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Which equation of a perfect conductor implies the field inside is zero?

E = J/σ (Ohm's law — as σ→∞, E→0 for finite J). In a perfect conductor σ→∞; finite current density J requires E = J/σ → 0 inside.

Short Answer

E = J/σ (Ohm's law — as σ→∞, E→0 for finite J) is the best answer.

Electromagnetism questions become manageable once you separate source, field, potential, current, and force. Most wrong answers mix those layers together or ignore direction.

In a perfect conductor σ→∞; finite current density J requires E = J/σ → 0 inside.

Why This Answer Is Correct

This is a Hard-level question in Electromagnetism. The prompt is really testing whether you can connect the concept to its defining physical relationship instead of picking a nearby-but-wrong term.

Keep charge, field, potential, and current distinct. That single habit fixes a large fraction of electromagnetism errors.

Choices At A Glance

  • A. E = J/σ (Ohm's law — as σ→∞, E→0 for finite J)
  • B. ∇·E = ρ/ε₀
  • C. Maxwell's third equation
  • D. Gauss's law for B

When similar options appear on an exam, eliminate the ones that break the core law, use the wrong units, or confuse a definition with a consequence.

Topic Snapshot

Topic: Electromagnetism

Difficulty: Hard

Best next move: Re-state the governing law in your own words, then solve one more example from the same topic before moving on.