# Learner lab record: Gauge-equivalent potential reconstruction

Course: Electromagnetic fields and potentials

Name: ____________________  Date: ____________________  Group: ____________________

## Investigation question

Which plotted quantities can change under a gauge transformation while electric and magnetic observables remain unchanged?

## Setup

Use the potential-and-gauge laboratory. Record a baseline scalar/vector potential, apply a declared gauge function, and compare potentials, fields, and any loop quantity separately.

## Variables

| Variable | Role | Unit |
| --- | --- | --- |
| Gauge-function amplitude | independent | model potential scale |
| Scalar and vector potentials | representation-dependent | V and field-potential units |
| Electric and magnetic fields | gauge-invariant dependent | V/m and T |
| Closed-loop phase/flux | gauge-invariant diagnostic | declared model unit |

## Predict before changing controls

1. Predict which potential components change after adding a gradient.

   ________________________________________________________________

2. Predict whether curl of the added gradient changes B.

   ________________________________________________________________

## Observation table

| gauge amplitude | potential change | E residual | B residual | loop quantity | invariant? |
| --- | --- | --- | --- | --- | --- |
|   |   |   |   |   |   |
|   |   |   |   |   |   |
|   |   |   |   |   |   |
|   |   |   |   |   |   |
|   |   |   |   |   |   |
|   |   |   |   |   |   |

## Analyze

1. Which quantities changed without changing local fields?

   ________________________________________________________________

2. What vector identity explains the magnetic result?

   ________________________________________________________________

3. Why is gauge freedom not permission to invent a new force?

   ________________________________________________________________

4. What combination would an experiment actually measure?

   ________________________________________________________________

## Evidence-bounded conclusion

The gauge transformation changed ___ by ___ while E and B residuals remained ___; the physical prediction is unchanged because ___.

________________________________________________________________