Magnetic flux density, a fundamental concept in electromagnetism, quantifies the strength and direction of a magnetic field. Understanding how magnetic flux density interacts with current-carrying conductors is essential for comprehending various physical phenomena and technological applications. This topic is pivotal for students studying Physics - 9702 under the AS & A Level board, providing foundational knowledge for advanced studies in magnetic fields and electromagnetic theory.

Key Concepts

Understanding Magnetic Flux Density

Magnetic flux density, often represented by the symbol B, measures the amount of magnetic flux passing through a unit area perpendicular to the direction of the magnetic field. It is a vector quantity, possessing both magnitude and direction, and is expressed in teslas (T) in the International System of Units (SI).

Force on a Current-Carrying Conductor

The interaction between a magnetic field and a current-carrying conductor results in a force, known as the Lorentz force. The magnitude of this force F can be determined using the equation:

$$ F = B \cdot I \cdot L \cdot \sin(\theta) $$

Where:

F = Force (newtons, N)
B = Magnetic flux density (teslas, T)
I = Current (amperes, A)
L = Length of the conductor in the magnetic field (meters, m)
θ = Angle between the direction of the current and the magnetic field

When the conductor is positioned at right angles to the magnetic field (θ = 90°), the equation simplifies to:

$$ F = B \cdot I \cdot L $$

Magnetic Flux Density Defined

Magnetic flux density can thus be interpreted as the force experienced per unit current per unit length of the conductor when positioned perpendicular to the magnetic field. Mathematically, it is defined as:

$$ B = \frac{F}{I \cdot L} $$

This definition highlights the relationship between the magnetic field strength, the current flowing through the conductor, and the resultant force.

Right-Hand Rule

To determine the direction of the force exerted on a current-carrying conductor in a magnetic field, the right-hand rule is employed. Point your thumb in the direction of the current, your fingers in the direction of the magnetic field, and your palm will indicate the direction of the force.

Applications of Magnetic Flux Density

Understanding magnetic flux density is crucial in various applications such as electric motors, generators, and transformers. It plays a vital role in the design and functioning of these devices by dictating the efficiency and magnitude of the forces involved.

Calculating Magnetic Flux

Magnetic flux (Φ) is related to magnetic flux density by the equation:

$$ Φ = B \cdot A \cdot \cos(\theta) $$

Where:

A = Area perpendicular to the magnetic field (square meters, m²)

This relationship is essential in understanding how magnetic fields interact with materials and conductors.

Unit of Magnetic Flux Density

The tesla (T) is the SI unit for magnetic flux density. One tesla is equivalent to one weber per square meter (1 T = 1 Wb/m²).

Biot-Savart Law

The Biot-Savart Law provides a mathematical expression for the magnetic flux density generated by a steady current. It states that the differential magnetic flux density (dB) at a point in space is directly proportional to the current (I) and the differential length of the conductor (dl), and inversely proportional to the square of the distance (r) from the conductor to the point:

$$ dB = \frac{\mu_0}{4\pi} \cdot \frac{I \cdot dl \times \hat{r}}{r^2} $$

Where:

μ₀ = Permeability of free space (μ₀ = 4π × 10⁻⁷ T.m/A)

Magnetic Field Produced by a Long Straight Conductor

A long straight conductor carrying a steady current produces a magnetic field that forms concentric circles around the conductor. The magnitude of the magnetic flux density at a distance r from the conductor is given by:

$$ B = \frac{\mu_0 I}{2\pi r} $$

This equation underscores the inverse relationship between the magnetic flux density and the distance from the current-carrying conductor.

Magnetic Flux Density in Materials

In materials, magnetic flux density is influenced by the material's magnetic permeability. The relationship is expressed as:

$$ B = \mu \cdot H $$

Where:

H = Magnetic field strength (A/m)
μ = Magnetic permeability of the material (T.m/A)

This relationship is fundamental in understanding how different materials respond to magnetic fields.

Measuring Magnetic Flux Density

Devices such as the gaussmeter and the Hall effect sensor are commonly used to measure magnetic flux density. These instruments are essential in both laboratory settings and industrial applications to quantify and monitor magnetic fields.

Impact of Magnetic Flux Density in Electromagnetic Induction

Electromagnetic induction relies heavily on the variation of magnetic flux density. According to Faraday's Law, a change in magnetic flux density within a closed loop induces an electromotive force (EMF) in the conductor:

$$ &mathcal;E = -\frac{dΦ}{dt} $$

This principle is the cornerstone of the functioning of generators and transformers.

Magnetic Flux Density and Energy Density

The energy density (u) of a magnetic field is related to the magnetic flux density by the equation:

$$ u = \frac{B^2}{2\mu_0} $$

This relationship is crucial in evaluating the energy stored within a magnetic field, which has implications in both theoretical studies and practical applications such as magnetic storage devices.

Practical Example: Calculating Magnetic Flux Density

Consider a straight conductor carrying a current of 5 A placed in a uniform magnetic field and perpendicular to it. If the force per unit length experienced by the conductor is 2 N/m, the magnetic flux density can be calculated using the formula:

$$ B = \frac{F}{I \cdot L} $$

Substituting the given values:

$$ B = \frac{2 \, \text{N/m}}{5 \, \text{A} \cdot 1 \, \text{m}} = 0.4 \, \text{T} $$>

Thus, the magnetic flux density is 0.4 teslas.

Significance in Electromechanical Systems

Magnetic flux density is integral in designing electromechanical systems. It influences the selection of materials and the configuration of components to ensure optimal performance and energy efficiency.

Advanced Concepts

Mathematical Derivation of Magnetic Flux Density Around a Current-Carrying Conductor

The magnetic flux density around a long straight conductor can be derived using the Biot-Savart Law. For a straight conductor of infinite length carrying a steady current I, the Biot-Savart Law simplifies as follows:

$$ B = \frac{\mu_0 I}{2\pi r} $$>

This derivation assumes a symmetrical distribution of the magnetic field and employs integration over the length of the conductor to arrive at the expression for B.

Biot-Savart Law in Depth

The Biot-Savart Law is foundational in electromagnetism, allowing the calculation of magnetic fields generated by arbitrary current distributions. For a differential current element Idl, the differential magnetic flux density at a point P is given by:

$$ dB = \frac{\mu_0}{4\pi} \cdot \frac{I \cdot dl \times \hat{r}}{r^2} $$>

Integrating this expression over the entire current distribution provides the total magnetic flux density at point P.

Magnetic Vector Potential

The magnetic vector potential (A) is a vector field whose curl is equal to the magnetic flux density:

$$ \nabla \times \mathbf{A} = \mathbf{B} $$>

In magnetostatics, the vector potential due to a current distribution is given by:

$$ \mathbf{A}(\mathbf{r}) = \frac{\mu_0}{4\pi} \int \frac{\mathbf{J}(\mathbf{r}')}{|\mathbf{r} - \mathbf{r}'|} dV' $$>

This formulation is particularly useful in solving complex electromagnetic problems involving boundary conditions and material interfaces.

Maxwell's Equations and Magnetic Flux Density

Maxwell's Equations provide a comprehensive framework for understanding electromagnetic phenomena. Specifically, Gauss's Law for Magnetism states that the net magnetic flux out of any closed surface is zero, implying that magnetic field lines are continuous and have no beginning or end:

$$ \nabla \cdot \mathbf{B} = 0 $$>

This fundamental principle underscores the absence of magnetic monopoles in classical electromagnetism.

Advanced Problem-Solving: Magnetic Field in a Solenoid

Consider a solenoid with N turns per unit length, carrying a current I. The magnetic flux density inside the solenoid is uniform and given by:

$$ B = \mu_0 n I $$>

Where:

n = Number of turns per unit length

This formula assumes an ideal solenoid with an infinitely long length, where edge effects are negligible.

Energy Stored in a Magnetic Field

The energy (E) stored in a magnetic field within a volume is calculated using the energy density formula integrated over that volume:

$$ E = \int \frac{B^2}{2\mu_0} dV $$>

This concept is vital in designing energy storage systems like inductors and magnetic capacitors.

Interdisciplinary Connections: Magnetic Flux Density in Medicine

Magnetic flux density plays a crucial role in medical imaging technologies such as Magnetic Resonance Imaging (MRI). In MRI machines, strong magnetic fields are generated to align nuclear spins, providing detailed images of internal body structures.

Non-Uniform Magnetic Fields

In practical scenarios, magnetic fields are often non-uniform. The variation of magnetic flux density with position requires the application of calculus-based methods to determine the resultant forces and field distributions.

Magnetic Flux Density in Electromagnetic Waves

In electromagnetic waves, magnetic flux density oscillates perpendicular to the electric field and the direction of wave propagation. The relationship between electric and magnetic fields in such waves is given by:

$$ c = \frac{E}{B} $$>

Where:

c = Speed of light
E = Electric field strength

This interplay is fundamental to the propagation of electromagnetic radiation through space.

Advanced Calculations: Superposition of Magnetic Fields

The principle of superposition states that the total magnetic flux density at a point due to multiple sources is the vector sum of the individual magnetic flux densities produced by each source. Mathematically:

$$ \mathbf{B}_{total} = \sum \mathbf{B}_i $$>

This principle is essential in analyzing complex magnetic environments with multiple current-carrying conductors.

Time-Varying Magnetic Fields and Induced EMF

When magnetic flux density varies with time, it induces an electromotive force (EMF) in conductors, as described by Faraday's Law of Induction:

$$ \mathcal{E} = -\frac{d\Phi}{dt} $$>

This phenomenon is exploited in the operation of electrical generators and inductors.

Magnetic Flux Density in Ferromagnetic Materials

Ferromagnetic materials exhibit high magnetic permeability, significantly enhancing the magnetic flux density within them when subjected to external magnetic fields. This property is harnessed in constructing transformers and magnetic cores to concentrate magnetic fields.

Complex Geometries and Magnetic Field Simulation

In engineering applications, magnetic flux density in complex geometries is often determined using numerical methods and simulation software. Finite Element Analysis (FEA) is a common technique used to model and predict magnetic field distributions in intricate systems.

Comparison Table

Aspect	Magnetic Flux Density (B)	Magnetic Field Strength (H)
Definition	Measure of the magnetic field's strength and direction	Measure of the magnetizing force
Unit	Tesla (T)	Ampere per meter (A/m)
Relation in Vacuum	$B = \mu_0 H$	$H = \frac{B}{\mu_0}$
Material Dependency	Directly influenced by the medium's permeability	Independent of the medium's properties
Applications	Used in calculating force on conductors, energy density	Used in characterizing magnetic materials and designing magnetic circuits
Mathematical Expression	$B = \mu H$	Derived from $B = \mu H$

Summary and Key Takeaways

Magnetic flux density (B) quantifies the strength and direction of a magnetic field.
It is defined as the force per unit current per unit length on a wire placed perpendicular to the magnetic field.
Understanding B is essential for analyzing forces in electromagnets, motors, and generators.
Advanced concepts include mathematical derivations, Maxwell's Equations, and applications in various technologies.
The comparison between B and H highlights their distinct roles in electromagnetic theory.

Examiner Tip

Tips

Remember the mnemonic "B is for Both force and field" to distinguish between B and H. When applying the right-hand rule, practice with physical objects like wires and magnets to build intuition. Additionally, always double-check the units in your calculations to ensure consistency and avoid common numerical errors.

Did You Know

Magnetic flux density isn't just a theoretical concept—it plays a crucial role in the functioning of particle accelerators like the Large Hadron Collider, where precise magnetic fields guide particle beams. Additionally, varying magnetic flux densities are harnessed in wireless charging technologies, enabling efficient power transfer without direct electrical connections.

Common Mistakes

Students often confuse magnetic flux density (B) with magnetic field strength (H), leading to incorrect calculations. Another frequent error is neglecting the angle between current and magnetic field vectors, which is crucial for accurate force determination. Lastly, assuming uniform magnetic fields in all scenarios can result in misunderstandings when dealing with real-world, non-uniform fields.

FAQ

What is the unit of magnetic flux density?

Magnetic flux density is measured in teslas (T), where 1 tesla equals 1 weber per square meter (1 T = 1 Wb/m²).

How does magnetic flux density differ from magnetic field strength?

Magnetic flux density (B) measures the strength and direction of the magnetic field, while magnetic field strength (H) quantifies the magnetizing force. They are related by the equation B = μH, where μ is the permeability of the medium.

How is magnetic flux density calculated for a current-carrying wire?

For a long straight conductor, magnetic flux density at a distance r from the wire is calculated using the formula B = (μ₀I)/(2πr), where μ₀ is the permeability of free space and I is the current.

What role does magnetic flux density play in electromagnetic induction?

Can magnetic flux density exist without a current?

Yes, magnetic flux density can exist without a current. Permanent magnets produce a magnetic flux density due to the alignment of magnetic domains within the material, independent of any external current.

How is magnetic flux density measured in practical applications?

Magnetic flux density is typically measured using instruments like gaussmeters and Hall effect sensors, which provide precise measurements of the magnetic field strength in various environments.

Define magnetic flux density as the force per unit current per unit length on a wire at right angles. Explore key and advanced concepts for AS & A Level Physics.

magnetic flux density, B field, Lorentz force, current-carrying conductor, AS A Level Physics, electromagnetic theory, Biot-Savart Law, magnetic fields, Physics 9702, magnetic induction

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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Define Magnetic Flux Density as the Force per Unit Current per Unit Length on a Wire at Right Angles

Introduction

Key Concepts

Understanding Magnetic Flux Density

Force on a Current-Carrying Conductor

Magnetic Flux Density Defined

Right-Hand Rule

Applications of Magnetic Flux Density

Calculating Magnetic Flux

Unit of Magnetic Flux Density

Biot-Savart Law

Magnetic Field Produced by a Long Straight Conductor

Magnetic Flux Density in Materials

Measuring Magnetic Flux Density

Impact of Magnetic Flux Density in Electromagnetic Induction

Magnetic Flux Density and Energy Density

Practical Example: Calculating Magnetic Flux Density

Significance in Electromechanical Systems

Advanced Concepts

Mathematical Derivation of Magnetic Flux Density Around a Current-Carrying Conductor

Biot-Savart Law in Depth

Magnetic Vector Potential

Maxwell's Equations and Magnetic Flux Density

Advanced Problem-Solving: Magnetic Field in a Solenoid

Energy Stored in a Magnetic Field

Interdisciplinary Connections: Magnetic Flux Density in Medicine

Non-Uniform Magnetic Fields

Magnetic Flux Density in Electromagnetic Waves

Advanced Calculations: Superposition of Magnetic Fields

Time-Varying Magnetic Fields and Induced EMF

Magnetic Flux Density in Ferromagnetic Materials

Complex Geometries and Magnetic Field Simulation

Comparison Table

Summary and Key Takeaways

Coming Soon!

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