Covariant Electrodynamics and the Field Tensor · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

One tensor for E and B

Science · Electricity & Magnetism · ages 22-24
Name ______________________   Date ____________
  1. A charge at rest shows pure E. You boost past it. What do you measure?

    • Pure E still, frames change nothing
    • A mix of E and B
    • Pure B only
  2. What does the field tensor F contain?

    • Only the electric field
    • Only the magnetic field
    • Electric and magnetic parts together
  3. Charge density and current form a single four-vector.

    Circle one:   True   False

  4. Gauss and Ampere-Maxwell laws come from which equation?

    • The divergence of F tied to the four-current
    • The antisymmetric-derivative equation
    • A gauge condition
  5. Which tensor equation covers the source-free pair of Maxwell laws?

    • The antisymmetric-derivative equation
    • The continuity equation alone
    • The divergence equation tied to J
  6. F is antisymmetric and 4 by 4. Type how many independent components it holds.

    Answer: ______________

  7. A problem mixes frames and asks for final E and B. What is the safe strategy?

    • Split into E and B first, then transform pieces
    • Write F and J, transform, split at the end
    • Guess the mixture from symmetry alone
  8. A student says new physics entered because B appeared after a boost. What is wrong?

    • B never appears in any frame
    • Boosts cannot change any measurement
    • The same tensor merely shows mixed in the new frame
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Answer key

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

One tensor for E and B W1-mt_RoxM9z6DfK-s1

  1. A mix of E and B · Boosting mixes the tensor components.
  2. Electric and magnetic parts together · All six components pack into the one tensor.
  3. True · That fusion is the four-current J.
  4. The divergence of F tied to the four-current · Sources enter through J on that side.
  5. The antisymmetric-derivative equation · No sources appear in that pair.
  6. 6 · Antisymmetry leaves 6 free: 3 electric plus 3 magnetic.
  7. Write F and J, transform, split at the end · Tensors transform cleanly; pieces do not.
  8. The same tensor merely shows mixed in the new frame · Only the frame changed, not the physics.
Worksheet · LightMySky