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Phase Shift

Δφ = 0.00 rad
Δφ/(2π) = 0.00 cycles
Phase accumulated from vector potential A around closed loop

Fringe Shift

Pattern shift: 0.00 fringes
Interference pattern shifts as flux changes

Key Physics

  • B = 0 outside solenoid (gray region)
  • A ≠ 0 in accessible region (vector potential)
  • Phase shift: Δφ = (e/ℏc) ∮ A·dl = 2π(Φ/Φ₀)
  • Flux quantum: Φ₀ = h/e ≈ 4.14×10⁻¹⁵ Wb

Instructions

  • Adjust magnetic flux to see phase shift
  • Watch interference pattern shift at detector
  • Flux increases by Φ₀ → pattern shifts by 1 fringe
  • Demonstrates gauge field physical reality

What This Shows

The Aharonov-Bohm effect proves that electromagnetic potentials (A, φ) are not mere mathematical conveniences—they have direct physical effects. Even though the electron never enters the region with B ≠ 0 (confined inside the solenoid), and thus experiences no Lorentz force, it still accumulates a quantum phase from the vector potential A. This phase is gauge-invariant and measurable through interference.