Course Description
PHY2049 / PHY2049C – General Physics with Calculus II is a calculus-based physics course (typically 3-4 credits, with PHY2049C as the lecture/lab integrated form and PHY2049 + PHY2049L as the separated lecture+lab pairing) in the Physics: General Physics taxonomy of Florida's Statewide Course Numbering System (SCNS). PHY2049 is the second semester of the year-long calculus-based general physics sequence designed for science, engineering, and mathematics majors. The course covers electricity and magnetism (electrostatics, electric fields and potential, capacitors, current and resistance, DC circuits, magnetism, electromagnetic induction, inductance, AC circuits, Maxwell's equations and electromagnetic waves) and optics (geometric optics including mirrors and lenses, physical/wave optics including interference and diffraction). Some institutional variants extend coverage to include thermodynamics or modern physics topics.
PHY2049 is offered at 43 Florida public institutions and transfers as equivalent across the state. The course is required, together with PHY2048 (General Physics with Calculus I), for engineering, physics, chemistry, mathematics, and computer science majors at all Florida public universities. PHY2049 follows PHY2048 (mechanics, oscillations, waves, sound, thermodynamics) and is the prerequisite for upper-division physics and engineering coursework. Calculus II (MAC2312) is a prerequisite or co-requisite, since the course uses derivatives and integrals throughout, including line integrals (Ampere's law) and surface integrals (Gauss's law) at an introductory level.
Learning Outcomes
Required Outcomes
Upon successful completion of this course, students will be able to:
- Demonstrate conceptual mastery of the principal ideas in electricity, magnetism, and topics of electromagnetism, including electric and magnetic fields, electric potential, electromagnetic induction, and Maxwell's equations.
- Demonstrate analytical mastery of these ideas through quantitative problem-solving in homework assignments and examinations.
- Apply Coulomb's law to compute the electric force between point charges and continuous charge distributions.
- Compute electric fields from point charges, continuous charge distributions (line charges, surface charges, volume charges), and dipoles using both Coulomb's law and the principle of superposition.
- Apply Gauss's law to compute electric fields from highly symmetric charge distributions (point charges, infinite line charges, infinite planes, spheres, cylinders).
- Compute electric potential and potential energy from charge distributions; relate the electric field to the gradient of the potential; apply conservation of energy in electric fields.
- Analyze capacitors: capacitance, capacitors in series and parallel, energy stored in capacitors, dielectrics.
- Apply Ohm's law and Kirchhoff's rules to analyze DC circuits including circuits with resistors in series and parallel, multi-loop circuits, RC circuits (charging and discharging).
- Compute magnetic forces and torques on moving charges and current-carrying conductors; analyze motion of charged particles in magnetic fields (cyclotron motion, mass spectrometers, velocity selectors).
- Compute magnetic fields from current-carrying conductors using the Biot-Savart law and Ampere's law.
- Apply Faraday's law of electromagnetic induction and Lenz's law to compute induced EMFs and currents; analyze applications including generators, transformers, and motional EMF.
- Analyze inductors and RL circuits; compute energy stored in magnetic fields; analyze LC and RLC circuits.
- Analyze AC circuits: phasors; impedance of resistors, capacitors, and inductors; series RLC circuits; resonance; power in AC circuits.
- Articulate Maxwell's equations in integral form and explain how they predict electromagnetic waves; describe properties of EM waves (speed, energy, momentum, the Poynting vector, polarization).
- Apply geometric optics to analyze image formation by plane and curved mirrors and by thin lenses; use the mirror and lens equations and ray diagrams.
- Analyze physical (wave) optics: two-slit and multi-slit interference; thin-film interference; single-slit diffraction; the diffraction grating; resolving power.
- Apply problem-solving strategies using fundamental physical concepts and equations, including unit analysis and order-of-magnitude estimation.
Optional Outcomes
Depending on institutional emphasis (some PHY2049 sections cover additional topics), students may also:
- Apply the laws of thermodynamics to common systems including the first law, the second law, and entropy (some sections that did not cover thermodynamics in PHY2048).
- Apply concepts of special relativity: time dilation, length contraction, relativistic momentum and energy.
- Examine introductory modern physics: photoelectric effect, blackbody radiation, the Bohr model, wave-particle duality, the uncertainty principle.
- Apply computational tools (Python with NumPy/Matplotlib, MATLAB, or simulation software like PhET) to model electromagnetic phenomena.
- Conduct laboratory experiments on electric fields, circuits, magnetic fields, induction, and optics (in PHY2049C or PHY2049L).
Major Topics
Required Topics
- Electric Charge and Coulomb's Law: Properties of electric charge; conductors and insulators; Coulomb's law; superposition principle for forces.
- Electric Fields: Electric field from point charges and continuous distributions; electric field lines; motion of charged particles in uniform fields; electric dipoles and torque.
- Gauss's Law: Electric flux; Gauss's law; applications to highly symmetric charge distributions; conductors in electrostatic equilibrium.
- Electric Potential: Potential difference and electric potential energy; potential due to point charges and continuous distributions; equipotential surfaces; relationship between field and potential (gradient).
- Capacitance and Dielectrics: Definition of capacitance; parallel-plate, cylindrical, and spherical capacitors; capacitors in series and parallel; energy stored; dielectrics and their effect on capacitance.
- Current, Resistance, and EMF: Electric current; current density; Ohm's law (microscopic and macroscopic forms); resistance and resistivity; electrical power; sources of EMF; internal resistance.
- Direct Current (DC) Circuits: Resistors in series and parallel; Kirchhoff's voltage and current rules; multi-loop circuit analysis; RC circuits — charging and discharging exponentials.
- Magnetic Fields: Magnetic force on a moving charge (Lorentz force); motion of charged particles in magnetic fields (cyclotron motion); applications (mass spectrometer, velocity selector); magnetic force on a current-carrying conductor; torque on a current loop and magnetic dipole moment.
- Sources of Magnetic Fields: Biot-Savart law; magnetic field of a long straight wire, circular loop, solenoid; force between parallel current-carrying wires; Ampere's law and applications.
- Electromagnetic Induction: Magnetic flux; Faraday's law of induction; Lenz's law; motional EMF; induced electric fields; eddy currents; generators; transformers (introduction).
- Inductance: Self-inductance and mutual inductance; RL circuits (current growth and decay); energy stored in a magnetic field; LC oscillations; RLC circuits (introduction).
- Alternating Current (AC) Circuits: AC sources and phasors; resistors, inductors, and capacitors in AC circuits; impedance; series RLC circuits; resonance; root-mean-square (RMS) values; power in AC circuits and the power factor; transformers in AC.
- Maxwell's Equations and Electromagnetic Waves: Displacement current; Maxwell's equations in integral form; electromagnetic wave equation and prediction; properties of EM waves (speed of light c, energy density, the Poynting vector, intensity, momentum and radiation pressure); the EM spectrum; polarization.
- Geometric Optics — Mirrors and Lenses: Reflection and refraction; total internal reflection; flat and spherical mirrors; mirror equation and magnification; ray diagrams; thin lenses; the lens-maker's equation and thin-lens equation; image formation; the human eye and corrective lenses; magnifiers, microscopes, and telescopes.
- Physical (Wave) Optics: Two-source interference (Young's double-slit experiment); thin-film interference; multi-slit interference and the diffraction grating; single-slit diffraction; resolving power and the Rayleigh criterion; circular-aperture diffraction.
Optional Topics
- Thermodynamics: Temperature and zeroth law; heat and the first law; ideal gases and kinetic theory; the second law; entropy and statistical mechanics introduction. (Often covered in PHY2048 instead.)
- Special Relativity: Postulates; time dilation; length contraction; relativistic momentum and energy; mass-energy equivalence (E = mc²).
- Introductory Modern Physics: Photoelectric effect; blackbody radiation and Planck's hypothesis; Compton scattering; wave-particle duality (de Broglie); uncertainty principle (Heisenberg); the Bohr model; introduction to quantum mechanics.
- Computational Physics: Use of Python (NumPy, Matplotlib, SciPy), MATLAB, or simulation tools (PhET, EJSS) for visualizing fields, simulating circuits, and modeling EM phenomena.
Resources & Tools
- Standard Textbooks: University Physics with Modern Physics by Young and Freedman (Pearson — widely adopted at UF, USF, and across Florida); Physics for Scientists and Engineers by Knight (Pearson); Physics for Scientists and Engineers with Modern Physics by Serway and Jewett (Cengage); Fundamentals of Physics by Halliday, Resnick, and Walker (Wiley); University Physics by OpenStax (free, openstax.org — Volumes 2 and 3 cover PHY2049 content).
- Online Homework Platforms: Pearson Mastering Physics (most common); WebAssign (Cengage); Wiley WileyPLUS; LON-CAPA (free at some institutions); McGraw-Hill Connect
- Required Calculator: Non-programmable scientific calculator at most institutions for exams. Programmable and graphing calculators (TI-84, etc.) are typically permitted for homework and labs but restricted on exams. Check institution's specific policy.
- Free Online Tools: PhET Interactive Simulations (phet.colorado.edu — outstanding for visualizing fields, circuits, and waves); Wolfram Alpha; Desmos for graphing; CircuitLab and Falstad's Circuit Simulator (free online circuit simulators).
- Tutoring and Practice Resources: Free college tutoring centers; The Physics Classroom (physicsclassroom.com); Khan Academy Physics; Walter Lewin's MIT 8.02 lectures (free on YouTube and MIT OpenCourseWare — exceptional E&M content); Professor Dave Explains; Organic Chemistry Tutor (yes, also covers physics).
- Professional Resources: American Association of Physics Teachers (AAPT, aapt.org); American Physical Society (APS, aps.org).
Career Pathways
PHY2049 is required for all engineering, physics, chemistry, mathematics, and computer science pathways at Florida public universities:
- Engineering Programs – Required for ALL engineering majors (mechanical, electrical, civil, aerospace, chemical, computer, biomedical, environmental, materials, industrial) at UF Herbert Wertheim College of Engineering, FAMU-FSU College of Engineering, USF College of Engineering, UCF College of Engineering and Computer Science, FAU College of Engineering and Computer Science, FIU College of Engineering and Computing, FGCU U.A. Whitaker College of Engineering, and UNF School of Engineering.
- Physics Major – Foundation for the physics B.S. major; required at all Florida public universities offering the major.
- Chemistry and Biochemistry Majors – Required for B.S. chemistry and biochemistry at most Florida public universities.
- Mathematics, Computer Science, Computer Engineering – Required for the B.S. tracks; the EM portions are particularly relevant for computer engineering and electrical engineering.
- Pre-Medical Track for Some Majors – Many medical schools accept either PHY2048+PHY2049 (calculus-based) or PHY2053+PHY2054 (algebra-based), but the calculus-based sequence is required for engineering majors who are also pre-med, and is preferred at competitive medical schools.
- Florida Industry Application – Foundation for careers across Florida's aerospace and defense sector (Lockheed Martin in Orlando, Boeing in Titusville, L3Harris in Melbourne, Northrop Grumman, Raytheon Technologies, Aerojet Rocketdyne, Blue Origin and SpaceX on the Space Coast), telecommunications, semiconductor manufacturing, optical engineering, energy (FPL), naval engineering at NSWC Panama City, and the rapidly growing Florida tech sector in Miami, Tampa, and Orlando.
Special Information
Prerequisites
Prerequisites are PHY2048 (General Physics with Calculus I) with a grade of C or better and MAC2312 (Calculus II) with a grade of C or better, or equivalents. MAC2312 may also be taken as a co-requisite at some institutions. The lab component (PHY2049L) is typically a co-requisite. Life-science majors should NOT take PHY2049 — they should take the algebra-based PHY2053/PHY2054 sequence instead, which has different content and rigor designed for that pathway.
Course Variants and Lab Component
PHY2049 is offered as PHY2049 (3-credit lecture only) at most institutions, paired with the separate PHY2049L (1-credit lab). Some institutions offer PHY2049C as a 4-credit integrated lecture-and-lab course. For transfer to engineering programs and pre-medical preparation, both lecture and lab credit are required.
Workload and Difficulty
PHY2049 is widely regarded as among the most challenging courses in the engineering/physics curriculum, particularly for the abstract nature of fields, Gauss's law, and the integration of vector calculus concepts. Most institutions expect 9-15 hours of weekly out-of-class work. Strong calculus skills are essential — students should be fluent with derivatives, integrals (including line and surface integrals at an introductory level), and vector operations. Class averages on early exams are often in the 60-70% range, and the course typically has a notable D/F/W rate.
Honors Sections
Many Florida institutions offer Honors sections (e.g., UF's PHY2049H) with smaller class sizes, more rigorous problem sets, and additional topics from modern physics. Often required for physics majors and recommended for highly competitive engineering programs.
Foundation for Upper-Division Coursework
PHY2049 is the prerequisite for upper-division electromagnetism, optics, electronics, electrical engineering circuits, signals and systems, and most upper-division engineering courses. Mastery of fields, potential, circuits, and Maxwell's equations is essential for further study in any electromagnetic-intensive area.
Connection to Calculus II
PHY2049 uses the integration techniques learned in MAC2312 — students apply integrals to compute fields and potentials from continuous charge distributions, line integrals to compute work done by electric fields, and surface integrals (intuitively) for Gauss's law. Students concurrently enrolled in MAC2312 should plan extra time to bridge between mathematical techniques and their physical applications.