PX1221: Electricity, Magnetism and Waves

School Cardiff School of Physics & Astronomy
Department Code PHYSX
Module Code PX1221
External Subject Code 100425
Number of Credits 20
Level L4
Language of Delivery English
Module Leader Professor Jonathan Davies
Semester Spring Semester
Academic Year 2013/4

Outline Description of Module

To introduce the mathematical language of waves to describe wave formation, wave propagation and interference and diffraction.

To examine matter at an atomic level to give insight into crystal bonding and the electrical, thermal and mechanical properties of matter.

To introduce concepts of electrostatics, of magnetic fields associated with currents and of electromagnetic induction to provide a firm foundation for the study of electromagnetism in Year 2.

To provide insight into forced vibration and resonance through examples of AC theory and mechanical analogues.

To give instruction and practice in solving physics problem.

On completion of the module a student should be able to

Distinguish between different wave types and describe wave and energy propagation mathematically in one or more dimensions.

Apply boundary conditions to wave equations to determine the formation of standing waves in strings and pipes and explain refraction.

Demonstrate an understanding of interference and diffraction, including crystal diffraction.

Describe the distinguishing features between conductors, insulators and semiconductors.

Discuss phase changes in matter.

Describe the origin and nature of the various forces and fields associated with static and moving charges.

Recall the basic laws of electromagnetism and use integration methods to apply Coulomb’s law and the Biot-Savart law to complex systems of charges or circuits.

Derive basic equations for free and forced oscillations of damped electrical and mechanical systems using both real and complex notation.

How the module will be delivered

Teaching methods: 44 contact hours including lectures, exercises and problem-solving sessions.

Feedback: marked Exercises and tutorials.

Skills that will be practised and developed

Mathematics.
Problem solving.
Investigative skills.
Analytical skills.

How the module will be assessed

Assessment: Examination 60%. Coursework 40%. [Examination duration: 3 hours]

Assessment Breakdown

Type % Title Duration(hrs)
Exam - Spring Semester 60 Electricity, Magnetism And Waves 3
Written Assessment 40 Electricity, Magnetism And Waves N/A

Syllabus content

Waves: Classification of waves. One-dimensional non-dispersive waves. D’Alembert’s solution. Harmonic waves: wavelength, frequency, period, wavenumber and propagation vector. Derivation of the wave equation for transverse waves on a string. Energy density and power flow in a travelling wave.

Refraction and dispersion: Plane waves at boundaries. Refraction and Snell’s laws.  Refracting optics. Dispersion.

Superposition: Beats. Longitudinal waves in solids and sound waves. Sound intensity.  Spherical waves and the inverse square law. Standing waves. Interference and diffraction.  Examples.

Waves and matter: Light interaction with matter and elementary spectroscopy (Bohr theory).  Diffraction studies of solids, leading to atoms, bonding and crystal structure.

Electronic properties of matter: Electrical properties of materials – conductors, insulators and semiconductors. Free electrons, energy bands and band gaps. Semiconductor doping and the pn junction.

Coulomb’s and Gauss’s Laws: Electric charge and Coulomb’s law. E and V fields. Field lines and forces. Electric flux. Gauss’ law. Examples of charge distributions, including sphere and line.

Capacitance: Electric potential, potential difference, relationship between E and V. Electric energy and energy density. Capacitance. Dielectrics. Energy stored on a capacitor.  Capacitance of sphere and coaxial cable.

Electricity and magnetism: Conductivity, resistivity and resistance. Electrical power. Magnetic effects of current-carrying wires. Magnetic field lines, flux and Lorenz force. Biot-Savart law and applications. Torque on a current loop.

Electromagnetic induction: Faraday’s law and electromagnetic induction. Mutual and self inductance. Inductors.

AC Theory: Circuit elements: R, C and L. RMS. Power factors. LCR circuits. Rotating vector and complex-exponential representation. Phasor diagrams.

Resonance: Damped free vibrations. Light, heavy and critical damping. Quality factor. Forced vibration. Response functions: displacement amplitude and phase as a function of frequency. Absorbed power. Steady-state and transient solutions. Electrical and mechanical analogues.

Essential Reading and Resource List

Principles of Physics (Extended Version), Halliday, Resnick and Walker (Wiley)


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