Learn All 58 finite-plan calculus-based destinations are authored, from electric source integrals and conductor boundaries through circuit states, magnetic geometry, induction and cumulative evidence. Independent scientific/source-action review covers 31 current topics and 299 LO/EK identifiers. Authored availability is not AP authorization, laboratory participation or learner mastery.
This is the course outline. Open a unit to choose a lesson; every lesson opens on its own page. Explanations and experiments live inside those lesson pages.
Preparation: Calculus-based mechanics, algebra, trigonometry and fixed-basis vectors. Definite integrals and source-coordinate conventions are refreshed where used; AP Physics 2 intuition is support, not evidence of completing this distinct calculus course.
Course outcome: Normalize continuous charge, integrate signed field components, distinguish local field from oriented flux and justify symmetry before inferring a piecewise electric field; derive scalar potential, gradients, path work and signed accessible energy; reconcile conductor boundaries, capacitance integrals and dielectric energy; derive signed circuit transients and test instrument-loading inference; derive magnetic source and force integrals and defend symmetry and carrier inference; derive induced electric circulation, linked flux, event-state dynamics and energy-constrained LC identification; defend finite-resistance charge sharing and cross-model calibration with retained first reasoning and revised evidence.
All lessons are directly accessible. Reused foundation explanations are identified where relevant; completing a different course does not award this course's evidence. The 58 registered lessons keep separate predictions, captures, practice responses and reflections.
Reconcile source, geometry, state and energy accounts across electric and magnetic models; identify what an independent record can actually establish.
Retain a first prediction, both state equations, charge invariant, difference-mode derivation and finite-time energy residual. Change one capacitance and independently recompute the limiting voltage. Then critique a claim that charge loss caused the energy decrease, and write a new-system prediction for a source that remains connected.
Fit the supplied trace under two different gain assumptions and show why both match. Retain an independent LC calculation and explicitly audit the known-capacitor, clock and unchanged-inductor premises. Submit a critique/revision pair and an unfamiliar changed response in the versioned course project, distinguishing generated evidence from real observation.
Integrate linked flux, derive induced-field and circuit dynamics, preserve event states and distinguish parameter inference from calibration assumptions.
Predict normal-reversal signs before running the model. Derive the area integral, check a zero-gradient limit and compare left-edge versus midpoint sampling. Retain a six-face closed-box account that explains why nonzero open flux does not violate magnetic Gauss law.
Predict the two terms separately at zero time and at a later orientation. Retain their algebraic sum, identify a sign-change or cancellation interval and test the fixed-field and fixed-orientation limits. Explain what additional force and source-work records would be needed for an energy claim.
Predict field direction under rate reversal, then compare inner and outer radii with equal field magnitude. Derive both branches and verify continuity and circulation. Write a closed-path contradiction for a purely electrostatic scalar-potential explanation and a separate conceptual Maxwell-wave prediction.
Predict the effect of doubling B at fixed resistance before replay. Derive speed, displacement and heat independently, then retain an energy residual. Sketch entering, fully immersed and leaving loop cases, identifying current direction and exactly which segments feel the external field.
Derive flux linkage, inductance and energy from geometry. Compare fixed-total-turns and fixed-turn-density length changes, and retain the field-energy cross-check. Explain how a nonlinear core or a resistive winding would invalidate one of the ideal reductions without implying energy nonconservation.
Derive and differentiate the general solution, then compare initial currents below, at and above E/R. Retain source work, heat and stored-energy change over a finite interval. Explain why the initial-voltage and 63-percent shortcuts apply only to their stated special cases.
Retain a node/path sketch for both topologies, predict which state is continuous and compute both one-sided voltages. Compare current and energy decay rates. Recompute the changed equivalent-resistance packet and explain why an open interruption is outside this finite model.
Derive both state functions and check their initial values and derivatives. Retain several phase snapshots with electric, magnetic and total energy. Contrast a general initial state with the initially charged special case and propose independent evidence for a hypothetical decaying envelope.
Construct an equal-period alternative, retain two independent relations and solve both parameters. Add a gain-confounded counterexample, then specify one genuinely independent observation that would resolve it. Separate synthetic record agreement from performed measurement and independent validation.
Differentiate and integrate the same history independently, retaining the missing-constant argument. Compare instantaneous and interval rates, compute the signed-area versus squared-area waveform packet and specify an independent observation that resolves one calibration ambiguity.
Integrate magnetic source geometry, solve classical deflection and distinguish symmetry-based field prediction from calibrated inverse inference.
Compare pure dipole and background-added component maps, retaining an equal-scale direction sketch. Independently sum the six flux faces. Classify the supplied three material histories with a stated alternative explanation and predict a discriminating zero-field recheck; do not infer composition from one response.
Predict both component signs before evaluating. Vary source speed and observer y separately and retain both perpendicularity checks. Then solve the supplied recipient-force and crossed-field packets while keeping source and test quantities distinct.
Compare negative, neutral and positive q/m. Derive the position functions by integration and check their initial values. Retain the no-work dot product and distinguish transverse from three-dimensional motion. Independently derive the Hall polarity under one reversal and explain the one-carrier assumption.
Compare source half-length and observation distance separately, retaining the exact ratio and two numerical resolutions. Sketch current, source displacement and cross-product direction for one negative-x and one positive-x element. Propose an observation that could reveal an omitted nearby return path.
Derive the axial projection and compare center, near-axis and far-axis values. Then construct the opposite-semicircle packet and retain each signed contribution instead of summing magnitudes. State which return segments are omitted and why.
Predict the right-wire force sign for positive, zero and negative I2. Double separation and retain the inverse-distance ratio. Then independently integrate the quadratic assigned-field packet and compare its exact average with the midpoint shortcut.
Normalize n = 0, 1 and 2 at fixed total I. Predict interior power laws, surface matching and common exterior values. Retain a proposed interior observation that distinguishes two profiles, then solve the written coaxial return packet.
Compare half-thicknesses at fixed K and retain signed interior/exterior predictions. Draw the two contributing loop sides. Then derive the solenoid expression, solve the opposing-solenoid packet and state why a broken symmetry or changing source requires a different argument.
Predict both component signs for negative, zero and positive right current. Reconstruct the two currents from the component ledger without substituting their known inputs. Compare a magnitude-only alternative and propose a calibrated observation that genuinely distinguishes it.
Integrate material and time-dependent current accounts, solve connected networks and defend signed transient energy and instrument inference.
Compare beta = 0, 1 and 2 at fixed radius. Predict the ratio of mean to edge density and retain the annular integral. Reverse the selected normal without changing physical flow. Then integrate the supplied time ramp and distinguish total charge from mean and endpoint current.
Compare uniform and linearly varying resistivity with the same rho0. Derive the cumulative voltage curve, then differentiate it. Predict both graph slopes. Finally use the supplied temperature and nonlinear packets to identify where a fixed-parameter ohmic model is no longer appropriate.
Compare loads below, equal to and above the internal resistance. Retain terminal voltage, source power, each resistor power and load fraction. Differentiate the load-power expression if choosing the optional maximum challenge, then contrast the result with efficiency.
Redraw the same node connections in a different layout before calculating. Compare equal and unequal branches, retain the junction residual and one complete loop voltage account, and predict the open-branch limit without performing any physical switching.
Predict bridge-current sign for right lower resistances 2, 6 and 8 ohm before solving. Retain both node residuals, a loop voltage account and total power. At balance, vary Rb and explain what remains unchanged and why.
Compare finite meter resistances at a fixed load, predict the infinite-input-resistance limit, and retain actual branch currents. Invert the indication once with and once without the known meter model. Explain why reading precision alone cannot remove loading bias.
Predict series voltage division for unequal capacitances, compare the equivalent against the smaller component, and sum energies. Then solve the supplied precharged-node counterexample to identify exactly why the equal-charge shortcut needs an initial inventory assumption.
Compare V0 = −2, 0, 6 and 8 V at the same R. Predict current sign, final voltage and source-work sign. Derive the solution and independently differentiate it. Retain the finite-time energy residual and explain why 63% applies to the zero-initial charging special case rather than every arbitrary V0.
Predict the event voltage for several charging durations, retain continuity and both one-sided currents, then compare voltage and energy decay ratios. Explain why restarting the discharge at the source voltage would invent stored charge after a finite charging time.
Compare inferred leakage with and without the known meter. Predict a second meter’s time constant while holding the leakage fixed, and identify the shared parameter. Write a baseline-offset counterexample showing why a straight two-point log fit is not always a valid physical inference.
Reconcile conductor charge redistribution, geometric potential integrals and controlled-boundary energy changes.
Compare q = −1, 0 and +1 nC at fixed shell charge. Retain inner/outer inventories and three spatial regions. Then set Q = −q and explain how exterior zero field can coexist with a nonzero cavity field. Sketch a noncentral-source alternative and identify which totals survive without claiming a spherical local field.
Compare radius ratios 0.5, 1 and 2 while holding total charge fixed. Predict charge, potential, density and field ratios separately. Retain the missing electrostatic energy account. Contrast the closed pair with the virtual ground-reservoir sequence and record which total is no longer conserved.
Change area at fixed gap and predict why trajectory is unchanged although charge changes. Then change gap, compare the exit and impact conditions, and retain a rejected exit calculation. Explain the geometric limit and why the supplied q/m does not identify a real particle species.
Derive both integrals before checking three radius pairs. Keep the fixed-Q constraint explicit while comparing energy. Test the outer-radius limit and the thin-gap approximation, stating what dimensionless ratio controls each.
Compare lengths 1, 2 and 3 m at fixed Q. Then write a separate fixed-lambda prediction without changing the simulator’s declared control. Integrate gap energy independently and identify which end-field evidence would be needed to assess a finite apparatus.
Compare two capacitances at fixed final voltage and two final voltages at fixed capacitance. Sketch both the charging line and accumulated-work curve. Then hold final Q fixed on paper and explain why changing C reverses the fixed-voltage energy trend.
For each kappa, predict the isolated and maintained-voltage ledgers before switching the boundary mode. Retain free charge, field, source work and mechanical work separately. Explain which microscopic polarization mechanism is shared and which external boundary produces different energy outcomes.
Predict both geometries for f = 0, 0.5 and 1 before checking. Draw the interface and indicate whether voltage or normal D is shared. Integrate the two layer energies and compare with the final-state capacitor expression.
Vary gain and parasitic offset separately, retaining which fit parameter changes. Predict a third-gap indication and explain why it does not resolve common gain. Then calculate the supplied finite-bound area interval and name an additional uncertainty that it omits.
Integrate scalar source potential, recover fields, reconcile pair energy and defend a signed-motion or calibration inference.
Predict all three signed terms for third charges −1, 0 and +1 nC before checking. Double all separations at fixed charges. Compare sequential assembly in a different order and explain why total work stays fixed while intermediate work changes.
Compare C = −4, 0 and +4 V at fixed A. Retain the same contour shapes with relabeled potential values and the unchanged field. Then change A, calculate a local normal and tangent at (1,1), and predict which contour shape changes.
Change B through −2, 0 and +2 while holding A fixed. Predict segment integrals, compare both cumulative curves, and independently integrate the straight path. Reverse the path and explain which signs reverse. Do not interpret the displayed segment parameter as physical distance or travel time.
Compare beta = 0, 1 and 2 at the same total charge. Predict how moving more charge toward the near endpoint changes potential. Derive the field separately, compare the centered derivative discrepancy and test a changed perpendicular-bisector observer using the written expression.
Compare center and axial records at two radii. Predict which quantities scale as inverse radius and inverse radius squared. Design a two-observation test for ring versus arc without claiming a single scalar value identifies the source.
Compare reference radii 1, 2 and 3 m at fixed lambda. Retain center, surface and exterior potentials, then subtract the same endpoint pair in every case. Independently differentiate both branches and verify continuity at the surface.
Compare positive, zero and negative charge at fixed initial K. Predict the minimum candidate energy and accessible branch before plotting. Retain one ordinary turning point, one threshold case and one crossing case; state why their endpoint criteria differ.
Vary gain and offset separately. Retain fitted charge, fitted offset and the independent field residual. Construct a same-instrument third-potential prediction and explain why it cannot by itself identify gain. Propose a controlled alternative test for a wrong source radius.
Reconcile source inventory, vector projection, surface orientation and independent evidence limits.
Compare transfers of 0, 2 and 4 billion electrons at separation 2 m. Retain each individual charge, combined charge and signed recipient force. Then double separation at fixed charges and predict the inverse-square change. Write a separate closed-system account for polarization with no transferred electrons, and an open account for a connection to a large charge reservoir. Compare the supplied two-insulator polarization packet with mobile-carrier redistribution, identifying the unchanged net charge and different constitutive assumptions.
Compare right-source charges −2, 0 and +2 nC at a fixed probe. Construct equal-scale vector arrows at (0,1) before checking the component slices. Then vary only the probe through negative, zero and positive values; retain the unchanged field and changed force. Explain why the displayed component curves are not physical particle trajectories.
At observer z = 2, compare beta = 0,1,2 while keeping total charge 2 nC fixed. Derive lambda 0 anew and compare exact,8-cell and 64-cell fields. Then increase observation distance and compare with the leading point-charge limit kQ/z². Explain why one small numerical discrepancy is not a general quadrature error bound.
Compare half-lengths.5,1,2 m at fixed Q and distance 1 m. Derive the exact vertical field, then separately compare each with the infinite-line expression at that case’s actual density. Sketch paired horizontal contributions and retain their cancellation before integration.
At fixed total Q, compare radii.5,1,2 m and equal axial coordinates. Predict the sign across the ring plane, the center value and far-field scale before plotting. Independently differentiate the analytic field if choosing the optional maximum-location challenge; distinguish that extension from the core projection integral.
Compare spanspi/4,pi/2 andpi at fixed total Q = 2 nC. Sketch the direction of each endpoint contribution, integrate both components and compare with the 16-cell sum. Then state how the comparison would change if line density, rather than total Q, were held fixed.
Hold field gradient 2 and compare transverse fields 0,2,4. Predict the individual face changes and unchanged total. Then set the gradient to 0 with transverse field 4: record nonzero field with zero net flux. Redraw each outward normal and independently integrate the actual face areas before using Gauss law. Independently integrate the written y² field over its open patch, change the upper y limit, and distinguish this surface integral from the closed box charge balance.
Compare density powers 0,1,2 at fixed Q and R. Integrate enclosed charge at radii.25,.5,.75 and 1, then derive the interior and exterior fields. Contrast the volume distribution with the same-charge conducting shell. Explain why an exterior measurement alone cannot distinguish these symmetric interior distributions. Independently normalize the written sigma(r) annulus and change its outer radius at fixed coefficient, then at fixed total charge.
Compare shell charges−2,−1 and+2 nC/m. Derive each enclosed-charge branch before plottingE. Check continuity at radii 1 and 2, then compare a point inside the core, inside the shell and outside both. State why this infinite insulating model is not a finite conducting cable calculation.
Compare half-thicknesses.5,1,2 m at fixed charge per area. Predict the changing interior slope and unchanged exterior magnitude. Reverse the observation coordinate to check sign. Then replace the verbal infinite-plane source with a finite patch and identify precisely which uniformity step can no longer be assumed from Gauss law alone.
Keep predictions before comparison, complete raw records and units, explain competing models and test a changed case. Supplied and simulated data are labeled in each lesson. A saved notebook is not proof of experimental technique or correct reasoning.
Evidence to retain: Retain a finite-resistance charge-sharing derivation, finite-time energy account and changed source boundary. Fit a gain-confounded LR trace, reconcile a separate known-capacitance period and critique whether its evidence is independent.
Boundary: Original synthetic records and conceptual plans only; no actual calibration, switching operation or performed practical time.
Evidence to retain: Retain surface-normal and boundary conventions, spatial integration, a product-rule separation and an inner/outer electric-circulation derivation. Compare a reconstructed field history with its missing additive anchor and a signed-area versus heat counterexample.
Boundary: Original virtual packets and conceptual designs only; no energized circuit operation, switch procedure, apparatus access or actual supervised laboratory time.
Evidence to retain: Derive a braking initial-value model and finite-time heat account, identify immersed force recipients, then independently reconcile a solenoid circuit-energy and field-energy calculation. Retain a changed geometry and a constitutive limitation.
Boundary: Original virtual packets and conceptual designs only; no energized circuit operation, switch procedure, apparatus access or actual supervised laboratory time.
Evidence to retain: Derive an arbitrary-current transient, preserve current at a supplied finite-voltage topology change, retain one-sided voltages and close source/heat/storage accounts. Compare current and squared-energy decay and an equivalent-resistance alternative.
Boundary: Original virtual packets and conceptual designs only; no energized circuit operation, switch procedure, apparatus access or actual supervised laboratory time.
Evidence to retain: Retain both initial conditions, state the current reference, derive phase-resolved energy and compare equal-period component alternatives. Introduce sensor-gain confounding and propose an independent observation that resolves it.
Boundary: Original virtual packets and conceptual designs only; no energized circuit operation, switch procedure, apparatus access or actual supervised laboratory time.
Evidence to retain: Retain equal-scale field directions, independent component records, a six-face flux sum and material-history alternatives. Separate source motion from test-charge response and distinguish inverse identifiability from a magnitude fit.
Boundary: Supplied virtual records and original models only; no current setup, particle apparatus, magnet handling or performed laboratory participation.
Evidence to retain: Derive velocity and position from the Lorentz equations, compare charged and neutral limits, and retain Hall polarity and carrier-density assumptions. Explain the zero magnetic work rate without erasing transverse acceleration.
Boundary: Supplied virtual records and original models only; no current setup, particle apparatus, magnet handling or performed laboratory participation.
Evidence to retain: Derive finite-wire, loop-axis and arc-center integrals; compare numerical resolution and remote-return assumptions. Retain recipient-specific force signs and a nonuniform-field force integral.
Boundary: Supplied virtual records and original models only; no current setup, particle apparatus, magnet handling or performed laboratory participation.
Evidence to retain: Normalize a radial current profile, retain interior/exterior continuity and compare a coaxial return. Derive the slab factor of two and long-solenoid limit, then state why circulation alone cannot identify local field without symmetry.
Boundary: Supplied virtual records and original models only; no current setup, particle apparatus, magnet handling or performed laboratory participation.
Evidence to retain: Derive spatial current and resistance integrals, distinguish local and mean quantities, integrate an independent time packet and compare reciprocal graph slopes. Retain a fixed-temperature versus varying-temperature model challenge.
Boundary: Original virtual diagrams and supplied numerical records; no actual electrical operation, instrument calibration or laboratory participation.
Evidence to retain: Draw exact nodes and component symbols, predict signed branch currents, solve a nonreducible bridge and retain junction/loop/power residuals. Compare a topology change with a mere redraw.
Boundary: Original virtual diagrams and supplied numerical records; no actual electrical operation, instrument calibration or laboratory participation.
Evidence to retain: Include instrument resistance and floating-node initial inventory explicitly. Retain a biased naive fit, a corrected fit using independent information, and a counterexample to equal series charge with a precharged node.
Boundary: Original virtual diagrams and supplied numerical records; no actual electrical operation, instrument calibration or laboratory participation.
Evidence to retain: Derive a general RC solution from loop and charge conservation, retain a negative-current initial state, match switching voltage and compare voltage versus energy decay. Close finite-time source/heat/stored-energy accounts.
Boundary: Original virtual diagrams and supplied numerical records; no actual electrical operation, instrument calibration or laboratory participation.
Evidence to retain: Retain induced inner/outer charge accounts, material/cavity fields, connected-sphere potential constraints and an isolated-versus-reservoir contrast. Predict an off-center or external-field alternative without asserting an invalid symmetric local field.
Boundary: Supplied or generated virtual records; no physical electrical procedure, genuine calibration or performed laboratory time.
Evidence to retain: Derive a field, integrate a voltage difference and form capacitance for three permitted geometries. Independently calculate charging and field energy, preserve controlled-Q versus controlled-V distinctions and reject a plate trajectory that reaches a boundary first.
Boundary: Supplied or generated virtual records; no physical electrical procedure, genuine calibration or performed laboratory time.
Evidence to retain: Predict isolated and maintained-voltage ledgers, retain source/mechanical energy terms and compare two interface orientations. State when a material region is absent and its field only a limiting construction.
Boundary: Supplied or generated virtual records; no physical electrical procedure, genuine calibration or performed laboratory time.
Evidence to retain: Fit source area and additive parasitic capacitance, test an independently stipulated area constraint and calculate an all-corner two-reading interval. Distinguish common gain, hard bounds and source-model alternatives.
Boundary: Supplied or generated virtual records; no physical electrical procedure, genuine calibration or performed laboratory time.
Evidence to retain: Retain unordered pair terms, an alternative assembly order, a gauge change, both segment integrals and a local equipotential tangent/normal prediction. Challenge a false inference from equal potential to equal field.
Boundary: Original supplied or generated virtual records only; no real charging, particle apparatus, calibration or laboratory participation.
Evidence to retain: Normalize the source, derive scalar potential and its spatial derivative, test an allowed geometry transfer, and distinguish finite and infinite reference conventions. Retain analytic and finite-difference discrepancies without calling them independent measurements.
Boundary: Original supplied or generated virtual records only; no real charging, particle apparatus, calibration or laboratory participation.
Evidence to retain: Retain signed energy branches, simple-turn/threshold/crossing distinctions and a gain-offset inverse fit. Predict a separately calibrated field before revealing it and distinguish source-geometry failure from calibration failure.
Boundary: Original supplied or generated virtual records only; no real charging, particle apparatus, calibration or laboratory participation.
Evidence to retain: Retain predicted individual/combined charges, equal-opposite recipient forces and contrasting passive probe signs. Construct a polarization-without-transfer alternative and identify the independent observation needed to distinguish it from actual charge transfer.
Boundary: Original integer-count and passive-probe packets; no actual charging, grounding or material measurement.
Evidence to retain: Derive normalized line/ring/arc charge elements and signed fields, compare at least two midpoint resolutions, and test a limiting case at the correct fixed inventory. Retain a rejected normalization and one independently recomputed component.
Boundary: Analytic and numerical calculations share a supplied source model; numerical agreement is not independent physical validation.
Evidence to retain: Record all face normals/areas and signed integrals, change a transverse field without changing net flux, then design a supplied-data comparison distinguishing symmetric and broken-symmetry sources. State which observations constrain local field rather than only total charge.
Boundary: Generated fields and stipulated geometric limits; no real field probe, high-voltage setup or physical technique.
Evidence to retain: Integrate enclosed inventory in each region, test branch matching and sign, and propose an interior observation that distinguishes sources sharing an exterior field. Preserve the conductor-versus-insulator and finite-versus-infinite alternatives.
Boundary: Exactly symmetric ideal source packets; finite-edge, material and calibration effects require new evidence.
Open the retained response and project workspaces. Practice, saved work and independently reviewed proficiency remain separate.
These 45 course-specific public tasks are practice, not a secure examination. Each retains up to three immutable written responses, known feedback exposure before each response, and human rubric critiques. Drafts remain editable. No text-length check or self-reported review certifies correctness, independence, laboratory skill or mastery.
Design a supplied-data comparison of two source distributions that agree at one exterior location. Choose at least one component or interior observation, normalize each distribution and predict which record separates them. State charge conservation and the passive-probe limit.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Propose an original changed geometry in which pair energy, potential at a point and external assembly work are different quantities. State the reference and what is held fixed; design an independent derivation or path comparison.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Design a virtual comparison between isolated-charge and maintained-voltage capacitor changes, or between cavity, metal and exterior observations of a conductor. Specify every source of charge/work and one changed boundary condition.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Create a node-labeled virtual network or transient inference with a finite meter. Specify two independent records, a known initial state and a topology change or calibration alternative. Predict an outcome that would reject the first model.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Design a magnetic comparison with equal exterior field but unequal interior current profiles, or equal field magnitude but unequal signed components. Choose a geometry and one independently calibrated observation; state why symmetry is required.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Propose a virtual induction or LR/LC investigation with two genuinely distinct records and an explicit initial state. Include a sensor-gain or missing-flux-anchor alternative and a source/heat/storage account.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
A uniformly charged thin spherical shell of radius 3 m has charge 27 nC. A second insulating sphere of that radius has density proportional to r² and the same total charge. Under spherical symmetry compare E at r = 1.5 and 6 m, using k = 8.9875517923e9 SI. Identify a discriminating observation and a limitation.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Three point charges +2, +1 and −1 nC are at positions (0,0), (3,0) and (0,4) m. Express total interaction energy divided by k(1 nC)^2/(1 m). Then double all distances and state the effect on energy and each pair-force magnitude.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
A 4 microfarad capacitor initially at 10 V shares charge with an uncharged 2 microfarad capacitor through a positive finite resistor, with all sources removed. Find final voltage, initial/final stored energy and total resistor heat.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
A 12 V emf with internal resistance 2 ohm feeds parallel loads of 6 and 3 ohm. Find total current, terminal voltage, both branch currents and the source/internal/load powers.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
A radius-2 m infinite cylinder carries +4 A along z with Jz proportional to r². Find J0 in Jz = J0(r/R)², current enclosed at r = 1 m and Bphi there using mu0 ≈ 4pi×10⁻⁷. Explain why the same exterior field could come from a uniform profile.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
An ideal circular region of radius 1 m has dBz/dt = +2 T/s. Find Ephi at r = 0.5 and 2 m and the outer circulation. A separate four-turn fixed loop has area 0.5 m² and the same uniform field rate along its normal; find its emf.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
A 2 H inductor carrying 3 A is transferred into a supplied closed 4 ohm discharge path. Find current, stored energy and resistor heat after one time constant. Separately, the same initial 9 J is transferred losslessly into a 2 F capacitor with zero current at its maximum-voltage instant; find voltage magnitude.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
An LR trace with source 10 V reports asymptotic current 5 A and normalized time constant 1 s. A separate known 1 F capacitor with the same linear inductor gives LC period 4pi s. Infer L, R and current-sensor gain, and identify one premise that could invalidate the inference.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
A two-turn fixed rectangle spans x from 0 to 3 m and y from 0 to 2 m, normal +z. Bz = (0.1 T)(1 + 2x/(3 m))(1 + t/(4 s)). Derive flux linkage and emf. Can the emf establish the initial uniform offset if the field formula is not supplied?
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
An ideal radius-2 m flux region has dBz/dt = −0.3 T/s. Find Ephi at r = 1 and 4 m and the outer closed circulation. State why the result cannot come solely from a single-valued electrostatic potential.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
A virtual sliding rod has m = 3 kg, l = 2 m, B = 1 T, R = 4 ohm and v0 = 2 m/s. Find speed time constant, speed at one tau and heat generated by then. Separately a linear inductor L = 0.5 H changes from 2 to 4 A; find stored-energy change.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
A driven LR circuit has E = 8 V, R = 2 ohm, L = 4 H and I0 = 6 A. Find current and passive inductor voltage after one tau. If its current at that instant is then transferred into a supplied closed 4 ohm discharge path, what is the immediate current and voltage, and what fraction of event magnetic energy remains after one discharge tau?
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
An ideal LC circuit has L = 4 H, C = 1 F, q0 = 2 C and i0 = 1 A with i = dq/dt. Find omega, total energy, charge after quarter period and peak current. In a separate initially charged experiment, a period 4pi s with V0 = 2 V and peak current 1 A is used to infer L and C; what happens if the current sensor has an unknown gain of two?
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A stipulated two-second emf record is +3t V for 0 to 1 s and −3(2 − t) V for 1 to 2 s. A fixed coil has N A = 3 m² turn; a separate ideal resistive-load calculation uses R = 3 ohm and negligible self-inductance. Find net field change and total heat. Explain one ambiguity not resolved by the emf trace alone.
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A hypothetical positive particle with q/m = 2 C/kg enters B = 3 T along +z with velocity (4,0,1) m/s. Find transverse radius, period and initial acceleration. Separately J = 2e6 A/m² along +x, electron density 1e28 m⁻³, B = 0.4 T along +z and width 0.02 m define a single-carrier Hall strip. Determine the sign and approximate upper-minus-lower voltage.
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A straight segment carries 3 A with half-length 2 m, observed 1 m from its perpendicular midpoint. Compare its field with an infinite wire. Separately, two semicircular arcs of radii 1 and 3 m carry 2 A in opposing senses; radial connectors contribute zero at the common center. Find the net magnitude from the arcs.
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A radius-2 m conductor carries 8 A with J proportional to r². Find J0 in J = J0(r/R)² and the field at r = 1 m. Separately a slab of half-thickness 2 m carries sheet current 4 A/m; find By at x = 1 m and exterior positive x.
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Two long z-directed wires separated by 2 m carry +3 A and −4 A. Find the right-wire force per length. Separately a straight +x wire of length 2 m carries 3 A in Bz(x) = (0.002 T)[1 + x/(2 m)]. Find its total force and contrast using only the field at its left endpoint.
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Wires at x = −1 and +1 m carry unknown signed z currents. At (0,1) m, Bx = −0.3 microtesla and By = +0.1 microtesla. Infer both currents with known geometry/calibration. Explain why magnitude alone and a second record on y = 0 cannot replace the two signed components. Separately compare pure axial dipole fields at 1 and 3 m.
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A circular section of radius 2 mm has Jz = J0[1 + 2(r/R)²], J0 = 1e6 A/m². Find current and mean density. Separately, a 2 m uniform-area resistor of area 2 mm² has rho(x) = (3 micro-ohm m)[1 + x/(2 m)]. Find R and the slope of I versus V.
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An emf of 10 V has internal resistance 1 ohm and feeds two parallel loads of 3 and 6 ohm. Find terminal voltage, branch currents and source/internal/load powers. Explain why the branch currents do not add as perpendicular spatial vectors.
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A 5 V source with series resistance 1 kohm feeds an unknown load and a parallel voltmeter of known resistance 6 kohm. The exact indication is 3 V. Infer the parallel equivalent and true load. What would ignoring the meter report?
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A 4 V ideal source, 2 kohm resistor and 3 microfarad capacitor start with V0 = 7 V. Derive V and I at one time constant; give source work, resistor heat and stored-energy change through that time in microjoules.
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Two 3 microfarad capacitors connect top 10 V to floating middle Vm to bottom 0 V. Middle-node net charge is +6 microcoulomb. Find Vm and the two capacitor charge magnitudes. Separately, a 1 microfarad capacitor has measured tau = 2 s while a known 3 Mohm meter is connected in parallel with leakage. Infer leakage resistance.
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A concentric conducting shell has cavity radius 1 m, outer radius 3 m and net charge +1 nC. A central −2 nC source is present. Find inner and outer surface charges, the metal potential relative to infinity and the cavity field at r = 0.5 m. Would setting the shell potential to zero by reservoir contact conserve its original net charge?
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A spherical capacitor has inner radius 0.5 m and outer radius 2 m, with charges ±3 nC. Derive capacitance and the potential difference. Give U/[k(1 nC)²/(1 m)] and predict that dimensionless energy after doubling both radii at fixed charge.
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A hypothetical body with q/m = −2 C/kg enters midway between ideal plates with E = +1000 N/C in the vertical direction, gap 2 mm, horizontal speed 50 m/s and zero vertical speed. The modeled horizontal length is 0.1 m. Find the candidate exit displacement, actual first-contact time and horizontal coordinate.
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An initially vacuum capacitor has C0 = 3 nF and V0 = 6 V. Insert a fully filling ideal dielectric with kappa = 3 while maintaining voltage. Find final charge, final stored energy, source work and reversible external mechanical work. Contrast final energy under isolated-charge insertion.
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At gaps 1 and 2 mm, supplied capacitance bounds are [96,100] pF and [52,54] pF. Under the unit-gain vacuum model, bound area from their difference. Then explain why these finite bounds do not exclude a common gain bias, and whether a third inverse-gap indication alone resolves it.
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Three charges +1, +1 and −2 nC occupy (0,0), (2,0) and (0,2) m. Find the dimensionless interaction-energy ratio U/[k(1 nC)²/(1 m)]. Compare adding the negative charge last with adding it first. Does zero total charge force zero interaction energy?
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Use V = x² + 4xy + 5y² + 7 in SI units. Find V and E at (1,1), delta V from the origin, and a tangent direction there. A negative elementary charge moves from the origin to (1,1); give delta U in eV and field work in eV.
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A line spans x = 0 to 2 m with lambda = c x, where c has units C/m², and total charge is 4 nC. Find potential at z = 3 m relative to infinity, and the field there. Explain whether a point-charge replacement is exact.
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Use V(x) = 4(2x − x²) V over 0..2 m. A hypothetical body starts at x = 0 with K0 = 3 eV. Compare q = +e and q = −e at x = 1. For the positive charge, find the initial turning point; then change K0 to 4 eV and classify access to the top.
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A stipulated ring has radius 1 m and true charge 3 nC. Potential indications share gain 0.8 and offset −2 V. A two-point fit assumes unit gain. What charge and offset result? What is the ratio of its predicted axial field to a separately calibrated true field? Would an extra potential from the same instrument necessarily expose the error?
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Two isolated bodies initially carry +4 and −2 billion elementary charges. Move 1 billion electrons from the right body to the left, keeping separation 1 m. Give both final charges, their net charge and the force on the right body in units k(10⁹e)²/(1 m)². Could an equally sized rearrangement entirely within either body produce those same net-charge changes?
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A different thin line spans x=0 to2 m with lambda(x)=c x, where c has units C/m². Total charge is4 nC. Determine c, the charge-weighted center and the field at z=3 m. Use k=8.9875517923e9 SI. Would holding c fixed while doubling line length preserve total charge?
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A uniform positive quarter-circle runs from angle0 topi/2, radius2 m and total charge3 nC. Derive Ex and Ey at the center. Rotate the entire arc bypi about the center while keeping the fixed axes. What changes, and what stays unchanged?
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A new assigned field is E=(2x,−y,0) in SI units inside a unit cube x,y,z in0..1 m. Calculate all six outward face fluxes and net enclosed charge. Does zero field at the origin imply zero enclosed charge? Is the source distribution uniquely reconstructed by one total-flux observation?
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An insulating sphere of radius2 m carries8 nC with rho(r)=C r². Normalize C, find charge enclosed at r=1 m and fields at r=1 and4 m. Compare a conducting spherical shell with the same radius and total charge. Which new observation can distinguish them?
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Reviewer identity and role are declarations, not authenticated credentials. Unsaved review fields below are lost on navigation. Review every criterion with an exact quotation, calculation or evidence citation and a next step.
Build a six-category original evidence dossier and a cross-model defense. Preserve the earlier fields-only project as an archived definition; this version is not awarded merely because the course acquired more lessons.
Design a supplied-data comparison of two source distributions that agree at one exterior location. Choose at least one component or interior observation, normalize each distribution and predict which record separates them. State charge conservation and the passive-probe limit.
Evidence to retain: Retained original prediction, diagram, derivation, controlled records, changed case, public-answer exposure and critique/revision history.
Propose an original changed geometry in which pair energy, potential at a point and external assembly work are different quantities. State the reference and what is held fixed; design an independent derivation or path comparison.
Evidence to retain: Retained original prediction, diagram, derivation, controlled records, changed case, public-answer exposure and critique/revision history.
Design a virtual comparison between isolated-charge and maintained-voltage capacitor changes, or between cavity, metal and exterior observations of a conductor. Specify every source of charge/work and one changed boundary condition.
Evidence to retain: Retained original prediction, diagram, derivation, controlled records, changed case, public-answer exposure and critique/revision history.
Create a node-labeled virtual network or transient inference with a finite meter. Specify two independent records, a known initial state and a topology change or calibration alternative. Predict an outcome that would reject the first model.
Evidence to retain: Retained original prediction, diagram, derivation, controlled records, changed case, public-answer exposure and critique/revision history.
Design a magnetic comparison with equal exterior field but unequal interior current profiles, or equal field magnitude but unequal signed components. Choose a geometry and one independently calibrated observation; state why symmetry is required.
Evidence to retain: Retained original prediction, diagram, derivation, controlled records, changed case, public-answer exposure and critique/revision history.
Propose a virtual induction or LR/LC investigation with two genuinely distinct records and an explicit initial state. Include a sensor-gain or missing-flux-anchor alternative and a source/heat/storage account.
Evidence to retain: Retained original prediction, diagram, derivation, controlled records, changed case, public-answer exposure and critique/revision history.
Complete the eight cumulative mixed packets before viewing public solutions where possible. Preserve first reasoning, disclose exposure, invite a qualified independent critique and submit a genuinely changed transfer.
Evidence to retain: Versioned attempts, exposure state, independently attributed critique and immutable unfamiliar response.
Prepare a proposed investigation with variables, calibration, repeats and risk boundaries for local science-educator review. Record execution and time only if they actually occur.
Evidence to retain: Actual learner records and qualified supervision remain external. Never fabricate raw measurements, performed time, AP authorization or independent mastery.
Retain raw-data identifiers, provenance, units, prior predictions, methods, calculations, competing explanations and safety boundaries. State explicitly when data are simulated, supplied or genuinely observed. This saved text cannot verify a real experiment; do not invent measurements or completed supervised work. Maximum 12,000 characters; retain larger evidence files separately and cite them.
A nonempty report is only a saved submission. First and revised reports remain separate and cannot be overwritten. A critique of the first report is required before retaining one revision.
Defend a new source geometry, changed circuit boundary and shared-bias inference. Explain what each observation measures, which invariant survives and what independent evidence could reject the model.
A human must supply the actual new task, evidence and conditions before the learner responds. The transfer-direction text is not itself an unseen assessment. Use the retained assignment form after the first project; exposed public task identifier: expanded-public:ap-physics-c-electricity.
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