Coulomb’s Law is a fundamental principle in physics that describes the interaction between electrically charged particles. Essential for understanding electric forces within the framework of electric fields, this law is pivotal for students studying the 'Electric Force Between Point Charges' under the 'Electric Fields' unit in the AS & A Level Physics curriculum (9702). Mastery of Coulomb’s Law not only aids in solving various physics problems but also lays the groundwork for exploring more complex electromagnetic phenomena.

Key Concepts

1. Coulomb's Law: An Overview

Coulomb’s Law, formulated by Charles-Augustin de Coulomb in the 18th century, quantifies the electric force between two point charges. The law states that the magnitude of the force ($F$) between two point charges ($Q_1$ and $Q_2$) is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance ($r$) separating them. Mathematically, it is expressed as:

$$F = \frac{Q_1Q_2}{4\pi\varepsilon_0 r^2}$$

Here, $\varepsilon_0$ represents the vacuum permittivity, a constant that characterizes the ability of a vacuum to permit electric field lines. The direction of the force is along the line joining the two charges: it is repulsive if the charges have the same sign and attractive if they have opposite signs.

2. Understanding the Variables

Charge ($Q$): Measured in coulombs (C), it represents the quantity of electricity held by an object. There are two types of charges: positive and negative.
Distance ($r$): The separation between the centers of the two charges, measured in meters (m).
Vacuum Permittivity ($\varepsilon_0$): A constant approximately equal to $8.854 \times 10^{-12} \, \text{C}^2/\text{N} \cdot \text{m}^2$, it quantifies the strength of the electric field in a vacuum.

3. The Inverse Square Law

The inverse square nature of Coulomb’s Law implies that the force decreases rapidly as the distance between the charges increases. Specifically, halving the distance between the charges increases the force by a factor of four, while doubling the distance decreases the force by a factor of four. This relationship highlights the significance of distance in electric interactions.

4. Direction of the Force

The force calculated using Coulomb’s Law acts along the line joining the two charges. If both charges are of the same sign, the force is repulsive, pushing the charges apart. Conversely, if the charges are of opposite signs, the force is attractive, pulling the charges toward each other.

5. Superposition Principle

Coulomb’s Law can be extended to systems with multiple charges through the principle of superposition. This principle states that the total electric force on a charge is the vector sum of the individual forces exerted by each of the other charges in the system. Mathematically:

$$\vec{F}_{\text{total}} = \sum_{i=1}^{n} \vec{F}_i$$

Where $\vec{F}_i$ is the force due to the $i^{th}$ charge.

6. Coulomb's Law vs. Gravitational Law

Coulomb’s Law is analogous to Newton’s Law of Universal Gravitation, which describes the gravitational force between two masses. While both laws follow an inverse square relationship, gravitational force is always attractive and involves masses, whereas electric force can be either attractive or repulsive and involves electric charges.

7. Practical Applications of Coulomb's Law

Electrostatics: Understanding static electricity phenomena, such as the behavior of charges on insulators.
Molecular Chemistry: Explaining the forces between ions in ionic compounds.
Electronics: Designing and analyzing components like capacitors where electric fields play a crucial role.

8. Mathematical Derivations and Examples

To apply Coulomb’s Law effectively, it’s essential to solve numerical problems involving varying charge magnitudes and distances. For instance, calculating the force between two charges of $3 \, \text{C}$ and $-2 \, \text{C}$ separated by $0.5 \, \text{m}$ requires plugging the values into the formula:

$$F = \frac{(3)(-2)}{4\pi(8.854 \times 10^{-12})(0.5)^2}$$ $$F = \frac{-6}{4\pi(8.854 \times 10^{-12})(0.25)}$$ $$F \approx -8.58 \times 10^{10} \, \text{N}$$

The negative sign indicates an attractive force, as expected for opposite charges.

9. Coulomb’s Constant ($k$)

For simplification, Coulomb’s constant ($k$) is often used, where:

$$k = \frac{1}{4\pi\varepsilon_0} \approx 8.988 \times 10^{9} \, \text{N} \cdot \text{m}^2/\text{C}^2$$

Thus, Coulomb’s Law can be rewritten as:

$$F = k \frac{Q_1Q_2}{r^2}$$

10. Units and Dimensional Analysis

Ensuring consistency in units is crucial for accurate calculations. In Coulomb’s Law:

Force ($F$) is measured in newtons (N).
Charge ($Q$) is measured in coulombs (C).
Distance ($r$) is measured in meters (m).

Dimensional analysis helps verify the correctness of equations by ensuring that both sides have the same units.

Advanced Concepts

1. Electric Field and Coulomb’s Law

An electric field ($\vec{E}$) represents the force per unit charge experienced by a test charge placed in the vicinity of another charge. It is directly related to Coulomb’s Law and is defined as:

$$\vec{E} = \frac{\vec{F}}{Q_{\text{test}}} = k \frac{Q}{r^2} \hat{r}$$

Where $\hat{r}$ is the unit vector pointing from the source charge to the test charge. This formulation allows for the analysis of electric fields generated by multiple charges using the superposition principle.

2. Electric Potential Energy

The work done in assembling a system of charges is stored as electric potential energy ($U$). For two point charges, it is given by:

$$U = k \frac{Q_1Q_2}{r}$$

This equation shows that potential energy depends linearly on charge magnitudes and inversely on the separation distance. Understanding potential energy is crucial for analyzing system stability and predicting charge distributions.

3. Gauss’s Law and Coulomb’s Law

Gauss’s Law provides a powerful tool for calculating electric fields in situations with high symmetry. It relates the electric flux through a closed surface to the enclosed charge:

$$\Phi_E = \oint \vec{E} \cdot d\vec{A} = \frac{Q_{\text{enc}}}{\varepsilon_0}$$

For point charges, applying Gauss’s Law leads back to Coulomb’s Law, demonstrating the law's foundational role in electrostatics.

4. Relativistic Considerations

At velocities approaching the speed of light, Coulomb’s Law is modified to account for relativistic effects, integrating electric and magnetic fields into a unified electromagnetic framework. These advanced considerations are typically explored in higher-level physics but underscore the limitations of Coulomb’s Law in classical contexts.

5. Coulomb’s Law in Conductors and Insulators

The behavior of charges in conductors and insulators differs due to the mobility of charges. In conductors, free electrons can redistribute in response to electric forces, often neutralizing internal fields. In contrast, insulators maintain fixed charge distributions, making Coulomb’s Law directly applicable without charge movement.

6. Multipole Expansion

For systems with multiple charges, multipole expansion allows the approximation of complex charge distributions through a series of dipole, quadrupole, and higher-order moments. This method simplifies the calculation of electric fields at large distances compared to the size of the charge distribution.

7. Coulomb Interaction in Quantum Mechanics

In quantum mechanics, Coulomb’s Law plays a pivotal role in the interactions between charged particles such as electrons and nuclei. It influences atomic structure, energy levels, and the formation of chemical bonds, bridging classical electrostatics with quantum phenomena.

8. Applications in Nanotechnology

At the nanoscale, Coulombic interactions dominate the behavior of nanoparticles, influencing their assembly, stability, and interactions. Understanding these forces is essential for designing nanomaterials with desired properties for various technological applications.

9. Screening and Debye Length

In plasmas and electrolytes, free charges can shield electric fields, reducing the effective range of Coulombic interactions. The Debye length quantifies the distance over which significant charge screening occurs, modifying Coulomb’s Law in such environments.

10. Computational Modeling of Electric Forces

Advanced computational techniques, such as molecular dynamics simulations, incorporate Coulomb’s Law to model interactions between large numbers of charged particles. These models are instrumental in studying complex systems in chemistry, biology, and materials science.

11. Experimental Validation of Coulomb’s Law

Historically, Coulomb’s Law has been validated through torsion balance experiments, where the force between charged spheres is measured with high precision. Modern experiments continue to test the law's limits, exploring scenarios with extreme charges and distances.

12. Limitations and Extensions of Coulomb’s Law

Coulomb’s Law assumes point charges and electrostatic conditions. It does not account for dynamic situations involving moving charges, where magnetic forces become significant. Extending beyond Coulomb's Law, Maxwell's equations provide a comprehensive framework for electromagnetism, encompassing both electric and magnetic fields.

13. Coulomb’s Law in Different Media

The presence of a medium alters the effective force between charges. In materials with a dielectric constant ($\kappa$), Coulomb’s Law is modified to:

$$F = \frac{Q_1Q_2}{4\pi\kappa\varepsilon_0 r^2}$$

This reduction accounts for the polarization of the medium, which screens the electric force between charges.

14. Force Between Continuous Charge Distributions

Coulomb’s Law is extended to continuous charge distributions by integrating the force contributions of infinitesimal charge elements. This approach is essential for calculating electric fields and forces in real-world objects with complex geometries.

15. Coulomb’s Law and Potential Theory

Potential theory relates Coulomb's Law to the concept of electric potential. By integrating the electric field, one can derive the potential energy distribution in a system of charges, facilitating the analysis of electric phenomena using scalar quantities.

Comparison Table

Aspect	Coulomb’s Law	Newton’s Law of Gravitation
Nature of Force	Can be attractive or repulsive	Always attractive
Fundamental Entities	Electric charges	Masses
Proportionality	Directly proportional to $Q_1Q_2$	Directly proportional to $m_1m_2$
Constant	$k = \frac{1}{4\pi\varepsilon_0}$	$G$ (gravitational constant)
Strength	Much stronger than gravitational force	Weaker compared to electric force
Dependence on Medium	Depends on the dielectric constant	Generally unaffected by medium

Summary and Key Takeaways

Coulomb’s Law quantifies the electric force between two point charges, depending on charge magnitudes and separation distance.
The force is inversely proportional to the square of the distance and directly proportional to the product of the charges.
The law is fundamental in understanding electric fields, potential energy, and various applications in physics and technology.
Advanced concepts include electric field theory, Gauss’s Law, and applications in quantum mechanics and nanotechnology.
Comparatively, Coulomb’s Law differs from Newton’s gravitational law in force nature, entities involved, and interaction strengths.

Examiner Tip

Tips

Use the mnemonic “Charges Interact Radially” to remember that Coulomb’s force acts along the line joining the charges. Always double-check units and signs of charges. Practice drawing free-body diagrams to visualize forces, and remember to apply the inverse square law correctly for accurate calculations.

Did You Know

Coulomb’s Law not only explains the force between static charges but also forms the basis for understanding lightning. Additionally, this law paved the way for the development of modern electronics, influencing everything from smartphones to electric cars. Interestingly, Coulomb’s original experiments used a torsion balance, a device still fundamental in precision measurements today.

Common Mistakes

Incorrect Application of Units: Students often mix up units, such as using centimeters instead of meters for distance. Always convert to SI units before calculations.
Mistaking Charge Signs: Forgetting to consider the signs of charges can lead to incorrect conclusions about the force direction. Remember, like charges repel and unlike charges attract.
Ignoring the Inverse Square Law: Some students forget to square the distance in the denominator, leading to significant errors in force magnitude.

FAQ

What is Coulomb’s Law?

Coulomb’s Law describes the electric force between two point charges, stating that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

How does Coulomb’s Law differ from Newton’s Law of Gravitation?

While both laws follow an inverse square relationship, Coulomb’s Law deals with electric charges and can produce attractive or repulsive forces, whereas Newton’s Law of Gravitation involves masses and always results in attractive forces.

What is the significance of the vacuum permittivity ($\varepsilon_0$) in Coulomb’s Law?

The vacuum permittivity ($\varepsilon_0$) is a constant that quantifies the ability of a vacuum to permit electric field lines. It affects the strength of the electric force between charges.

Can Coulomb’s Law be applied to continuous charge distributions?

Yes, Coulomb’s Law can be extended to continuous charge distributions by integrating the force contributions of infinitesimal charge elements, allowing the calculation of electric fields and forces in complex geometries.

What role does Coulomb’s Law play in modern electronics?

Coulomb’s Law is fundamental in designing and analyzing electronic components like capacitors, where the interaction between charges determines the component’s behavior and functionality.

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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Recall and Use Coulomb’s Law $F = \frac{Q_1Q_2}{4\pi\varepsilon_0 r^2}$ for the Force Between Two Point Charges

Introduction