# Biomedical Engineering (MEng)

## Electromagnetics 2

### Module aims

• To further explore the behaviour of static and dynamic electric and magnetic fields from a physical optics perspective. To introduce simple electromagnetic wave motion.
• To get an overview of the spectrum of electromagnetic radiation, and the applications of different frequencies, especially in the Biomedical field.
• To understand how electromagnetic waves behave at material boundaries, and the mechanism of their propagation along waveguides and optical fibres.
• To get an overview of the significance of special relativity to electromagnetic effects.
• To understand how waves diffrac

### Learning outcomes

Learning Outcomes - Knowledge and Understanding

• explain the relevance of EM spectrum in Biomedical context
• state Maxwell's equations and explain dispacement current
• an overview of the relevance of special relativity to EM
• describe vector fields in simple geometries
• interpret div and curl in the context of EM fields
• explain the boundary conditions between conductors and insulators
• explain the mechanism of EM plane wave propagation and surface waves
• describe polarization phenomena
• describe diffraction effects through apertures in far field

Learning Outcomes - Intellectual Skills

• determine boundary continuity relations
• solve Laplace's equation for static fields and simple boundary conditions
• solve the wave equation for conducting wall waveguides
• solve problems in optical waveguide transmission and dispersion
Learning Outcomes - Practical Skills
• To be able easily to measure the separation between tracks on a compact disc.
Learning Outcomes - Transferable Skills
• Further insight into vector calculus operators - div, grad, curl, Laplacian

### Module syllabus

Electromagnetic Waves: Differential forms; for electrostatics, the divergence of an electrostatic field; Laplace’s and Poisson’s equations; for magnetostatics; the curl of a vector field. Continuity of charge and concept of displacement current. Maxwell’s equations in differential form. Special relativity as significant to EM. The Helmholtz equation; plane waves, phase velocity, polarization, impedance, power flow, Poynting’s theorem. Boundary conditions; reflection and refraction of plane waves from conductors and dielectrics at plane and oblique incidence, total reflection, Brewster angle. Waveguides; conducting boundaries; dielectric waveguides; optical fibres.

Physical Optics :Spherical Waves, Huygens Principle, Diffraction, Diffraction from a rectangular aperture,

### Pre-requisites

BE1-HVAW Vibrations and Waves, BE1-HEM1 Electromagnetics 1 Vector calculus - div grad curl, Solution of 2nd order PDEs by separation of variables

### Teaching methods

Lectures: 18 hours
Study groups: 9 hours

### Assessments

Examinations:
●  Written exam: ; 80% weighting
Rubrics: 2 hour exam. Answer all four questions (100 marks each).
No type of previous exam answers or solutions will be available

Feedback : Feedback on Valentine's Day problem within two weeks of submission

### Supplementary

• #### Fields and waves in communication electronics

Ramo, Simon.

3rd ed., New York ; Chichester : Wiley

• #### Electromagnetic fields and waves : including electric circuits

Lorrain, Paul.

3rd ed., New York : Freeman

• #### Classical electromagnetism

Good, Robert H.

Fort Worth : Saunders College Pub.

• #### Electromagnetics : with applications

Kraus, John Daniel, 1910-

5th ed., Boston, Mass.; London : WCB/McGraw-Hill

• #### Lectures on electromagnetic theory

Solymar, L.

2nd ed., Oxford : Oxford University Press

• #### Sears and Zemansky's university physics : with modern physics /

Young, Hugh D.,

Fourteenth edition, Global edition., Pearson,

• #### Microwave engineering

Pozar, David M.

4th ed., Wiley

• #### Optics

Smith, Francis Graham, Sir, 1923-

2nd ed., Chichester : Wiley

• #### The Feynman lectures on physics. Vol. I, mainly mechanics, radiation and heat

Feynman, Richard Phillips, 1918-1988

• #### The Feynman lectures on physics. Volume II, Mainly electromagnetism and matter

Feynman, Richard Phillips.

Definitive ed., San Francisco, Calif. ; London : Pearson/Addison-Wesley

• #### The Feynman lectures on physics. Vol. III, Quantum mechanics

Feynman, Richard Phillips, 1918-1988

• #### The Feynman lectures on physics, vol. 1 for tablets

Feynman, Richard P.

New York : Basic Books

• #### The Feynman lectures on physics, vol. 2 for tablets

Feynman, Richard P.

New York : Basic Books

• #### The Feynman lectures on physics, vol. 3 for tablets

Feynman, Richard P.

New York : Basic Books

• #### Optical guided waves and devices

Syms, R.R.A.

London : McGraw-Hill