A shielded solenoid of radius carries a uniform internal field

PHYSICS · Multi-part · Fermi University Physics · Oscillations, Waves & Acoustics · Electricity, Magnetism & Electromagnetism · Superposition, boundaries and interference

The Structure of Quantum Mechanics, Ch Charged particles in electromagnetic fields

Problem

A shielded solenoid of radius r=100 nmr = 100\,\mathrm{nm} carries a uniform internal field B=0.30 TB = 0.30\,\mathrm T, entirely confined inside the solenoid, and sits between the two arms of an electron interferometer. The Aharonov-Bohm phase difference between the arms has size ∣δ∣=2πΦ/∣Φ0∣|\delta| = 2\pi\Phi/|\Phi_0|, with ∣Φ0∣=h/e=4.136×10−15 Wb|\Phi_0| = h/e = 4.136\times10^{-15}\,\mathrm{Wb} for an electron. ((a)) Estimate the enclosed flux Φ=Bπr2\Phi = B\pi r^2, in fWb\mathrm{fWb} (1 fWb=10−15 Wb1\,\mathrm{fWb}=10^{-15}\,\mathrm{Wb}). ((b)) Estimate the number of interference fringes, Φ/∣Φ0∣\Phi/|\Phi_0|, by which the pattern shifts as the solenoid current is switched on.

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