If A is the vector potential for the magnetic field produced by a steady current I in aclosed-loop filament, show that div A = 0 off the filament

Question

If A is the vector potential for the magnetic field produced by a steady current I in aclosed-loop filament, show that div A = 0 off the filament
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Solution 1

The vector potential A for a magnetic field produced by a steady current I in a closed-loop filament is given by the Biot-Savart law:

A = μ₀/4π ∫(I dl' / |r - r'|)

where:

  • μ₀ is the permeability of free space,
  • dl' is an infinitesimal element of the current loop,
  • r is the position vector in th Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob
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