Electromagnetism / Electrodynamics I · Magnetostatics and vector potential
An ideal solenoid leaves vector potential outside its field
Problem
An infinite ideal solenoid of radius R has uniform field $B_0\hat{\mathbf z}$ inside and zero field outside. Seek $\mathbf A=A_\phi(r)\hat{\boldsymbol\phi}$ that is regular at the axis and continuous at R. Find A inside and outside, and compute the circulation around a circle with $r>R$.
Hint
Integrate the cylindrical curl equation separately in the two radial regions.
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