PHY4323: Electricity and Magnetism I

Course Description

PHY4323 Electricity and Magnetism I is the physics major's serious treatment of electromagnetism — the same subject met in introductory physics, rebuilt on vector calculus and carried through to Maxwell's equations.

The course is offered at approximately four Florida institutions: Florida A&M University, Florida International University, Florida State University and the University of West Florida.

The University of West Florida places it in the College of Science and Engineering, Department of Physics at 3 semester hours, requires MAC 2313 AND MAP 2302 AND PHY 2049 AND PHZ 4113, and covers "electrostatics, Gauss's Theorem, magnetic fields, Biot-Savart Law, electromagnetic induction, introduction to Maxwell's Equations, and electromagnetic waves." ⚠ It adds that "a grade of C- or better is required for prerequisite courses."

Florida State University carries it at 3 credits with prerequisites PHY 3221 and PHZ 3113, covering "electric fields for static charge distributions, electric fields in matter, magnetic fields for constant current configurations, magnetic fields in matter, and Maxwell's equations."

The two descriptions cover the same syllabus — FSU names the treatment of fields in matter explicitly, UWF names electromagnetic waves — and both are standard. ⚠ The prerequisite structures differ in an instructive way: both require a mathematical methods course, but they place it differently in the sequence. See Special Information.

What makes this course a genuine step up, and it is the step most physics majors find hardest. Introductory electricity and magnetism teaches the same physical laws with the mathematics kept manageable — symmetric charge distributions, integrals you can evaluate by inspection. This course removes the training wheels. The subject is expressed in vector calculus: divergence, curl, gradient, line and surface and volume integrals, and the theorems of Gauss and Stokes that connect them. ⚠ The physics is not new; the mathematics is, and the mathematics is where students struggle.

The structure of the course is an argument, and seeing it as one helps enormously. Electrostatics comes first — Coulomb's law, the electric field, potential, and the enormously useful observation that a static electric field is curl-free, so it can be written as the gradient of a scalar potential, which converts a vector problem into a scalar one. Then boundary-value problems and the methods for solving them: separation of variables, the method of images, multipole expansion. Then fields in matter — polarisation, bound charge, the displacement field. Then magnetostatics, which is structurally parallel but where the field is divergence-free rather than curl-free, so the potential is a vector rather than a scalar. Then magnetic materials. And then induction, which couples the two, and the assembly of the whole into Maxwell's equations.

⚠ The moment the course exists for is Maxwell's displacement current term. Adding it to Ampère's law is required for consistency with charge conservation — and the resulting equations immediately predict waves propagating at a speed calculable from two measured electrical constants, a speed that turns out to be the speed of light. Light is an electromagnetic wave, and this is where a student derives that rather than being told it. It is one of the genuine intellectual high points of an undergraduate physics degree.

Position and consequence. This is a required core course in every physics major, normally the second of the theory sequence after classical mechanics. It gates PHY4324 (Electricity and Magnetism II), and its mathematical methods underpin quantum mechanics, optics and electrodynamics-heavy applied work. ⚠ It is also, along with quantum mechanics, one of the two courses graduate admissions committees look at hardest, and its material is a substantial share of the Physics GRE.

Learning Outcomes

Required Outcomes

• Apply vector calculus — gradient, divergence, curl, the Laplacian — in Cartesian, cylindrical and spherical coordinates.
• Apply the divergence and Stokes theorems to convert between integral and differential formulations.
• Apply the Dirac delta function to represent point and surface charge distributions.
• Compute electric fields from discrete and continuous charge distributions by direct integration.
• Apply Gauss's law in integral and differential form, and recognise when symmetry makes it tractable.
• Compute and use the electric potential; relate it to the field; compute the energy of a charge configuration.
• Explain the behaviour of conductors in electrostatic equilibrium — surface charge, field at the surface, screening, induced charge.
• Solve Laplace's and Poisson's equations with boundary conditions using separation of variables.
• Apply the method of images to appropriate boundary-value problems.
• Apply the multipole expansion and interpret monopole, dipole and quadrupole terms.
• Explain polarisation, bound charge and the displacement field; apply boundary conditions at dielectric interfaces.
• Compute magnetic fields using the Biot-Savart law and Ampère's law.
• Apply the magnetic vector potential and explain why magnetostatics requires one where electrostatics does not.
• Explain magnetisation, bound currents and the H field; distinguish diamagnetism, paramagnetism and ferromagnetism.
• Apply Faraday's law and analyse motional and transformer EMF; compute inductance.
• Explain energy stored in electric and magnetic fields.
• Explain the origin and necessity of the displacement current, and assemble Maxwell's equations in differential and integral form.
• Derive the wave equation from Maxwell's equations and identify the propagation speed with the speed of light.
• Explain electromagnetic wave properties — transversality, the relationship of E and B, polarisation, energy transport and the Poynting vector.
• Check results by dimensional analysis and limiting cases, and assess whether an answer is physically reasonable.

Optional Outcomes

• Apply Green's functions to boundary-value problems.
• Analyse waves in matter — reflection, refraction, dispersion, absorption.
• Analyse guided waves and transmission lines.
• Explain electromagnetic radiation from accelerating charges and dipole radiation.
• Explain the relativistic formulation of electromagnetism and the field tensor.
• Explain gauge transformations and the choice of gauge.
• Use numerical methods — relaxation, finite difference — for field problems.
• Explain magnetohydrodynamics or plasma applications at an introductory level.
• Apply computational tools (Python, Mathematica, MATLAB) to visualise fields and solve problems numerically.

Major Topics

Required Topics

• Vector analysis — operators, theorems, curvilinear coordinates, the delta function.
• Electrostatics — Coulomb's law, the field, Gauss's law, potential, energy.
• Conductors and electrostatic boundary conditions.
• Boundary-value problems — Laplace's equation, separation of variables, method of images, multipole expansion.
• Electric fields in matter — polarisation, bound charge, D, susceptibility, dielectrics.
• Magnetostatics — Lorentz force, Biot-Savart, Ampère's law, vector potential.
• Magnetic fields in matter — magnetisation, bound currents, H, magnetic materials.
• Electrodynamics — Ohm's law, EMF, Faraday's law, inductance, field energy.
• Maxwell's equations — the displacement current, the complete set, boundary conditions.
• Electromagnetic waves — the wave equation, plane waves, polarisation, the Poynting vector.

Optional Topics

• Green's functions.
• Waves in matter — dispersion, reflection and transmission at interfaces.
• Waveguides and transmission lines.
• Radiation from accelerated charges.
• Relativistic electrodynamics.
• Gauge freedom and potentials.
• Numerical and computational methods.
• Plasma and MHD introduction.

Resources & Tools

• The standard text is Griffiths, Introduction to Electrodynamics — ⚠ near-universal at this level, and unusually well written for a physics textbook. Its problems are the course, and working them is not optional. Alternatives: Purcell and Morin, Electricity and Magnetism (a genuinely different and illuminating approach that develops magnetism from relativity); Ulaby for an engineering-flavoured treatment; and Jackson, Classical Electrodynamics — ⚠ the graduate standard, and famously difficult; do not start here.
• Mathematical methods support: Boas, Mathematical Methods in the Physical Sciences — ⚠ the book to have on the desk if the vector calculus is the obstacle, which for most students it is; Arfken and Weber for more depth.
• Free supplementary instruction, and this course is well served: MIT OpenCourseWare 8.02 and 8.07, with full lecture video and problem sets; Walter Lewin's 8.02 lectures, which are famous for the demonstrations; 3Blue1Brown for genuinely excellent visual intuition on divergence, curl and the vector calculus generally; and Khan Academy for the multivariable calculus foundations.
• Computational tools: Python with NumPy, SciPy, Matplotlib and SymPy — free, and increasingly the standard; Mathematica or MATLAB where the institution licenses them; VPython/GlowScript for field visualisation. ⚠ Plotting a field you have just computed is one of the fastest ways to find an error and to build intuition.
• Graduate examination preparation: the Physics GRE practice tests (ETS publishes them free) — ⚠ electromagnetism is one of the largest content blocks, and working GRE problems alongside the course is efficient double use of the time.
• Professional bodies: the American Physical Society and the Society of Physics Students — ⚠ SPS chapters exist at most Florida physics departments and are the usual route to research opportunities and to the informal support that makes this course survivable.

Career Pathways

⚠ This course is a required core course rather than a career qualification — but the material and the mathematical fluency it builds are directly used in several fields, and its absence closes doors in all of them.

• Physicists and research staff (SOC 19-2012) — ⚠ required for graduate study in physics, and a course admissions committees examine closely.
• Electrical and electronics engineers (SOC 17-2071, 17-2072) — antennas, RF and microwave design, electromagnetic compatibility, power systems. ⚠ A physics graduate with strong E&M is a credible candidate for RF and antenna work, which is a specialism with persistent demand.
• Optics and photonics (SOC 17-2199, 19-2012) — ⚠ Florida's cluster centres on CREOL at UCF in Orlando, one of the largest optics research and education centres in the country, with associated laser and imaging companies.
• Aerospace and defence (SOC 17-2011, 17-2072) — radar, electronic warfare, satellite communications, signature management. ⚠ A substantial Florida sector: L3Harris (Melbourne, Palm Bay), Lockheed Martin (Orlando), Northrop Grumman (Melbourne, St. Augustine), Raytheon/RTX, and the Space Coast base around Kennedy Space Center and Cape Canaveral. Most require US citizenship and a clearance.
• Semiconductor and materials (SOC 17-2072, 19-2032).
• Medical physics (SOC 19-2012) — ⚠ requires a CAMPEP-accredited graduate programme and board certification; imaging physics in particular uses this material.
• National laboratory and large-facility staff — ⚠ the National High Magnetic Field Laboratory at FSU in Tallahassee is Florida's flagship and is directly an electromagnetism facility.
• Accelerator and plasma physics (SOC 19-2012).
• Quantitative and data roles (SOC 15-2051) — the analytical training transfers, and physics graduates are routinely hired for it.
• Physics teaching (SOC 25-1054, 25-2031).

Special Information

⚠⚠ The prerequisite chains differ — and the mathematical methods course is the key difference

	UWF	FSU
Prerequisites	MAC 2313 (calculus III) AND MAP 2302 (differential equations) AND PHY 2049 (intro E&M) AND PHZ 4113 (mathematical physics)	PHY 3221 (mechanics) and PHZ 3113 (mathematical physics)
Maths methods course	PHZ4113 — a 4000-level number	PHZ3113 — a 3000-level number
Mechanics required first?	not listed	yes (PHY3221)
Grade condition	⚠ C− or better in prerequisite courses	not stated

Both institutions require a mathematical physics course, and both are right to — the vector calculus is where this course is won or lost. ⚠ But they number it at different levels (PHZ4113 versus PHZ3113), which is a number divergence in the PREREQUISITE rather than in this course — the same shape documented for CIS4368, where UWF required COP4710 and FGCU COP3710.

⚠ The practical consequence is a prerequisite check that can fail despite the preparation being present. A student arriving with PHZ3113 at an institution expecting PHZ4113 may be blocked at registration. In a gated sequence — and this course gates PHY4324 — that costs a term, not just an audit note. Resolve substitutions before the registration window opens.

⚠ FSU additionally requires classical mechanics first. That is a defensible sequencing choice — mechanics is where students first meet the mathematical methods in a physics context — and it means FSU's version can assume more mathematical maturity than UWF's.

⚠ UWF's C− grade condition is worth noting as a pattern. Grade conditions on prerequisites are common in physics and engineering and are enforced. Passing a prerequisite is not always sufficient to proceed — check the condition, not just the pass.

Prerequisites — what they actually buy

⚠ Every one of these prerequisites is genuine content, and students who treat them as box-ticking suffer for it:

• Calculus III — multivariable and vector calculus. This is the course's language. A student shaky on line and surface integrals will be translating rather than reasoning all semester.
• Differential equations — Laplace's equation and the wave equation are PDEs, and separation of variables reduces them to ODEs you must be able to solve.
• Introductory E&M — the physical concepts are assumed, not reintroduced.
• Mathematical physics — ⚠ the highest-leverage of the four. Curvilinear coordinates, special functions (Legendre polynomials and spherical harmonics appear directly in the boundary-value problems), and series methods.

⚠ The honest advice: if your vector calculus is weak, fix it before the term starts rather than during it. The course does not slow down for it, and 3Blue1Brown plus a few days with Boas is a genuinely effective intervention.

Course format and workload

3 credits, 45 contact hours — lecture, three hours per week. ⚠ No laboratory; this is theory.

⚠⚠ Expect 10–15 hours per week outside class. This is routinely reported as the hardest course in an undergraduate physics degree, along with quantum mechanics, and the reason is that the problems are long. A single Griffiths problem can take two hours and produce three lines of final answer. Problem sets of five or six such problems are normal weekly assignments.

Assessment is typically weekly problem sets — carrying substantial weight — plus two or three examinations and a final.

⚠ Work with other people. This is standard practice in physics and it is not a workaround: discussing a hard problem is how physicists actually work, and students who attempt this course alone fare measurably worse. Check your instructor's collaboration policy — most permit discussion while requiring independently written solutions — and then use it.

⚠ What students find hardest

• The mathematics, not the physics. Almost universally. Set up the integral in the right coordinate system and the physics is usually clear; set it up wrongly and no amount of physical insight rescues it.
• Boundary-value problems. Separation of variables produces an infinite series whose coefficients are determined by the boundary conditions, and the bookkeeping defeats people. It rewards working many examples, not rereading the method.
• Knowing when Gauss's or Ampère's law helps. Both are always true and only sometimes useful — they are useful when symmetry lets you pull the field out of the integral, and recognising that is a judgement built by practice.
• Fields in matter. Bound charge and bound current are genuinely conceptual, and D and H are frequently misunderstood as "the real field". ⚠ They are bookkeeping devices that absorb the bound sources; E and B are the physical fields. Getting that straight early prevents months of confusion.
• The volume of new notation arriving at once in the first three weeks.

Articulation and transfer

PHY4323 is a 4000-level upper-division course, not offered at Florida College System institutions, and taken after transfer. The number is used consistently at the four Florida institutions that carry it, so SCNS articulation is clean — subject to the prerequisite-numbering issue above, which is the real risk.

⚠ Prefix note. PHY is physics; PHZ is physics-adjacent and mathematical physics; AST astronomy; MAC/MAP/MAS mathematics; EEL electrical engineering. ⚠ An EEL electromagnetics course covers overlapping material with a different emphasis — applications and engineering practice rather than the boundary-value formalism — and departments do sometimes accept it as a substitution, but it is a substitution rather than an articulation. Ask before taking it, not after. Related: PHY4324 (E&M II, which this gates), PHY3221 (mechanics), PHZ3113/PHZ4113 (mathematical physics), PHY3722C (electronics — a different subject despite the shared vocabulary).

AI Integration

⚠ This is a course where AI tools are seductive and specifically unreliable, and the reason is worth understanding rather than just asserting.

Where they help:

• Explaining a concept a second way. Why the curl of a static E field vanishes; what the vector potential is for; the physical meaning of the displacement current. ⚠ Genuinely useful — a different framing frequently unlocks a stuck student.
• Symbolic algebra assistance. ⚠ But use a computer algebra system — SymPy, Mathematica — rather than a language model for this. A CAS is correct by construction; a language model is guessing at algebra.
• Coding for numerical solutions and visualisation. Python for field plots and relaxation solvers is a legitimate and now-normal use.
• Checking a limiting case. "What should this reduce to when the sphere radius goes to zero?" is a good question to think through with a tool.

⚠⚠ Where they fail, and the failure is specific to this subject:

• Multi-step derivations break down silently. A Griffiths-level problem involves a chain of coordinate choices, integrals and boundary conditions, and models produce fluent, confident, wrong derivations in which a sign error or a mishandled limit appears in the middle and everything after inherits it. The output looks exactly like a correct solution.
• Vector calculus in curvilinear coordinates. ⚠ Models routinely drop the metric factors in cylindrical and spherical divergence and curl — an error that produces a plausible expression with the wrong dimensions.
• Setting up the wrong integral. The setup is the assessed skill and it is where models are weakest.
• Fabricated intermediate steps to reach a remembered final answer — which is the most dangerous failure, because the answer looks right.

⚠ A discipline-specific defence worth adopting regardless of tools: check every result by dimensional analysis and by limiting cases. Does it have units of field? Does it reduce to the point-charge result at large distance? Does it vanish where it should? These checks catch both your errors and a model's, and physicists do them habitually for exactly that reason.

The deeper argument, and it is not a scolding. The reason to spend two hours on one problem is that the two hours are the course. What is being built is the ability to look at an unfamiliar physical situation, choose a coordinate system, set up the mathematics and carry it through — and that is a capacity, not information. ⚠ It is also precisely what the examinations, the Physics GRE and graduate qualifying examinations test, all closed-book. Anything outsourced now reappears without help later.

Worth knowing as context: computational electromagnetics — finite element and finite difference solvers — is standard professional practice, and machine-learned surrogates for field solvers are an active research area. ⚠ The consistent message from that work is that analytical understanding is what lets a practitioner know when a solver's output is wrong, which is the same argument this course makes for itself.

Academic integrity. Read the syllabus; physics departments have generally written specific policies, and most permit collaboration on problem sets while requiring independent write-up. ⚠ Submitting generated solutions is both detectable — the failure modes above are distinctive — and self-defeating in a course whose examinations are worked by hand.