A toroid of mean radius is wound uniformly with turns carrying a steady current

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Magnetostatics · Magnetostatics

The Boundary-Value Problem, Ch The magnetic multipole expansion and the magnetic scalar potential

Problem

A toroid of mean radius bb is wound uniformly with N=500N = 500 turns carrying a steady current I=2.0 AI = 2.0\,\mathrm{A}, all the winding current staying on the coil and none of it flowing through the core. Someone argues: ((a)) "No free current flows inside the core itself, so J=0\mathbf{J} = 0 there, hence ∇×H=0\nabla\times\mathbf{H} = 0 there, and ΦM\Phi_M may be used as an ordinary single-valued potential throughout the core with no cut needed." ((b)) "Across the cut that has to be made, ΦM\Phi_M jumps by NI=1000 ANI = 1000\,\mathrm{A}. Since H=−∇ΦM\mathbf{H} = -\nabla\Phi_M, a jump in ΦM\Phi_M means H\mathbf{H} itself jumps by a corresponding amount there." Identify the error in each claim, and state what is true instead in each case.

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