UPII · First-year undergraduate · Calculus-based electricity, magnetism, optics, and modern physics
Fields, circuits, and light—connected by evidence.
A fifteen-week calculus-based continuation from mechanics into electric charge and fields, circuits, magnetism, induction, electromagnetic waves, geometric and physical optics, and a carefully bounded introduction to modern physics.
Independent pathway notice. GioPhysics University & College Physics is an independent learning pathway. GioPhysics is not a university, does not award academic credit or degrees, and is not accredited by or affiliated with any university or professional body. This is not a universal programme specification. Course coverage and degree requirements vary by institution; confirm requirements with your university.
Before unit 01
Bring mechanics forward. Make the vector calculus operational.
Physics II normally follows a calculus-based mechanics course. It uses vectors, integrals, first-order differential equations, and sinusoidal models without pretending that every learner has completed a formal multivariable-calculus course.Readiness, not gatekeeping
Know which mathematics must be refreshed.
Field notation becomes manageable when every vector, integral, and sign is connected to geometry, units, and a measurable physical quantity.
- University Physics I or an equivalent calculus-based mechanics course
- Single-variable calculus, algebra, trigonometry, vectors, and scientific notation
- Working knowledge of force, energy, momentum, and oscillations; use the unnumbered wave preflight if mechanical waves were not completed in Physics I
- No formal multivariable calculus is assumed; flux, circulation, and field integrals are introduced operationally
How calculus enters: derivatives describe current, induction, and transient response; integrals accumulate distributed charge, field circulation, flux, potential change, and wave energy. Symmetry and geometry determine which calculation is useful.
Mathematical tools used explicitly
- Vector components, dot products, cross products, and symmetry arguments
- Derivatives and definite integrals for fields, current, induction, and transients
- Operational line, surface, and volume integrals without assuming a full vector-calculus course
- First-order differential equations for RC and LR circuits
- Sinusoidal functions, phasors, logarithms, and small-angle approximations
- Dimensional, limiting-case, conservation, and order-of-magnitude checks
Fifteen units · suggested fifteen-week rhythm
Move from source to field, then from field to wave.
The sequence links electrostatics, circuits, magnetism, induction, electromagnetic waves, optics, and modern-physics evidence without hiding the model changes between them.Units 1–11 form the shared electricity-and-magnetism spine, from Coulomb interactions through inductance and AC circuits.
Unit 12 is a common electricity-and-magnetism capstone, but the mathematical depth of Maxwell's equations and electromagnetic waves varies by institution.
Units 13–14 are an institution-dependent optics endpoint and may instead appear in a separate waves or optics course.
Unit 15 is an optional, institution-dependent introductory modern-physics bridge, not a complete relativity, quantum, atomic, nuclear, or particle-physics course.
Course scope: This GioPhysics course map is an adaptable learning sequence, not academic credit, accreditation, or a universal university syllabus. Departments may redistribute weeks, laboratory hours, optics, or the modern-physics survey to match local requirements. This GioPhysics course map is an adaptable learning sequence, not academic credit, accreditation, or a universal university syllabus. Departments may redistribute weeks, laboratory hours, optics, or the modern-physics survey to match local requirements. Thermal physics appears as an unnumbered institutional extension: some universities assess it within Physics II, while others teach it in a separate course, so include the thermal extensions only where the local syllabus requires them.
Complete interactive course map
All fifteen units, searchable by concept and evidence.
Search 120 numbered subsections, inspect outcomes and prerequisites, and expand the laboratory and problem-practice plan for each unit plus 25 unnumbered preflight or extension topics.Mapped lesson links: linked topics open relevant existing GioPhysics material. Use them as conceptual and problem-solving support while following your institution's required depth, notation, laboratory programme, and assessment rules.
Interactive course map
Choose one phase. Open one unit. Learn by doing.
Search includes unit titles, topics, skills, outcomes, prerequisites, and laboratory questions across all 15 units and the 3 unnumbered institutional extensions.
Private study checklist
0 of 15 units reviewedWeek 1 · UPII-01 · Heavy
Electric Charge and Coulomb's Law
Establish charge, conservation, quantisation, material response, charging processes, Coulomb's law, and superposition as the foundation of electrostatics.
8 topics4 outcomes2 lab directions150 min practiceOpen Electric Charge and Coulomb's Law: topics, evidence, and practice
Topics and mapped lessons
- Charge, conservation, and quantisation
Positive and negative charge, the elementary charge, conservation in closed systems, quantised transfer, and net-charge accounting.
- Conductors, insulators, and polarization
Mobile and bound charge, redistribution, polarization, grounding, and the microscopic limits of ideal material models.
- Charging by friction, contact, and induction
Electron transfer, contact charging, induction sequences, grounding, sign predictions, and conservation checks.
- Coulomb's law
Magnitude and vector form for point charges, inverse-square scaling, signs, units, and the point-particle approximation.
- Force superposition and charge equilibrium
Vector addition for several charges, symmetry, equilibrium locations, null-force conditions, and stability cautions.
- Forces from continuous charge distributions
Linear, surface, and volume charge density; differential charge elements; integration strategy; and limiting-case checks.
- Electrostatic material response
Charge redistribution at surfaces, induced dipoles, attraction of neutral matter, shielding intuition, and breakdown limitations.
- Electrostatic applications and safety
Sparks, discharge, lightning protection, electrostatic separation, sensitive electronics, and evidence-based risk controls.
Learning outcomes
- Use conservation and quantisation to track charge through physical processes.
- Apply Coulomb's law with a declared coordinate system and vector directions.
- Superpose forces from multiple point charges and continuous distributions.
- Explain charging and polarization using conductor and insulator models.
Prerequisite thread
- Vector components and unit vectors
- Newton's laws and force diagrams
- Scientific notation and inverse-square scaling
Laboratory directions
hands-onCoulomb-force scaling Does the measured electric force follow an inverse-square distance model?
Evidence: Force and separation data, competing fits, residuals, uncertainty, and a stated range of validitydesign investigationCharging method evidence Which observations distinguish charging by contact from charging by induction?
Evidence: A controlled sequence, sign tests, charge conservation, repeat trials, and an evidence-based mechanism claimProblem practice
Charge conservation and vector force models before algebraic magnitude calculations
Capstone: Design two distinguishable charge configurations that produce the same net force magnitude at one point, then explain how another measurement separates them.
- Concept checks that require an explanation, not only a numerical answer
- Multi-step quantitative modelling with unit and limiting-case checks
- A calculus or data-interpretation challenge
Interactive concept map
Follow the model from claim to evidence.
01 · Physical claimElectric Charge and Coulomb's Law Establish charge, conservation, quantisation, material response, charging processes, Coulomb's law, and superposition as the foundation of electrostatics.
02 · RepresentationCharge-transfer diagrams Charge accounting
03 · TestPrediction before measurement Does the measured electric force follow an inverse-square distance model?
04 · Evidence & boundaryDecide, then qualify Force and separation data, competing fits, residuals, uncertainty, and a stated range of validity
Interactive diagram for Electric Charge and Coulomb's Law: follow the physical claim through its representation, proposed test, evidence, and model boundary. modelCharge accounting turns the stated idea into a representation that can make a prediction.
Example questions
Try the reasoning before revealing the structure.
Concept Using Electric Charge and Coulomb's Law, explain how a physicist can: Use conservation and quantisation to track charge through physical processes.
- Charge, conservation, and quantisation
Week 2 · UPII-02 · Heavy
Electric Fields
Represent electric interactions with vector fields, field lines, superposition, continuous charge models, dipoles, conductors, and field mapping.
8 topics4 outcomes2 lab directions170 min practiceOpen Electric Fields: topics, evidence, and practice
Topics and mapped lessons
- Electric field and the test-charge model
Force per unit positive test charge, field direction, source versus probe charges, units, and the negligible-probe assumption.
- Fields of point charges
Vector fields from isolated point charges, radial direction, inverse-square scaling, sign, and near- or far-field interpretation.
- Field superposition and null points
Component addition, symmetry, zero-field locations, unequal sources, and distinguishing zero field from zero potential.
- Electric field lines
Tangent direction, line density, sources and sinks, crossing prohibition, conductor boundaries, and qualitative comparison.
- Fields from continuous charge
Charge-density models and vector integration for rods, rings, disks, and infinite sheets; symmetry, numerical evaluation, and limiting cases when closed forms are unavailable.
- Electric dipoles
Dipole moment, axial and equatorial fields, far-field approximation, torque, energy, and alignment in uniform fields.
- Uniform fields and parallel plates
Approximately uniform fields, force and acceleration of charged particles, edge effects, and the limits of the plate model.
- Conductors, shielding, and field mapping
Electrostatic equilibrium, surface charge, zero internal field, cavities, shielding, boundary directions, and experimental maps.
Learning outcomes
- Define electric field operationally and distinguish field from force.
- Calculate fields from point charges and continuous distributions.
- Use symmetry, components, and limiting cases to evaluate field models.
- Interpret field lines and measured equipotential maps without treating lines as material objects.
Prerequisite thread
- Coulomb's law
- Vector components and superposition
- Derivatives and definite integrals
Laboratory directions
hands-onMap an electric field How well do measured equipotentials reconstruct the direction and relative strength of an electric field?
Evidence: Voltage coordinates, equipotential contours, inferred field vectors, spatial uncertainty, and conductor-boundary checkscomputationalBuild a field-line engine How do charge geometry and numerical step size change a computed field map?
Evidence: Vector-grid and streamline plots, convergence checks, symmetry tests, and comparison with an analytic special caseProblem practice
Choosing a field source model and exploiting vector symmetry before integration
Capstone: Construct a charge distribution whose field has a required direction at two locations, then test the design numerically and with limiting cases.
- Concept checks that require an explanation, not only a numerical answer
- Multi-step quantitative modelling with unit and limiting-case checks
- A calculus or data-interpretation challenge
Interactive concept map
Follow the model from claim to evidence.
01 · Physical claimElectric Fields Represent electric interactions with vector fields, field lines, superposition, continuous charge models, dipoles, conductors, and field mapping.
02 · RepresentationField-vector grids Field-vector mapping
03 · TestPrediction before measurement How well do measured equipotentials reconstruct the direction and relative strength of an electric field?
04 · Evidence & boundaryDecide, then qualify Voltage coordinates, equipotential contours, inferred field vectors, spatial uncertainty, and conductor-boundary checks
Interactive diagram for Electric Fields: follow the physical claim through its representation, proposed test, evidence, and model boundary. modelField-vector mapping turns the stated idea into a representation that can make a prediction.
Example questions
Try the reasoning before revealing the structure.
Concept Using Electric Fields, explain how a physicist can: Define electric field operationally and distinguish field from force.
- Electric field and the test-charge model
Week 3 · UPII-03 · Heavy
Gauss's Law
Connect electric flux to enclosed charge and use Gauss's law with spherical, cylindrical, and planar symmetry while making its limitations explicit.
8 topics4 outcomes2 lab directions180 min practiceOpen Gauss's Law: topics, evidence, and practice
Topics and mapped lessons
- Electric flux
Area vectors, field-normal components, uniform and nonuniform fields, sign, open surfaces, and geometric interpretation.
- Gauss's law in integral form
Closed-surface flux, enclosed charge, permittivity, source interpretation, and independence from external charges.
- Choosing a Gaussian surface
Spherical, cylindrical, and planar symmetry tests; constant-field regions; zero-flux pieces; and common invalid choices.
- Spherical charge distributions
Point charges, conducting shells, solid spheres, volume charge, interior and exterior fields, and boundary behaviour.
- Cylindrical symmetry
Infinite line charge, long cylinders, coaxial geometries, radial fields, linear charge density, and end-effect limits.
- Planar symmetry
Infinite sheets, slabs, paired plates, field discontinuities, surface charge density, and finite-size limitations.
- Gauss's law and conductors
Zero field within conducting material, surface charge, cavities, induced charge, field immediately outside, and shielding.
- Numerical flux and limits of symmetry
Discrete flux estimates, mesh refinement, irregular charge distributions, computational verification, and why truth does not guarantee convenience.
Learning outcomes
- Calculate electric flux through open and closed surfaces.
- Apply Gauss's law to symmetric charge distributions with a justified Gaussian surface.
- Relate conductor equilibrium to surface charge and boundary fields.
- Explain why Gauss's law remains true when it is not computationally useful.
Prerequisite thread
- Electric fields and superposition
- Area vectors and dot products
- Charge density and geometric symmetry
Laboratory directions
computationalFlux without field uniformity Does numerical flux through differently shaped closed surfaces depend only on enclosed charge?
Evidence: Surface meshes, flux sums, refinement convergence, enclosed-charge cases, and numerical error estimateshands-onShielding and cavity test What measurements support the electrostatic shielding model for a conductor?
Evidence: Internal and external field proxies, controlled grounding states, spatial maps, repeatability, and sensitivity limitsProblem practice
Matching the Gaussian surface to actual field symmetry rather than to the shape of a drawing
Capstone: Compare two charge distributions with equal total charge but different symmetry, showing when Gauss's law yields a field directly and when it does not.
- Concept checks that require an explanation, not only a numerical answer
- Multi-step quantitative modelling with unit and limiting-case checks
- A calculus or data-interpretation challenge
Interactive concept map
Follow the model from claim to evidence.
01 · Physical claimGauss's Law Connect electric flux to enclosed charge and use Gauss's law with spherical, cylindrical, and planar symmetry while making its limitations explicit.
02 · RepresentationArea-vector maps Flux calculation
03 · TestPrediction before measurement Does numerical flux through differently shaped closed surfaces depend only on enclosed charge?
04 · Evidence & boundaryDecide, then qualify Surface meshes, flux sums, refinement convergence, enclosed-charge cases, and numerical error estimates
Interactive diagram for Gauss's Law: follow the physical claim through its representation, proposed test, evidence, and model boundary. modelFlux calculation turns the stated idea into a representation that can make a prediction.
Example questions
Try the reasoning before revealing the structure.
Concept Using Gauss's Law, explain how a physicist can: Calculate electric flux through open and closed surfaces.
- Electric flux
Week 4 · UPII-04 · Heavy
Electric Potential
Use electric potential and potential energy as scalar alternatives to force and field, relating work, equipotentials, gradients, conductors, and continuous charge.
8 topics4 outcomes2 lab directions170 min practiceOpen Electric Potential: topics, evidence, and practice
Topics and mapped lessons
- Electric potential energy
System energy for charge configurations, work by the electric force, reference choices, signs, and energy conservation.
- Electric potential and potential difference
Potential energy per unit charge, voltage, work, reference zero, units, and measurable differences rather than absolute values.
- Potential of point charges
The scalar potential of a point source, sign, reference at infinity, radial dependence, and comparison with the field.
- Potential superposition and electric dipoles
Scalar addition for discrete charges, cancellation, electric-dipole potential and its far-field angular dependence, zero-potential surfaces, and why zero potential need not mean zero field.
- Equipotentials and work
Zero work along an equipotential, perpendicular field direction, contour spacing, conductor surfaces, and path independence.
- Electric field from potential
The negative spatial derivative or gradient of potential, components, graph slopes, equilibrium, and stability.
- Potential from continuous charge
Line, surface, and volume charge elements; scalar integration; axis potentials; numerical methods; and far-field limits.
- Conductors and electric potential
Equipotential conductors, surface fields, cavities, grounding, sharp-curvature effects, and electrostatic boundary conditions.
Learning outcomes
- Relate electric work, potential energy, potential difference, and field.
- Calculate potential from point charges and continuous charge distributions.
- Recover field components from spatial potential variation.
- Interpret equipotentials, conductor potentials, and reference choices.
Prerequisite thread
- Electric fields
- Work and potential energy
- Definite integrals and derivatives
Laboratory directions
hands-onEquipotential cartography Can measured voltage contours predict the force direction on a positive test charge?
Evidence: Calibrated voltage data, contour maps, inferred gradients, uncertainty, and comparison with electrode geometrycomputationalRecover field from potential How accurately can numerical derivatives recover a known electric field from sampled potential data?
Evidence: Sampled potentials, derivative schemes, error-versus-step plots, boundary effects, and analytic comparisonProblem practice
Selecting scalar potential or vector field methods and checking consistent reference levels
Capstone: Design a one-dimensional potential landscape with specified equilibrium points, then infer the field, stability, and charged-particle motion.
- Concept checks that require an explanation, not only a numerical answer
- Multi-step quantitative modelling with unit and limiting-case checks
- A calculus or data-interpretation challenge
Interactive concept map
Follow the model from claim to evidence.
01 · Physical claimElectric Potential Use electric potential and potential energy as scalar alternatives to force and field, relating work, equipotentials, gradients, conductors, and continuous charge.
02 · RepresentationEquipotential maps Scalar superposition
03 · TestPrediction before measurement Can measured voltage contours predict the force direction on a positive test charge?
04 · Evidence & boundaryDecide, then qualify Calibrated voltage data, contour maps, inferred gradients, uncertainty, and comparison with electrode geometry
Interactive diagram for Electric Potential: follow the physical claim through its representation, proposed test, evidence, and model boundary. modelScalar superposition turns the stated idea into a representation that can make a prediction.
Example questions
Try the reasoning before revealing the structure.
Concept Using Electric Potential, explain how a physicist can: Relate electric work, potential energy, potential difference, and field.
- Electric potential energy
Week 5 · UPII-05 · Medium-heavy
Capacitance and Dielectrics
Model capacitors as charge-and-energy storage systems, combine networks, derive common geometries, and explain dielectric response and breakdown.
8 topics4 outcomes2 lab directions160 min practiceOpen Capacitance and Dielectrics: topics, evidence, and practice
Topics and mapped lessons
- Capacitance and parallel plates
Capacitance as charge per potential difference, plate geometry, permittivity, uniform-field approximation, and fringing limits.
- Capacitors in series and parallel
Equivalent capacitance, common-charge and common-voltage constraints, network reduction, and internal-node charge conservation.
- Energy stored in capacitors
Work of charging, one-half CV squared forms, energy density in the electric field, and source-energy accounting.
- Dielectric polarization
Induced and orientational polarization, bound charge, reduced internal field, susceptibility intuition, and ideal-linear limits.
- Capacitors with dielectrics
Dielectric constant, fixed-free-charge versus fixed-voltage cases, inserted slabs, forces, energy changes, and source work.
- Gauss's law in dielectric media
Free and bound charge distinction, electric displacement as an optional tool, symmetry, polarization charge, and assumptions.
- Cylindrical and spherical capacitors
Field integration, potential difference, capacitance by geometry, limiting cases, and coaxial or spherical applications.
- Dielectric strength and capacitor design
Breakdown field, leakage, tolerances, energy and voltage ratings, safety margins, and real-capacitor limitations.
Learning outcomes
- Relate charge, potential difference, geometry, and capacitance.
- Reduce series and parallel capacitor networks and track charge or voltage constraints.
- Calculate stored energy and electric energy density.
- Explain polarization, dielectric response, and breakdown under fixed-charge or fixed-voltage conditions.
Prerequisite thread
- Gauss's law
- Potential difference
- Electric-field energy and work
Laboratory directions
hands-onCapacitance versus geometry How do plate area and separation control measured capacitance?
Evidence: Capacitance data, geometric measurements, a linearized model, residuals, uncertainty, and edge-effect discussiondesign investigationIdentify an unknown dielectric Can capacitance measurements identify an inserted dielectric and its useful operating range?
Evidence: Baseline and loaded capacitance, inferred dielectric constant, repeat trials, uncertainty, and breakdown-risk limitsProblem practice
Separating geometric capacitance from circuit charge-voltage constraints and source work
Capstone: Compare two capacitor designs under both fixed-charge and fixed-voltage conditions, then recommend one design with energy, field, and breakdown evidence.
- Concept checks that require an explanation, not only a numerical answer
- Multi-step quantitative modelling with unit and limiting-case checks
- A calculus or data-interpretation challenge
Interactive concept map
Follow the model from claim to evidence.
01 · Physical claimCapacitance and Dielectrics Model capacitors as charge-and-energy storage systems, combine networks, derive common geometries, and explain dielectric response and breakdown.
02 · RepresentationCapacitor cross-sections Capacitor-network reduction
03 · TestPrediction before measurement How do plate area and separation control measured capacitance?
04 · Evidence & boundaryDecide, then qualify Capacitance data, geometric measurements, a linearized model, residuals, uncertainty, and edge-effect discussion
Interactive diagram for Capacitance and Dielectrics: follow the physical claim through its representation, proposed test, evidence, and model boundary. modelCapacitor-network reduction turns the stated idea into a representation that can make a prediction.
Example questions
Try the reasoning before revealing the structure.
Concept Using Capacitance and Dielectrics, explain how a physicist can: Relate charge, potential difference, geometry, and capacitance.
- Capacitance and parallel plates
Labs and problem solving
Make every field model answer to measurement.
The 30 laboratory directions and unit-specific problem plans use one repeatable loop from prediction to defensible evidence. Simulation or video analysis supplements—not replaces—hands-on work required by a learner's institution.Predict
Use symmetry, direction rules, limiting cases, and qualitative field or ray sketches before calculating.
Derive
Connect definitions and field laws symbolically, with every integral and sign tied to physical meaning.
Measure
Design circuit, field, induction, or optical measurements with calibration and uncertainty visible.
Test
Compare the model with data, conservation constraints, residuals, scale, and competing explanations.
Communicate
State assumptions, model boundaries, evidence, uncertainty, and what the result does not establish.
Course-level outcomes
What successful study should make possible.
These are learning capabilities, not promises of a grade, academic credit, transfer approval, professional status, or course completion.- Model electric and magnetic interactions using fields, potentials, flux, and superposition.
- Use Gauss's law, Ampere's law, Faraday's law, and circuit laws with their assumptions stated.
- Analyse steady and transient DC circuits and introductory sinusoidal AC systems.
- Connect Maxwell's equations to electromagnetic-wave propagation, energy transport, and polarization.
- Use ray and wave models of light, selecting the model appropriate to the scale and evidence.
- Plan investigations and interpret laboratory data with uncertainty, residuals, calibration, and competing-model checks.
- Apply calculus and computational methods when symmetry or analytic methods are insufficient.
- Explain where classical models fail and what introductory modern-physics evidence replaces them.
Choose the right starting point
Mechanics ready? Begin with charge and superposition.
Start at unit 01 even if circuit techniques feel familiar. Charge, superposition, symmetry, vector direction, and model boundaries set the standard used throughout fields, induction, waves, and optics.