Understanding the direction of the force exerted on a moving charge within a magnetic field is a fundamental concept in physics. This topic is pivotal for students pursuing the AS & A Level curriculum, particularly within the Physics - 9702 syllabus. Grasping this concept not only lays the groundwork for electromagnetism but also has practical applications in various technological advancements.

Key Concepts

Magnetic Force on a Moving Charge

When a charge moves through a magnetic field, it experiences a force perpendicular to both its velocity and the magnetic field direction. This phenomenon is described by the Lorentz force law, which is fundamental in understanding electromagnetic interactions.

$$ \vec{F} = q\vec{v} \times \vec{B} $$

Here,

$\vec{F}$ is the force experienced by the charge.
$q$ is the electric charge.
$\vec{v}$ is the velocity of the charge.
$\vec{B}$ is the magnetic field.

The cross product ($\times$) indicates that the force is orthogonal to both the velocity and the magnetic field vectors. This relationship ensures that the magnetic force does not do work on the charge, as it only changes the direction of the velocity, not its magnitude.

Right-Hand Rule

Determining the direction of the magnetic force involves the use of the right-hand rule. This mnemonic helps visualize the orientation of the vectors involved in the Lorentz force equation.

Point your right hand's fingers in the direction of the velocity ($\vec{v}$).
Rotate your hand so that when you curl your fingers, they point in the direction of the magnetic field ($\vec{B}$).
Your thumb will then point in the direction of the force ($\vec{F}$) for a positively charged particle.

For negatively charged particles, the force direction is opposite to the thumb's direction.

Magnetic Field Lines

Magnetic fields are represented by field lines that indicate the direction and strength of the magnetic force. The density of these lines correlates with the field's intensity; closely spaced lines signify a stronger magnetic field.

Motion of Charged Particles in Magnetic Fields

When a charged particle moves in a uniform magnetic field, it experiences a centripetal force that causes it to move in a circular or helical path, depending on the angle between its velocity and the magnetic field.

$$ r = \frac{mv}{qB} $$

Where:

$r$ is the radius of the circular path.
$m$ is the mass of the particle.
$v$ is the velocity.
$q$ is the charge.
$B$ is the magnetic field strength.

Applications of Magnetic Force on Moving Charges

This principle is applied in various technologies, including:

Electric Motors: Utilize magnetic forces to convert electrical energy into mechanical motion.
Mass Spectrometers: Determine the mass-to-charge ratio of ions by observing their trajectories in magnetic fields.
Cyclotrons: Accelerate charged particles using magnetic and electric fields for nuclear physics experiments.

Mathematical Derivation of the Lorentz Force

The Lorentz force can be derived from fundamental electromagnetic principles. Starting with the Biot-Savart law and integrating the contributions of infinitesimal magnetic fields, the force on a moving charge is obtained as:

$$ \vec{F} = q\vec{v} \times \vec{B} $$

This equation encapsulates the mutual perpendicularity of the force, velocity, and magnetic field vectors.

Units and Dimensions

In the International System of Units (SI):

Force ($\vec{F}$) is measured in newtons (N).
Charge ($q$) is measured in coulombs (C).
Velocity ($\vec{v}$) is measured in meters per second (m/s).
Magnetic field ($\vec{B}$) is measured in teslas (T).

Example Calculation

Consider a proton ($q = +1.6 \times 10^{-19}$ C) moving with a velocity of $2 \times 10^{5}$ m/s perpendicular to a magnetic field of $0.5$ T. The force experienced by the proton is:

$$ F = qvB = (1.6 \times 10^{-19}\ \text{C}) \times (2 \times 10^{5}\ \text{m/s}) \times (0.5\ \text{T}) = 1.6 \times 10^{-14}\ \text{N} $$

This force directs the proton perpendicular to both its velocity and the magnetic field.

Magnetic Flux Density

Magnetic flux density ($\vec{B}$) quantifies the number of magnetic field lines passing through a unit area perpendicular to the field. It is a vector quantity with both magnitude and direction.

Force on a Charge Moving at an Angle

If a charge moves at an angle $\theta$ to the magnetic field, only the component of velocity perpendicular to the field contributes to the magnetic force:

$$ F = qvB\sin\theta $$

This relationship highlights that the force is maximal when $\theta = 90^\circ$ and zero when the velocity is parallel to the field.

Velocity Selector

A velocity selector uses perpendicular electric and magnetic fields to allow only particles with a specific velocity to pass through undeflected. The condition for no deflection is when the electric force equals the magnetic force:

$$ qE = qvB \quad \Rightarrow \quad v = \frac{E}{B} $$

This principle is fundamental in devices like mass spectrometers and cathode ray tubes.

Equilibrium Conditions

For a charge to move in equilibrium within crossed electric and magnetic fields, the net force must be zero:

$$ \vec{F}_{\text{electric}} + \vec{F}_{\text{magnetic}} = 0 $$ $$ q\vec{E} + q\vec{v} \times \vec{B} = 0 $$

Solving for velocity gives the condition for equilibrium:

$$ \vec{v} = \frac{\vec{E} \times \vec{B}}{B^2} $$

Magnetic Braking

Magnetic braking employs the magnetic force to reduce the speed of moving charges, effectively converting kinetic energy into other forms. This method is used in applications like electromagnetic railguns and certain types of particle accelerators.

Force on Current-Carrying Conductors

While the primary focus is on point charges, the magnetic force also acts on current-carrying conductors. The force per unit length on a conductor is given by:

$$ \frac{d\vec{F}}{dl} = I\vec{L} \times \vec{B} $$

Where $I$ is the current, $\vec{L}$ is the length vector, and $\vec{B}$ is the magnetic field.

Advanced Concepts

Magnetic Moment and Torque

A moving charge or a current loop possesses a magnetic moment, which interacts with external magnetic fields to experience torque. The torque ($\vec{\tau}$) on a magnetic moment ($\vec{\mu}$) is given by:

$$ \vec{\tau} = \vec{\mu} \times \vec{B} $$

This interaction is crucial in understanding the behavior of magnetic materials and the operation of devices like electric motors and generators.

Relativistic Considerations

From a relativistic perspective, electric and magnetic fields are interrelated and transform into each other under changes in reference frames. This interplay explains why a moving charge experiences a magnetic force, as viewed from different inertial frames.

Derivation from Special Relativity

Using Lorentz transformations, one can derive the magnetic field as a consequence of moving electric charges, highlighting the unified nature of electromagnetism.

Quantum Mechanical Perspective

At the quantum level, the interaction between moving charges and magnetic fields involves the coupling of the charge's spin and orbital motion with the magnetic field, leading to phenomena like the Zeeman effect.

Magnetohydrodynamics (MHD)

MHD studies the dynamics of electrically conducting fluids like plasmas, liquid metals, and saltwater in the presence of magnetic fields. The Lorentz force plays a significant role in the behavior of these fluids, influencing astrophysical phenomena and industrial processes.

Applications in Particle Accelerators

Magnetic fields are integral in steering and focusing charged particles in accelerators. Advanced concepts like synchrotrons use varying magnetic fields to maintain particle trajectories at high velocities.

Force on Multiple Charges

When dealing with multiple moving charges, the net force is the vector sum of the individual Lorentz forces. This principle is essential in understanding current interactions in conductors and the behavior of charge distributions in magnetic fields.

Magnetic Fields in Relativistic Electrodynamics

In high-velocity scenarios approaching the speed of light, magnetic fields must be treated within the framework of relativistic electrodynamics to accurately describe the force interactions.

Advanced Problem-Solving Techniques

Solving complex problems involving the direction of magnetic force on moving charges often requires breaking down vector components, applying multiple right-hand rule applications, and integrating calculus-based methods for non-uniform fields.

Interdisciplinary Connections

The principles governing the direction of magnetic force on moving charges intersect with various disciplines:

Engineering: Design of electric motors, generators, and magnetic storage devices.
Astronomy: Understanding stellar magnetism and cosmic ray propagation.
Medicine: Development of MRI machines relies on magnetic field interactions with charged particles.
Chemistry: Magnetic fields influence reaction rates and molecular alignments in certain conditions.

Helical Motion in Magnetic Fields

When a charged particle has velocity components both parallel and perpendicular to a magnetic field, it undergoes helical motion. The perpendicular component causes circular motion, while the parallel component results in linear motion along the field lines.

Force in Non-Uniform Magnetic Fields

In varying magnetic fields, additional considerations like magnetic field gradients and induced electric fields come into play, affecting the overall force experienced by moving charges.

Magnetic Shielding

Understanding the direction and behavior of magnetic forces aids in designing effective magnetic shielding to protect sensitive equipment and environments from external magnetic disturbances.

Electron Beam Deflection

Electron beams in devices like cathode ray tubes and electron microscopes are deflected using magnetic fields. Precise control over the force direction is essential for accurate imaging and manipulation.

Plasma Confinement in Fusion Reactors

Magnetic confinement is a critical aspect of containing plasma in fusion reactors. The direction of the magnetic force on ions and electrons ensures stability and prevents plasma leakage.

Force on Charges in Electromagnetic Waves

In electromagnetic waves, oscillating electric and magnetic fields exert forces on charges. The direction of these forces changes with the wave's propagation, leading to energy transfer and wave propagation dynamics.

Advanced Mathematical Techniques

Solving for force directions in complex magnetic field configurations may involve tensor calculus, vector analysis, and numerical methods to handle non-linear and time-varying fields.

Experimental Methods to Determine Force Direction

Techniques such as the Hall effect measurements, magnetic deflection experiments, and using electron microscopes allow experimental determination of force directions and verification of theoretical models.

Comparison Table

Aspect	Electric Force	Magnetic Force
Dependence on Velocity	Independent of velocity	Depends on velocity
Direction Relative to Fields	Along electric field lines	Perpendicular to velocity and magnetic field
Force Equation	$\vec{F} = q\vec{E}$	$\vec{F} = q\vec{v} \times \vec{B}$
Work Done	Can do work on charge	Does not do work on charge
Field Sources	Static charges	Moving charges or changing electric fields

Summary and Key Takeaways

The Lorentz force governs the magnetic force on a moving charge.
The right-hand rule is essential for determining force direction.
Magnetic force is perpendicular to both velocity and magnetic field vectors.
Advanced applications span across engineering, astronomy, and medicine.
Understanding force directions is crucial for designing electromagnetic devices.

Examiner Tip

Tips

- **Master the Right-Hand Rule:** Practice consistently to ensure accurate determination of force direction.
- **Visualize Vector Components:** Break down velocity into perpendicular and parallel components to simplify calculations.
- **Remember the Lorentz Equation:** Keep $\vec{F} = q\vec{v} \times \vec{B}$ handy for quick reference during exams.

Did You Know

1. The Earth's magnetic field plays a crucial role in protecting our planet from solar wind, influencing the motion of charged particles in the magnetosphere.
2. Magnetic forces are essential in the operation of MRI machines, which use strong magnetic fields to generate detailed images of the inside of the human body.
3. The concept of magnetic force on moving charges was instrumental in the development of the first particle accelerators, paving the way for advancements in nuclear physics.

Common Mistakes

1. **Incorrect Application of the Right-Hand Rule:** Students often point their thumb in the wrong direction, leading to an incorrect force direction.
2. **Assuming Magnetic Force Does Work:** Forgetting that the magnetic force only changes the direction of velocity, not its magnitude.
3. **Neglecting Velocity Components:** Ignoring the angle between velocity and magnetic field, resulting in incomplete force calculations.

FAQ

What is the Lorentz force?

The Lorentz force is the total force exerted on a charged particle moving through electric and magnetic fields, given by $\vec{F} = q\vec{E} + q\vec{v} \times \vec{B}$.

How does the right-hand rule determine force direction?

By aligning your right hand with the velocity and magnetic field vectors, your thumb points in the direction of the force for positive charges.

Why doesn't the magnetic force do work on the charge?

Because the magnetic force is always perpendicular to the velocity of the charge, it only changes the direction of motion, not its speed.

What happens to a charge moving parallel to a magnetic field?

When a charge moves parallel to a magnetic field, the magnetic force on it is zero since $\sin(0^\circ) = 0$.

Can magnetic fields influence stationary charges?

No, magnetic fields only exert forces on moving charges. Stationary charges are unaffected by magnetic fields.

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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Determine the Direction of the Force on a Charge Moving in a Magnetic Field

Introduction