A uniform magnetic field

PHYSICS · Subjective · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Magnetostatics · Magnetostatics

The Boundary-Value Problem, Ch The vector potential and the magnetostatic boundary-value problem

Problem

A uniform magnetic field B=B0x^\mathbf{B}=B_0\hat{\mathbf{x}}, with B0=0.60 TB_0=0.60\,\mathrm{T}, fills some region. Someone proposes the vector potential A=B0z y^\mathbf{A}=B_0z\,\hat{\mathbf{y}} and asserts that ∇×A=B0x^\nabla\times\mathbf{A}=B_0\hat{\mathbf{x}}. Compute ∇×A\nabla\times\mathbf{A} directly, find the error, and give a vector potential that is actually correct for this field.

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