Gauge Freedom and the Potentials as the Working Variables · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Many potentials, same fields

Science · Electricity & Magnetism · ages 22-24
Name ______________________   Date ____________

  1. Why pick the Lorenz gauge for a radiation problem?

    • It freezes time dependence
    • It removes all sources
    • It gives sourced wave equations

  2. A gauge transformation acts. What stays the same?

    • The measured fields
    • The gauge condition
    • The potentials

  3. Final physical answers must be reported in fields, which never depended on the gauge.

    Circle one:   True   False

  4. A static charge layout needs its potential. Which gauge suits it?

    • Lorenz, for propagating waves
    • No gauge, potentials are unique
    • Coulomb, with its Poisson-like scalar law

  5. You add a gradient to A and match the scalar shift. What happens to E and B?

    • Both change unpredictably
    • Both stay exactly unchanged
    • E stays but B doubles

  6. Two potentials yield identical E and B. How are they related?

    • By a gauge transformation
    • They must be numerically equal
    • By a change of units

  7. Two gauges give different intermediate potentials but one shared E. What do you trust?

    • The Lorenz intermediate, always
    • The shared E, since fields are gauge-free
    • Neither until a third gauge votes

  8. A student says Coulomb gauge makes physics instantaneous. What is wrong?

    • Coulomb gauge forbids static problems
    • Only the description changed; fields still propagate
    • Gauges change measured arrival times
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Many potentials, same fields W1-mt_BovDzq3WZm-s1

  1. It gives sourced wave equations · Waves want wave equations.
  2. The measured fields · Fields are gauge-blind by construction.
  3. True · Fields are the gauge-free quantities.
  4. Coulomb, with its Poisson-like scalar law · Statics want the instantaneous scalar form.
  5. Both stay exactly unchanged · Matched shifts cancel in the fields.
  6. By a gauge transformation · Same fields means same gauge family.
  7. The shared E, since fields are gauge-free · Agreement in fields is the physical signal.
  8. Only the description changed; fields still propagate · Gauge picks language, never physics.
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