Electromagnetic Fields and Applications I

Course Description

Electromagnetic Fields and Applications I covers electric and magnetic fields and forces, Maxwell's equations in point and integral form, plane wave propagation, and energy and power.

Within the SCNS taxonomy, EEL is the Electrical Engineering prefix. The University of West Florida publishes this at 3 semester hours through the Department of Electrical and Computer Engineering, College of Science and Engineering. Institutions carrying the integrated EEL3472C offer it at approximately 8 Florida institutions, making this joint-most widely taught in the prefix.

⚠ The SCNS title for this number is "Fundamentals of Electromagnetic Fields"; UWF publishes it as "Electromagnetic Fields and Applications I." The Roman numeral matters: UWF's title implies a sequence, and a student should ask whether a second course exists and whether it is required for their track. Carry a syllabus when transferring.

This is the course electrical engineering students most often name as the hardest in the programme, and the reason is that it is a mathematics course wearing an engineering title. Circuit theory is a simplification of electromagnetics that holds when a circuit is electrically small; this course removes that simplification and works with the fields themselves. Vector calculus is the working language — divergence, curl, gradient, and the integral theorems — and students whose vector calculus is shaky experience the course as impossible rather than merely hard.

The payoff is that Maxwell's equations explain what circuits cannot. Why a signal reflects from an impedance discontinuity, why a wire radiates, why two traces on a board couple, why an antenna works at all — none of these has a circuit-theory answer. Everything in RF, antennas, high-speed digital design, and electromagnetic compatibility descends from this material.

⚠ Why this guide exists under this number

Many Florida institutions carry this material as a single integrated course with a C suffix. UWF instead runs a separate lecture and a separate laboratory, each with its own SCNS number, and this guide documents the UWF lecture. Its laboratory partner is documented separately in this repository. ⚠ SCNS equivalency does not cross numbers, so a transfer between the integrated and split forms is evaluated by hand rather than automatically — carry a syllabus in either direction.

⚠ The contact-hour figure is derived — the University of West Florida publishes none

UWF's catalog publishes a credit value in semester hours, the college and department, prerequisites, and a description. It does not publish contact hours, a lecture and laboratory split, or terms of offering for any course. It does publish a material and supply fee notice on the minority of courses that carry one — and maintains a separate Material & Supply and Equipment Fees section of the catalog — so the absence of a fee notice on this entry is meaningful, while the fee amount is not published here. Every contact-hour value in a UWF guide in this repository is therefore derived. The figure here applies the standard lecture convention of 15 contact hours per credit, giving 45 hours for a 3-semester-hour course. Confirm the meeting schedule with the department.

Learning Outcomes

Required Outcomes

• Apply vector algebra and coordinate systems including cylindrical and spherical.
• Compute gradient, divergence, and curl in the appropriate coordinate system.
• Apply the divergence theorem and Stokes' theorem.
• Apply Coulomb's law and compute electric field from charge distributions.
• Apply Gauss's law to symmetric charge distributions.
• Relate electric potential to electric field.
• Solve Laplace's and Poisson's equations in simple geometries.
• Apply boundary conditions at material interfaces for electric fields.
• Describe dielectric materials, polarisation, and permittivity.
• Compute capacitance for standard geometries.
• Compute electrostatic energy and force.
• Apply the Biot-Savart law and Ampere's circuital law.
• Describe magnetic materials, magnetisation, and permeability.
• Apply boundary conditions for magnetic fields.
• Compute inductance for standard geometries.
• Apply Faraday's law of induction.
• State Maxwell's equations in both point and integral form and explain each term.
• Explain displacement current and its necessity.
• Derive and solve the wave equation for plane waves.
• Analyse plane wave propagation in lossless and lossy media.
• Apply the Poynting vector to compute power flow.

Optional Outcomes

• Analyse reflection and transmission at normal incidence.
• Analyse transmission lines from a field perspective.
• Describe skin effect and its engineering consequences.
• Describe waveguide propagation at an introductory level.
• Describe radiation and antenna fundamentals.
• Use field simulation software for a simple geometry.

Major Topics

Required Topics

• Vector algebra and coordinate systems
• Gradient, divergence, curl
• Divergence and Stokes' theorems
• Coulomb's law and electric field
• Gauss's law
• Electric potential
• Laplace and Poisson equations
• Electric boundary conditions
• Dielectrics and polarisation
• Capacitance
• Electrostatic energy and force
• Biot-Savart and Ampere's law
• Magnetic materials
• Magnetic boundary conditions
• Inductance
• Faraday's law
• Maxwell's equations: point and integral form
• Displacement current
• The wave equation and plane waves
• Propagation in lossy media
• The Poynting vector and power flow

Optional Topics

• Reflection and transmission at interfaces
• Transmission lines from field theory
• Skin effect
• Waveguides
• Radiation and antennas
• Field simulation

Resources & Tools

• Hayt and Buck, Engineering Electromagnetics — the most widely adopted text for this course, and the one most Florida programmes use.
• Sadiku, Elements of Electromagnetics — the common alternative, and generally regarded as gentler.
• Ulaby, Fundamentals of Applied Electromagnetics — strong on applications, with useful interactive modules.
• Griffiths, Introduction to Electrodynamics — a physics text, and unusually good at explaining why if the engineering texts feel mechanical.
• MIT OpenCourseWare 8.02 and 6.013 — free; 8.02's visualisations of field configurations are excellent for intuition.
• Paul Falstad's electromagnetics applets — free; seeing a plane wave propagate and reflect animated is worth several pages of algebra.
• MATLAB or Python with Matplotlib — plotting field configurations yourself builds intuition faster than reading about them.
• A vector calculus refresher — Khan Academy and MIT 18.02 are both free, and this is the single highest-value preparation for the course.
• ANSYS HFSS or the free tier of field solvers — the professional tool class; ask what UWF provides.

Career Pathways

• Electrical and electronics engineers — SOC 17-2071, 17-2072.
• RF and microwave engineering — a shortage specialism, and this course is its foundation.
• Antenna design — narrow and well compensated.
• Radar and electronic warfare — the strongest Florida connection: L3Harris (Melbourne, Palm Bay), Northrop Grumman (Melbourne), Lockheed Martin (Orlando), and the programmes at Eglin Air Force Base in UWF's region.
• Naval systems — NSA Panama City and NAS Pensacola, local to UWF.
• Satellite and space communications — the Space Coast.
• Electromagnetic compatibility engineering — every electronic product must pass emissions testing, and EMC engineers are in steady demand and short supply.
• High-speed digital and signal integrity — at modern data rates, board traces are transmission lines, and this material is what makes that tractable.
• Medical imaging — MRI is applied electromagnetics.
• ⚠ A practical note: this course is a filter. Students who do well here have a real advantage entering RF, and it is the course most often asked about in RF interviews.

Special Information

⚠⚠ The asterisk in a UWF prerequisite means the course may be taken at the same time

• UWF's catalog marks a concurrent course with an asterisk, defined on the catalog's Course Information page as: "This course may be taken prior to or during the same term."
• ⚠ This is the single most useful piece of notation in the UWF engineering catalog, and it is easy to miss. A prerequisite written without an asterisk must be completed first; one written with an asterisk may be taken in the same term.
• The practical effect is on time to degree. Reading an asterisked prerequisite as a hard prerequisite adds a term to the sequence for no reason, and in a tightly chained major like electrical engineering that error compounds down the whole plan.
• Confirm with an advisor before relying on it, and note that the registration system, not the catalog text, is what actually enforces the rule.

⚠ The prerequisite is EEL3111 — and the mathematics requirement is implicit

• UWF publishes EEL3111 Circuits I as the sole prerequisite, not asterisked, so it must be complete.
• ⚠⚠ No vector calculus prerequisite is published, and vector calculus is the working language of the course. Calculus III normally supplies it, and it is reached through the mathematics chain rather than named here — which means a student can be eligible to enrol without having consolidated the mathematics the course depends on.
• ⚠ Refresh vector calculus before the term starts. Line, surface, and volume integrals in cylindrical and spherical coordinates, plus divergence and curl, are used from week one. This is the most valuable preparation available for this course, and it costs a few days.
• Physics with electricity and magnetism (PHY2049) is genuine preparation even though the requirement reaches this course indirectly through Circuits I.

⚠⚠ Why this course is hard, stated honestly

• It is abstract in a way earlier engineering courses are not. Circuits have a schematic to point at; fields exist in three-dimensional space and must be visualised.
• ⚠ The mathematical load is genuinely heavy. Multivariable integration in three coordinate systems, vector identities, and partial differential equations all appear, and students frequently discover that their calculus was passed rather than learned.
• ⚠⚠ Choosing the coordinate system correctly is most of the work. A problem that is brutal in Cartesian coordinates is often a few lines in spherical, and recognising the symmetry before starting is the skill being taught.
• Gauss's and Ampere's laws only give easy answers under symmetry. Applying them where symmetry does not hold is the classic error — they remain true and stop being useful.
• Budget 10 to 12 hours a week outside class. This is at the top of the range for the whole curriculum, and students who treat it like an average 3-credit course fall behind irrecoverably around the magnetostatics unit.
• Draw the geometry for every problem. Students who attempt these problems without a sketch produce integrals with the wrong limits.
• ⚠ Do not take this alongside two other analysis-heavy courses if the schedule can be arranged otherwise.

⚠ What the course explains that circuit theory cannot

• Circuit theory is an approximation valid when the circuit is small compared with a wavelength. This course is where that assumption is named and then removed, and knowing when circuit theory stops applying is itself a professional skill.
• ⚠⚠ At high frequency every conductor is a transmission line. A signal that takes appreciable time to traverse a trace reflects at discontinuities, and this is why high-speed digital design is an electromagnetics problem rather than a logic problem.
• Skin effect means current crowds toward the conductor surface as frequency rises, so resistance is frequency-dependent — which explains conductor sizing at RF and why hollow conductors are used.
• Displacement current is what makes electromagnetic waves possible. Maxwell's addition to Ampere's law is the term that lets a changing electric field produce a magnetic field, closing the loop that permits propagation through empty space.
• The Poynting vector shows that energy flows in the fields between conductors, not inside them — a genuinely counterintuitive result and one of the more satisfying moments in the course.

FE exam relevance

The Fundamentals of Engineering (FE) exam is the first step toward Professional Engineer licensure, and in Florida it is administered under the Florida Board of Professional Engineers. Most students take the FE Electrical and Computer exam in their final year. Licensure matters less in electrical engineering than in civil — the industrial exemption means most electrical engineers in manufacturing and product work never need a PE — but it is required for consulting practice, for sealing designs, and for power and building-systems work, which is exactly where Florida's utility and infrastructure employment sits.

Course format and position in the curriculum

• Lecture with substantial problem sets and examinations.
• Typically taken in the third year, after Circuits I.
• ⚠ The title's "I" implies a sequence — ask the department whether a second electromagnetics course exists and whether your track requires it.
• Essential preparation for RF and antenna work, including EEL4514 and its laboratory.
• UWF publishes no contact hours, lecture and laboratory split, or terms of offering for any course, and no material and supply fee is noted on this entry. Confirm the offering pattern with the department.

How Florida course levels affect transfer

The first digit of an SCNS number denotes the year of offering, not transferability. Courses at the 1000 and 2000 levels transfer transparently between Florida public institutions, and 3000 to 4000 is unproblematic since both are upper division. The boundary that actually matters is 2000 to 3000, where lower-division credit generally cannot satisfy an upper-division requirement. ⚠ For engineering specifically, ABET-accredited programmes commonly require that upper-division engineering coursework be taken in residence, so transferability of the credit and applicability to the degree are separate questions.

EEL3472 is 3 semester hours at the University of West Florida. Institutions carrying the integrated EEL3472C combine this with laboratory work in one course, and because the SCNS and local titles differ, students transferring credit should carry a syllabus.