Introduction to Electrodynamics · Problem 5.25

Magnetic Fields in Matter — David J. Griffiths

Physics · magnetic-vector-potential

Problem

If B\mathbf{B} is uniform, show that A(r)=−12(r×B)\mathbf{A}(\mathbf{r}) = -\frac{1}{2}(\mathbf{r} \times \mathbf{B}) works. That is, check that ∇⋅A=0\nabla \cdot \mathbf{A} = 0 and ∇×A=B\nabla \times \mathbf{A} = \mathbf{B}. Is this result unique, or are there other functions with the same divergence and curl?

Related theory

Browse the problem library