical waves transmit energy via particle interactions.
Polarization	Only transverse mechanical waves can be polarized

Summary and Key Takeaways

All electromagnetic waves are transverse, with electric and magnetic fields perpendicular to propagation direction.
They travel at a constant speed of $3 \times 10^8 \, m/s$ in free space, independent of frequency or wavelength.
Maxwell's equations underpin the theoretical framework, confirming the transverse and uniform speed characteristics.
Advanced concepts include relativistic implications, quantum descriptions, and applications in modern technology.
Understanding these properties is essential for various scientific and engineering disciplines.

Examiner Tip

Tips

To remember that all electromagnetic waves travel at the same speed in free space, use the mnemonic "Constant Speed of Light" (CSL). Break down Maxwell's equation $c = \frac{1}{\sqrt{\epsilon_0 \mu_0}}$ to understand how permittivity and permeability define $c$. Additionally, practice visualizing the transverse nature by drawing the electric and magnetic fields perpendicular to the direction of propagation. This visualization aids in solving problems related to polarization and wave interactions effectively.

Did You Know

Did you know that electromagnetic waves played a crucial role in the discovery of cosmic microwave background radiation, providing evidence for the Big Bang theory? Additionally, the fact that all electromagnetic waves travel at the same speed in a vacuum allows technologies like GPS to function with remarkable precision. Another fascinating aspect is that visible light is just a small portion of the electromagnetic spectrum, with many waves like gamma rays and radio waves having significant real-world applications.

Common Mistakes

Confusing Wave Speed with Frequency: Students often mix up the speed of electromagnetic waves ($c$) with their frequency ($f$) or wavelength ($\lambda$). Remember, $c = \lambda \cdot f$, and in free space, $c$ remains constant.

Assuming Electromagnetic Waves Require a Medium: Unlike mechanical waves, electromagnetic waves do not need a medium to travel. They can propagate through the vacuum of space.

Incorrect Polarization Understanding: Some students mistakenly believe that polarization affects the speed of electromagnetic waves. Polarization only describes the direction of the electric field oscillation, not the wave's speed.

FAQ

Are all electromagnetic waves transverse?

Yes, all electromagnetic waves are inherently transverse, with electric and magnetic fields oscillating perpendicular to the direction of wave propagation.

Do electromagnetic waves always travel at the same speed?

In a vacuum, all electromagnetic waves travel at the same speed, approximately $3 \times 10^8 \, m/s$. However, their speed can vary when passing through different media.

What determines the speed of electromagnetic waves in free space?

The speed is determined by the vacuum permittivity ($\epsilon_0$) and permeability ($\mu_0$), as described by the equation $c = \frac{1}{\sqrt{\epsilon_0 \mu_0}}$.

Can electromagnetic waves be polarized?

Yes, electromagnetic waves can exhibit various polarization states, including linear, circular, and elliptical, due to the transverse nature of their electric fields.

How do Maxwell's equations relate to electromagnetic waves?

Maxwell's equations describe how electric and magnetic fields generate and propagate electromagnetic waves, confirming their transverse nature and constant speed in free space.

Why don't electromagnetic waves require a medium?

Unlike mechanical waves, electromagnetic waves consist of oscillating electric and magnetic fields that can sustain each other, allowing propagation without a physical medium.

1. Capacitance

1.1 Energy Stored in a Capacitor

1.1.1 Determine electric potential energy stored in a capacitor from the area under the potential–charge g

1.1.2 Recall and use W = ½QV = ½CV²

1.2 Discharging a Capacitor

1.2.1 Analyze graphs of potential difference, charge, and current during capacitor discharge

1.2.2 Recall and use τ = RC for the time constant during discharge

1.2.3 Use equations of the form x = x₀e^(-t / RC) for current, charge, or potential during discharge

1.3 Capacitors and Capacitance

1.3.1 Define capacitance for isolated spherical conductors and parallel plate capacitors

1.3.2 Recall and use C = Q / V

1.3.3 Derive formulae for combined capacitance of capacitors in series and parallel

1.3.4 Use capacitance formulae for capacitors in series and parallel

2. Nuclear Physics

2.1 Mass Defect and Nuclear Binding Energy

2.1.1 Sketch the variation of binding energy per nucleon with nucleon number

2.1.2 Explain nuclear fusion and nuclear fission

2.1.3 Calculate the energy released in nuclear reactions using E = c²∆m

2.1.4 Understand the equivalence between energy and mass (E = mc²)

2.1.5 Define and use the terms mass defect and binding energy

2.2 Radioactive Decay

2.2.1 Understand that fluctuations in count rate provide evidence for random decay

2.2.2 Understand that radioactive decay is spontaneous and random

2.2.3 Define activity and decay constant, and recall A = λN

2.2.4 Define half-life

2.2.5 Use λ = 0.693 / t₁/₂ for the half-life relationship

2.2.6 Understand exponential decay and use the relationship x = x₀e^(-λt)

3. Kinematics

3.1 Equations of Motion

3.1.1 Define and use distance, displacement, speed, velocity, acceleration

3.1.2 Use graphical methods to represent motion

3.1.3 Determine displacement from velocity–time graph

3.1.4 Determine velocity using gradient of displacement–time graph

3.1.5 Determine acceleration using gradient of velocity–time graph

3.1.6 Derive equations for uniformly accelerated motion

3.1.7 Solve problems of uniformly accelerated motion

3.1.8 Describe experiment to determine acceleration due to gravity

3.1.9 Explain motion with uniform velocity and perpendicular acceleration

4. Deformation of Solids

4.1 Stress and Strain

4.1.1 Understand and use the terms load, extension, compression, and limit of proportionality

4.1.2 Recall and use Hooke’s law

4.1.3 Recall and use the formula for spring constant k = F / x

4.1.4 Define and use terms stress, strain, and Young's modulus

4.1.5 Describe an experiment to determine Young’s modulus

4.1.6 Understand deformation caused by tensile or compressive forces

4.2 Elastic and Plastic Behaviour

4.2.1 Understand elastic and plastic deformation and elastic limit

4.2.2 Understand area under the force–extension graph as work done

4.2.3 Calculate elastic potential energy using EP = ½kx²

5. Gravitational Fields

5.1 Gravitational Field of a Point Mass

5.1.1 Understand that g is approximately constant for small height changes near Earth's surface

5.1.2 Recall and use g = GM / r²

5.1.3 Derive and use g = GM / r² for gravitational field strength

5.2 Gravitational Potential

5.2.1 Define gravitational potential as work done per unit mass in bringing a test mass from infinity

5.2.2 Use ϕ = -GM / r for gravitational potential due to a point mass

5.2.3 Use EP = -GMm / r for gravitational potential energy between two point masses

5.3 Gravitational Field

5.3.1 Define gravitational field as force per unit mass

5.3.2 Represent a gravitational field using field lines

5.4 Gravitational Force Between Point Masses

5.4.1 For point outside uniform sphere, treat mass as a point mass at its center

5.4.2 Analyze circular orbits in gravitational fields

5.4.3 Recall and use Newton's law of gravitation F = Gm₁m₂ / r²

6. Electricity

6.1 Resistance and Resistivity

6.1.1 Understand that the resistance of a thermistor decreases as temperature increases

6.1.2 Define resistance and recall and use V = IR

6.1.3 Sketch I–V characteristics for metallic conductor, semiconductor diode, and filament lamp

6.1.4 Explain that the resistance of a filament lamp increases as current increases

6.1.5 State Ohm’s law and recall and use R = ρL / A

6.1.6 Understand that the resistance of an LDR decreases as light intensity increases

6.2 Electric Current

6.2.1 Understand that an electric current is a flow of charge carriers

6.2.2 Understand that the charge on charge carriers is quantised

6.2.3 Recall and use Q = It

6.2.4 Use I = Anvq for current-carrying conductors

6.3 Potential Difference and Power

6.3.1 Define potential difference as energy transferred per unit charge

6.3.2 Recall and use V = W / Q

6.3.3 Recall and use P = VI, P = I²R, P = V² / R

7. D.C. Circuits

7.1 Practical Circuits

7.1.1 Recall and use the circuit symbols in the syllabus

7.1.2 Draw and interpret circuit diagrams using circuit symbols

7.1.3 Define electromotive force (e.m.f.) of a source as energy transferred per unit charge

7.1.4 Distinguish between e.m.f. and potential difference (p.d.)

7.1.5 Understand the effects of internal resistance on terminal potential difference

7.2 Kirchhoff’s Laws

7.2.1 Recall Kirchhoff’s first law: conservation of charge

7.2.2 Recall Kirchhoff’s second law: conservation of energy

7.2.3 Derive the formula for combined resistance of resistors in series using Kirchhoff’s laws

7.2.4 Use the formula for combined resistance of resistors in series

7.2.5 Derive the formula for combined resistance of resistors in parallel using Kirchhoff’s laws

7.2.6 Use the formula for combined resistance of resistors in parallel

7.2.7 Use Kirchhoff’s laws to solve simple circuit problems

7.3 Potential Dividers

7.3.1 Understand the principle of a potential divider circuit

7.3.2 Recall and use the principle of the potentiometer for comparing potential differences

7.3.3 Understand the use of a galvanometer in null methods

7.3.4 Explain the use of thermistors and LDRs in potential dividers to provide a potential dependent on te

8. Thermal Equilibrium

8.1 Thermal Energy Transfer

8.1.1 Understand that thermal energy transfers from higher to lower temperature

8.1.2 Understand that regions of equal temperature are in thermal equilibrium

9. Temperature Scales

9.1 Temperature Measurement

9.1.1 Understand physical properties that vary with temperature (e.g., density, gas volume, resistance)

9.1.2 Convert temperatures between Kelvin and Celsius, and recall T(K) = θ(°C) + 273.15

10. Magnetic Fields

10.1 Concept of a Magnetic Field

10.1.1 Understand that a magnetic field is a field of force produced by moving charges or permanent magnets

10.1.2 Represent a magnetic field using field lines

10.2 Force on a Current-Carrying Conductor

10.2.1 Understand that a force acts on a current-carrying conductor in a magnetic field

10.2.2 Recall and use F = BIL sin θ for the force on a current-carrying conductor in a magnetic field

10.2.3 Define magnetic flux density as the force per unit current per unit length on a wire at right angles

10.3 Force on a Moving Charge

10.3.1 Determine the direction of the force on a charge moving in a magnetic field

10.3.2 Recall and use F = BQv sin θ for the force on a moving charge in a magnetic field

10.3.3 Understand the origin of the Hall voltage and use the expression VH = BI / (ntq) for the Hall voltag

10.3.4 Understand the use of a Hall probe to measure magnetic flux density

10.4 Magnetic Fields Due to Currents

10.4.1 Sketch magnetic field patterns due to currents in a straight wire, flat coil, and solenoid

10.4.2 Understand that magnetic field in a solenoid is increased by a ferrous core

10.4.3 Explain the origin of forces between current-carrying conductors and determine the direction of the

10.5 Electromagnetic Induction

10.5.1 Define magnetic flux as the product of magnetic flux density and area perpendicular to flux directio

10.5.2 Recall and use Φ = BA for magnetic flux

10.5.3 Understand and use the concept of magnetic flux linkage

10.5.4 Explain experiments that show changing magnetic flux induces an e.m.f.

10.5.5 Recall and use Faraday’s and Lenz’s laws of electromagnetic induction

11. Specific Heat Capacity and Latent Heat

11.1 Specific Heat Capacity

11.1.1 Define and use specific heat capacity

11.2 Latent Heat

11.2.1 Define and use specific latent heat; distinguish between fusion and vaporisation

12. Dynamics

12.1 Momentum and Newton’s Laws of Motion

12.1.1 Mass resists change in motion

12.1.2 Recall F = ma and solve related problems

12.1.3 Define and use linear momentum

12.1.4 Force as rate of change of momentum

12.1.5 State and apply Newton’s laws

12.1.6 Describe weight as effect of gravitational field

12.1.7 Weight of an object is mass × gravitational acceleration

12.2 Non-uniform Motion

12.2.1 Understand frictional and drag forces

12.2.2 Describe motion in uniform gravitational field with air resistance

12.2.3 Objects moving against resistive force may reach terminal velocity

12.3 Linear Momentum and its Conservation

12.3.1 State conservation of momentum

12.3.2 Apply conservation of momentum to solve problems

12.3.3 For elastic collision, kinetic energy and relative speed are conserved

12.3.4 Momentum is conserved, but some kinetic energy may change

13. Medical Physics

13.1 Production and Use of Ultrasound

13.1.1 Understand that a piezo-electric crystal changes shape when a p.d. is applied and generates an e.m.f

13.1.2 Understand how ultrasound waves are generated and detected by a piezoelectric transducer

13.1.3 Understand how ultrasound reflection at boundaries provides diagnostic information about internal st

13.1.4 Define specific acoustic impedance as Z = ρc

13.1.5 Use the equation IR / I₀ = (Z₁ – Z₂)² / (Z₁ + Z₂)² for the intensity reflection coefficient

13.2 Production and Use of X-rays

13.2.1 Explain that X-rays are produced by electron bombardment of a metal target and calculate the minimum

13.2.2 Understand the use of X-rays in imaging internal body structures and the term 'contrast' in X-ray im

13.2.3 Recall and use I = I₀e^(-μx) for the attenuation of X-rays in matter

13.2.4 Understand how computed tomography (CT) produces 3D images by combining multiple 2D X-ray images

13.3 PET Scanning

13.3.1 Understand that a tracer contains radioactive nuclei and is introduced into the body for imaging

13.3.2 Understand that β+ decay is used in positron emission tomography (PET)

13.3.3 Understand that annihilation occurs when a particle interacts with its antiparticle, conserving mass

13.3.4 Explain how gamma-ray photons from annihilation are detected to create an image of tracer concentrat

14. Waves

14.1 Progressive Waves

14.1.1 Describe wave motion in ropes, springs, and ripple tanks

14.1.2 Understand and use the terms displacement, amplitude, phase difference, period, frequency, wavelengt

14.1.3 Use time-base and y-gain on a cathode-ray oscilloscope (CRO) to determine frequency and amplitude

14.1.4 Derive and use v = f λ for the wave equation

14.1.5 Recall and use v = f λ

14.1.6 Understand energy transfer by a progressive wave

14.1.7 Recall and use intensity = power / area, intensity ∝ (amplitude)²

14.2 Transverse and Longitudinal Waves

14.2.1 Compare transverse and longitudinal waves

14.2.2 Analyze and interpret graphical representations of transverse and longitudinal waves

14.3 Doppler Effect for Sound Waves

14.3.1 Understand the change in frequency when a sound source moves relative to a stationary observer

14.3.2 Use the expression f₀ = fₛ(v / (v ± vₛ)) for the observed frequency

14.4 Electromagnetic Spectrum

14.4.1 State all electromagnetic waves are transverse waves traveling at the same speed in free space

14.4.2 Recall the range of wavelengths from radio waves to γ-rays

14.4.3 Recall that wavelengths 400–700 nm are visible to the human eye

14.5 Polarisation

14.5.1 Understand that polarisation is a phenomenon associated with transverse waves

14.5.2 Recall and use Malus's law (I = I₀ cos²θ) to calculate intensity of a plane-polarised wave after pas

15. The Mole

15.1 The Mole

15.1.1 Understand that amount of substance is an SI base quantity with the unit mol

15.1.2 Use molar quantities where one mole contains Avogadro's constant of particles

16. Equation of State

16.1 Ideal Gas Law

16.1.1 Understand that a gas obeying pV ∝ T is an ideal gas

16.1.2 Recall and use the equation pV = nRT for an ideal gas

16.1.3 Recall pV = NkT, where N = number of molecules and k is Boltzmann constant

16.1.4 Use the relationship k = R / NA

17. Kinetic Theory of Gases

17.1 Kinetic Theory

17.1.1 State the basic assumptions of the kinetic theory of gases

17.1.2 Explain pressure exerted by a gas due to molecular movement

17.1.3 Derive and use pV = (3/2)NmkT for pressure of a gas

17.1.4 Compare pV = (3/2)NmkT with pV = NkT to deduce average kinetic energy of a molecule

18. Particle Physics

18.1 Atoms, Nuclei and Radiation

18.1.1 Infer the existence and small size of the nucleus from α-particle scattering

18.1.2 Describe the nuclear atom model: protons, neutrons, and electrons

18.1.3 Distinguish between nucleon number and proton number

18.1.4 Understand isotopes as forms of the same element with different neutrons

18.1.5 Use the notation AZX for nuclides representation

18.1.6 Understand conservation of nucleon number and charge in nuclear processes

18.1.7 Describe the composition, mass, and charge of α-, β-, and γ-radiations

18.1.8 Understand antiparticles and positrons as antiparticles of electrons

18.1.9 State that (electron) antineutrinos are produced during β- decay and neutrinos during β+ decay

18.1.10 Represent α- and β-decay using radioactive decay equations

18.1.11 Use unified atomic mass unit (u) for mass

18.2 Fundamental Particles

18.2.1 Understand quarks as fundamental particles with six flavours

18.2.2 Understand hadrons as baryons (three quarks) or mesons (one quark and one antiquark)

18.2.3 Describe changes in quark composition during β- and β+ decay

18.2.4 Describe protons and neutrons as composed of quarks

18.2.5 Recall and use the charge of each quark and its respective antiquark

18.2.6 Recall electrons and neutrinos as fundamental particles (leptons)

19. Internal Energy

19.1 Internal Energy

19.1.1 Understand that internal energy is the sum of kinetic and potential energies of molecules in a syste

19.1.2 Relate rise in temperature to an increase in internal energy

20. Forces, Density and Pressure

20.1 Turning Effects of Forces

20.1.1 Weight acts at a single point: centre of gravity

20.1.2 Define and apply the moment of a force

20.1.3 Understand the concept of a couple

20.1.4 Define and apply torque of a couple

20.2 Equilibrium of Forces

20.2.1 State and apply the principle of moments

20.2.2 System in equilibrium has no resultant force or torque

20.2.3 Use a vector triangle to represent coplanar forces in equilibrium

20.3 Density and Pressure

20.3.1 Define and use density

20.3.2 Define and use pressure

20.3.3 Derive equation for hydrostatic pressure ∆p = ρg∆h

20.3.4 Use the equation ∆p = ρg∆h

20.3.5 Understand upthrust as the effect of hydrostatic pressure

20.3.6 Calculate upthrust using F = ρgV (Archimedes' principle)

21. Astronomy and Cosmology

21.1 Standard Candles

21.1.1 Understand luminosity as the total power radiated by a star

21.1.2 Recall and use the inverse square law F = L / (4πd²) for radiant flux intensity

21.1.3 Understand that an object with known luminosity is a standard candle

21.1.4 Use standard candles to determine distances to galaxies

21.2 Stellar Radii

21.2.1 Recall and use Wien’s displacement law λmax ∝ 1 / T to estimate the surface temperature of a star

21.2.2 Use Stefan–Boltzmann law L = 4πσr²T⁴

21.2.3 Use Wien’s law and Stefan–Boltzmann law to estimate the radius of a star

21.3 Hubble’s Law and Big Bang Theory

21.3.1 Understand redshift and the increase in wavelength of light from distant objects

21.3.2 Use ∆λ / λ = ∆f / f = v / c for redshift

21.3.3 Explain why redshift suggests the Universe is expanding

21.3.4 Recall and use Hubble’s law v = H₀d to explain the Big Bang theory

22. First Law of Thermodynamics

22.1 First Law

22.1.1 Recall and use W = p∆V for work done when the volume of a gas changes at constant pressure

22.1.2 Understand the difference between work done by a gas and work done on a gas

22.1.3 Recall and use the first law of thermodynamics: ∆U = q + W

23. Alternating Currents

23.1 Characteristics of Alternating Currents

23.1.1 Understand and use terms period, frequency, and peak value for alternating current or voltage

23.1.2 Use x = x₀ sin(ωt) for sinusoidal alternating current or voltage

23.1.3 Recall that the mean power in a resistive load is half the maximum power for sinusoidal current

23.1.4 Distinguish between root-mean-square (r.m.s.) and peak values and recall I₀r.m.s = I₀ / √2 and V₀r.m

23.2 Rectification and Smoothing

23.2.1 Distinguish graphically between half-wave and full-wave rectification

23.2.2 Explain the use of a single diode for half-wave rectification

23.2.3 Explain the use of four diodes (bridge rectifier) for full-wave rectification

23.2.4 Analyze the effect of a capacitor in smoothing, including the effect of capacitance and load resista

24. Superposition

24.1 Stationary Waves

24.1.1 Explain and use the principle of superposition

24.1.2 Understand experiments demonstrating stationary waves using microwaves, stretched strings, and air c

24.1.3 Explain the formation of stationary waves using graphical methods and identify nodes and antinodes

24.1.4 Determine wavelength from the positions of nodes or antinodes

24.2 Diffraction

24.2.1 Explain diffraction and show understanding of related experiments

24.2.2 Understand the effect of gap width relative to wavelength in diffraction experiments

24.3 Interference

24.3.1 Understand the terms interference and coherence

24.3.2 Demonstrate two-source interference using water waves, sound, light, and microwaves

24.3.3 Understand the conditions required for two-source interference fringes

24.3.4 Recall and use λ = ax / D for double-slit interference with light

24.4 Diffraction Grating

24.4.1 Recall and use d sin θ = nλ for diffraction grating calculations

24.4.2 Describe the use of a diffraction grating to determine the wavelength of light

25. Simple Harmonic Oscillations

25.1 Simple Harmonic Motion

25.1.1 Understand and use terms displacement, amplitude, period, frequency, angular frequency, and phase di

25.1.2 Understand that simple harmonic motion occurs when acceleration is proportional to displacement from

25.1.3 Use a = -ω²x and recall x = x₀ sin(ωt) as the solution

25.1.4 Use v = v₀ cos(ωt) and v = ±ω√(x₀² - x²) for velocity

26. Energy in Simple Harmonic Motion

26.1 Energy in SHM

26.1.1 Describe the interchange between kinetic and potential energy during SHM

26.1.2 Recall and use E = ½mω²x₀² for the total energy of a system undergoing SHM

27. Quantum Physics

27.1 Energy and Momentum of a Photon

27.1.1 Understand that electromagnetic radiation has a particulate nature

27.1.2 Recall and use E = hf for the energy of a photon

27.1.3 Use the electronvolt (eV) as a unit of energy

27.1.4 Understand that a photon has momentum and use p = E / c for photon momentum

27.2 Photoelectric Effect

27.2.1 Understand that photoelectrons are emitted from a metal surface when illuminated by electromagnetic

27.2.2 Understand and use the terms threshold frequency and threshold wavelength

27.2.3 Explain photoelectric emission in terms of photon energy and work function

27.2.4 Recall and use hf = Φ + ½mv² for the maximum kinetic energy of photoelectrons

27.2.5 Explain why the maximum kinetic energy of photoelectrons is independent of intensity, while current

27.3 Wave-Particle Duality

27.3.1 Understand that the photoelectric effect shows the particulate nature of light, while diffraction sh

27.3.2 Describe and interpret electron diffraction as evidence for the wave nature of particles

27.3.3 Understand the de Broglie wavelength as the wavelength associated with a moving particle

27.3.4 Recall and use λ = h / p for de Broglie wavelength

27.4 Energy Levels in Atoms and Line Spectra

27.4.1 Understand discrete electron energy levels in atoms (e.g., atomic hydrogen)

27.4.2 Understand the appearance and formation of emission and absorption line spectra

27.4.3 Recall and use hf = E₁ – E₂ for the energy difference between electron energy levels

28. Damped and Forced Oscillations, Resonance

28.1 Damped Oscillations

28.1.1 Understand that damping occurs due to resistive forces

28.1.2 Understand the types of damping: light, critical, and heavy damping

28.2 Resonance

28.2.1 Understand that resonance occurs when an oscillating system is forced to oscillate at its natural fr

29. Work, Energy and Power

29.1 Energy Conservation

29.1.1 Understand the concept of work, and recall W = F × s

29.1.2 Apply the principle of conservation of energy

29.1.3 Understand efficiency as useful energy output / total energy input

29.1.4 Use efficiency concept to solve problems

29.1.5 Define power as work done per unit time

29.1.6 Solve problems using P = W / t

29.1.7 Derive P = Fv and solve problems

29.2 Gravitational Potential Energy and Kinetic Energy

29.2.1 Derive ∆EP = mg∆h for gravitational potential energy changes

29.2.2 Recall and use ∆EP = mg∆h for gravitational potential energy changes

29.2.3 Derive EK = ½mv² for kinetic energy

29.2.4 Recall and use EK = ½mv² for kinetic energy

30. Electric Fields

30.1 Electric Fields and Field Lines

30.1.1 Understand that an electric field is a field of force and define it as force per unit positive charg

30.1.2 Represent an electric field using field lines

30.2 Uniform Electric Fields

30.2.1 Recall and use E = ∆V / ∆d to calculate electric field strength between charged parallel plates

30.2.2 Describe the effect of a uniform electric field on the motion of charged particles

30.3 Electric Force Between Point Charges

30.3.1 Understand that, for a point outside a spherical conductor, the charge may be considered a point mas

30.3.2 Recall and use Coulomb’s law F = Q₁Q₂ / (4πε₀r²) for the force between two point charges

30.4 Electric Field of a Point Charge

30.4.1 Recall and use E = Q / (4πε₀r²) for the electric field strength due to a point charge

30.5 Electric Potential

30.5.1 Define electric potential as work done per unit positive charge in bringing a test charge from infin

30.5.2 Recall and use V = Q / (4πε₀r) for electric potential due to a point charge

30.5.3 Understand how electric potential leads to electric potential energy of two point charges and use EP

31. Physical Quantities and Units

31.1 Physical Quantities

31.1.1 Physical quantities consist of magnitude and unit

31.1.2 Estimate physical quantities from the syllabus

31.2 SI Units

31.2.1 SI base units: mass, length, time, current, temperature

31.2.2 Express derived units from SI base units

31.2.3 Check homogeneity of physical equations

31.2.4 Use prefixes (pico, nano, micro, kilo, etc.)

31.3 Errors and Uncertainties

31.3.1 Understand systematic and random errors

31.3.2 Assess uncertainty in derived quantities

31.4 uniform Electric Fields

31.4.1 Distinguish between precision and accuracy

31.5 Scalars and Vectors

31.5.1 Difference between scalar and vector quantities

31.5.2 Add and subtract coplanar vectors

31.5.3 Represent a vector as components

32. Motion in a Circle

32.1 Centripetal Acceleration

32.1.1 Understand centripetal acceleration and its role in circular motion

32.1.2 Recall and use a = rω² and a = v² / r

32.1.3 Recall and use F = mrω² and F = mv² / r

32.1.4 Understand force causing centripetal acceleration is always perpendicular to motion

32.2 Kinematics of Uniform Circular Motion

32.2.1 Recall and use ω = 2π / T and v = rω

32.2.2 Understand and use angular speed

32.2.3 Define and express angular displacement in radians

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State All Electromagnetic Waves Are Transverse Waves Traveling at the Same Speed in Free Space

Introduction