Magnetic Flux & Flux Linkage

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Magnetic Flux Definitions

Three terms that are closely related but different are magnetic flux, magnetic flux density and magnetic flux linkage.

Definitions

Magnetic flux is a measure of the number of field lines passing through a region of space.
Magnetic flux density is a measure of the number of field lines passing through a region of space per unit cross-sectional area.
Magnetic flux linkage is the product of the magnetic flux and the number of turns on a coil through which the field passes.

Different flux density

The two loops in the diagram have the same flux but different flux densities since area Y is larger than area X.

Different flux

The two loops in the diagram have the same flux density but different flux since area Y is larger than area X.

Different flux linkage

The two loops in the diagram have the same flux and flux density, but as loop Y has twice the number of turns as loop X, the flux linkage in Y is twice that of loop X.

Magnetic Flux and Flux Linkage

The formulae for magnetic flux and magnetic flux linkage are:

Magnetic flux, Φ

The magnetic flux is the amount of magnetic field passing through a surface.
The equation for magnetic flux is:
- $\Phi = BA \cos \theta = B_\perp A$
  - Where $\phi$ is the flux, B is the field strength, A is the area and theta is the angle between the normal of the surface and the field.

Magnetic flux linkage, nΦ

The magnetic flux linkage is the amount of field passing through a coil of wire. It is the flux 'linked' to a wire.
The equation for the flux linkage is:
- $N \Phi = BAN \cos \theta$
  - Where N is the number of coils in the wire.

Magnetic Flux Linkage Experiment

This experiment investigates how magnetic flux linkage varies with the angle between a search coil and the magnetic field direction. This is done using a search coil and an oscilloscope.

Apparatus

Set up the apparatus as shown in the diagram.
The search coil will experience a flux linkage as determined by the formula:
- $N \Phi = BAN \cos \theta$ .

Underlying theory

The magnetic field inside the coil will be uniform and running parallel to the length of the spring (across the page horizontally in the diagram).
As the current is a.c., there will be a varying magnetic flux density through the search coil, and hence a varying flux linkage.

Underlying theory 2

This will induce an EMF in the search coil which is detected by the oscilloscope.
The time base (time axis) of the oscilloscope is turned off, so that the a.c. induced gives a vertical line on the screen. The amplitude of this line (from the peak to the middle) gives the magnitude of the induced EMF.

Method

The search coil can now be rotated so that the angle between the plane of the coil and the magnetic field lines changes.
By recording the amplitude of the induced EMF every 10 degrees, a graph of EMF induced against angle can be plotted, showing the relationship between the flux linkage and the angle between the normal to the plane of the coil and the magnetic field lines.

1Measurements & Errors

1.1Measurements & Errors

1.1.1Use of SI Units

1.1.2SI Prefixes, Standard Form & Converting Units

1.1.3End of Topic Test - Units & Prefixes

1.1.4Limitation of Physical Measurements

1.1.5Uncertainty

1.1.6Estimation

1.1.7End of Topic Test - Measurements & Errors

2Particles & Radiation

2.1Particles

2.1.1Atomic Model

2.1.2Specific Charge, Protons & Neutron Numbers

2.1.3End of Topic Test - Atomic Model

2.1.4Isotopes

2.1.5Stable & Unstable Nuclei

2.1.6End of Topic Test - Isotopes & Nuclei

2.1.7A-A* (AO3/4) - Stable & Unstable Nuclei

2.1.8Particles, Antiparticles & Photons

2.1.9Particle Interactions

2.1.10Classification of Particles

2.1.11End of Topic Test - Particles & Interactions

2.1.12Quarks & Antiquarks

2.1.13Application of Conservation Laws

2.1.14End of Topic Test - Leptons & Quarks

2.1.15Exam-Style Question - Radioactive Decay

2.2Electromagnetic Radiation & Quantum Phenomena

2.2.1The Photoelectric Effect

2.2.2The Photoelectric Effect Explanation

2.2.3End of Topic Test - The Photoelectric Effect

2.2.4Collisions of Electrons with Atoms

2.2.5Energy Levels & Photon Emission

2.2.6Wave-Particle Duality

2.2.7End of Topic Test - Absorption & Emission

3Waves

3.1Progressive & Stationary Waves

3.1.1Progressive Waves

3.1.2Wave Speed & Phase Difference

3.1.3Longitudinal & Transverse Waves

3.1.4End of Topic Test - Progressive Waves

3.1.5Polarisation

3.1.6Stationary Waves

3.1.7Stationary Waves 2

3.1.8End of Topic Test - Polarisation & Stationary Wave

3.1.9A-A* (AO3/4) - Stationary Waves

3.2Refraction, Diffraction & Interference

3.2.1Interference

3.2.2Interference 2

3.2.3End of Topic Test - Interference

3.2.4Diffraction

3.2.5Diffraction Gratings

3.2.6End of Topic Test - Diffraction

3.2.7Refraction at a Plane Surface

3.2.8Internal Reflection & Fibre Optics

3.2.9End of Topic Test - Refraction

3.2.10Exam-Style Question - Waves

4Mechanics & Materials

4.1Force, Energy & Momentum

4.2Materials

4.2.1Density

4.2.2Bulk Properties of Solids

4.2.3Energy in Materials

4.2.4Young Modulus

4.2.5End of Topic Test - Materials

5Electricity

5.1Current Electricity

5.1.1Basics of Electricity

5.1.2Current-Voltage Characteristics

5.1.3End of Topic Test - Basics of Electricity

5.1.4Resistivity

5.1.5Superconductivity

5.1.6A-A* (AO3/4) - Superconductivity

5.1.7End of Topic Test - Resistivity & Superconductors

5.1.8Circuits

5.1.9Power and Conservation

5.1.10Potential Divider

5.1.11Emf & Internal Resistance

5.1.12End of Topic Test - Power & Potential

5.1.13Exam-Style Question - Resistance

6Further Mechanics & Thermal Physics (A2 only)

6.1Periodic Motion (A2 only)

6.1.1Circular Motion

6.1.2Circular Motion 2

6.1.3End of Topic Test - Circular Motion

6.1.4Simple Harmonic Motion

6.1.5Simple Harmonic Systems

6.1.6Energy in Simple Harmonic Motion

6.1.7Resonance

6.1.8End of Topic Test - Simple Harmonic Motion

6.1.9A-A* (AO3/4) - Simple Harmonic Motion

6.2Thermal Physics (A2 only)

6.2.1Thermal Energy Transfer

6.2.2Thermal Energy Transfer Experiments

6.2.3Ideal Gases

6.2.4Ideal Gases 2

6.2.5Boyle's Law & Charles' Law

6.2.6Molecular Kinetic Theory Model

6.2.7Molecular Kinetic Theory Model 2

6.2.8End of Topic Test - Thermal Energy & Ideal Gases

6.2.9Exam-Style Question - Ideal Gases

7Fields & Their Consequences (A2 only)

7.1Fields (A2 only)

7.1.1Fields

7.2Gravitational Fields (A2 only)

7.2.1Newton's Law

7.2.2Gravitational Field Strength

7.2.3Gravitational Potential

7.2.4Orbits of Planets & Satellites

7.2.5Escape Velocity & Synchronous Orbits

7.2.6End of Topic Test - Gravitational Fields

7.3Electric Fields (A2 only)

7.3.1Coulomb's Law

7.3.2Electric Field Strength

7.3.3Electric Field Strength 2

7.3.4Electric Potential

7.3.5End of Topic Test - Electric Fields

7.3.6A-A* (AO3/4) - Electric and Gravitational Field

7.4Capacitance (A2 only)

7.4.1Capacitance

7.4.2Parallel Plate Capacitor

7.4.3Energy Stored by a Capacitor

7.4.4Capacitor Discharge

7.4.5Capacitor Charge

7.5Magnetic Fields (A2 only)

7.5.1Magnetic Flux Density

7.5.2End of Topic Test - Capacitance & Flux Density

7.5.3Moving Charges in a Magnetic Field

7.5.4Magnetic Flux & Flux Linkage

7.5.5Electromagnetic Induction

7.5.6Electromagnetic Induction 2

7.5.7Alternating Currents

7.5.8Operation of a Transformer

7.5.9Magnetic Flux Density

7.5.10End of Topic Test - Electromagnetic Induction

8Nuclear Physics (A2 only)

8.1Radioactivity (A2 only)

8.1.1Rutherford Scattering

8.1.2Alpha & Beta Radiation

8.1.3Gamma Radiation

8.1.4Radioactive Decay

8.1.5Half Life

8.1.6End of Topic Test - Radioactivity

8.1.7Nuclear Instability

8.1.8Nuclear Radius

8.1.9Mass & Energy

8.1.10Binding Energy

8.1.11Induced Fission

8.1.12Safety Aspects of Nuclear Reactors

8.1.13End of Topic Test - Nuclear Physics

8.1.14A-A* (AO3/4) - Nuclear Fusion

9Option: Astrophysics (A2 only)

9.1Telescopes (A2 only)

9.1.1Astronomical Telescopes

9.1.2Reflecting Telescopes

9.1.3Single Dish Radio Telescopes

9.1.4Large Diameter Telescopes

9.2Classification of Stars (A2 only)

9.2.1Classification by Luminosity

9.2.2Absolute Magnitude

9.2.3Black Body Radiation

9.2.4Stellar Spectral Classes

9.2.5Hertzsprung-Russell Diagrams

9.2.6Astronomical Objects

9.3Cosmology (A2 only)

9.3.1Doppler Effect

9.3.2Hubble's Law

9.3.3Quasars

9.3.4Detecting Exoplanets

10Option: Medical Physics (A2 only)

10.1Physics of the Eye (A2 only)

10.1.1Physics of Vision

10.1.2Defects of Vision

10.1.3Lenses

10.1.4Correcting Defects of Vision

10.2Physics of the Ear (A2 only)

10.2.1Structure of the Ear

10.2.2Sensitivity of the Ear

10.2.3Hearing Defects

10.3Biological Measurement (A2 only)

10.3.1Electrocardiography (ECG)

10.4Non-Ionising Imaging (A2 only)

10.4.1Ultrasound Imaging

10.4.2Ultrasound Imaging 2

10.4.3Fibre Optics & Endoscopy

10.4.4Magnetic Resonance Scanning

10.5X-Ray Imaging (A2 only)

10.5.1Diagnostic X-Rays

10.5.2X-Ray Image Processing

10.5.3Absorption of X-Rays

10.5.4CT Scanners

10.6Radionuclide Imaging & Therapy (A2 only)

10.6.1Imaging Techniques

10.6.2Half Life

10.6.3Gamma Camera

10.6.4High Energy X-Rays

10.6.5Radioactive Implants

10.6.6Imaging Comparisons

11Option: Engineering Physics (A2 only)

11.1Rotational Dynamics (A2 only)

11.1.1Moment of Inertia

11.1.2Rotational Kinetic Energy

11.1.3Rotational Motion

11.1.4Torque & Angular Acceleration

11.1.5Angular Momentum

11.1.6Angular Work & Power

11.2Thermodynamics & Engines (A2 only)

11.2.1First Law of Thermodynamics

11.2.2Non-Flow Processes

11.2.3p-V Diagrams

11.2.4Engine Cycles

11.2.5Second Law & Engines

11.2.6Reversed Heat Engines

12Option: Turning Points in Physics (A2 only)

12.1Discovery of the Electron (A2 only)

12.1.1Cathode Rays

12.1.2Thermionic Electron Emission

12.1.3Electron Specific Charge

12.1.4Millikan's Experiment

12.2Wave-Particle Duality (A2 only)

12.2.1Newton's & Huygen's Theories of Light

12.2.2Electromagnetic Waves

12.2.3Photoelectricity

12.2.4Wave-Particle Duality

12.2.5Electron Microscopes

12.3Special Relativity (A2 only)

12.3.1Michelson-Morley Experiment

12.3.2Einstein's Theory of Special Relativity

12.3.3Time Dilation

12.3.4Length Contraction

12.3.5Mass & Energy

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