# Instructor guide: Gauge-equivalent potential reconstruction

Course: Electromagnetic fields and potentials

Suggested time: 50–65 minutes

## Learning target

Learners distinguish representational gauge freedom from gauge-invariant fields, loops, and measured forces.

## Prepare

- Review gradient, curl, and ∇×∇χ=0.
- Declare the laboratory's gauge transformation.
- Prepare one claim that mistakes potential magnitude for local force.

## Facilitation moves

- Ask what the detector measures.
- Compare potentials and fields in separate columns.
- Require a named invariant before accepting a physical claim.

## Misconception checks

- **Changing A mathematically creates a new magnetic field.** A pure gauge gradient changes the representation while its curl vanishes.
- **Potentials are therefore meaningless.** They are central computational objects, and gauge-invariant path or flux combinations can be observable.

## Accessibility and participation

- Use numeric residuals alongside vector plots.
- Describe gradient and curl operations verbally.
- Ensure changed and invariant quantities use labels, not color alone.

## Evidence of learning

- A potential-versus-field comparison
- A correct vector-identity explanation
- One operationally measurable invariant

## Extension

Construct two gauges for the same uniform magnetic field and verify a closed-loop integral around the same contour.

## Evidence boundary

Assess the learner's reasoning only within the declared model and recorded observations. Do not upgrade a simulation result into a claim about an unmodeled physical system.