9 Magnetic Field
With \(J = 0\) (since \(b_0 = 0\)), \(\nabla \times B = 0\). Combined with \(\nabla \cdot B = 0\) and the torus axiom that curl-free div-free fields are harmonic (hence constant): \(\exists B_0,\, \forall x,\, B(x) = B_0\).
With \(J = 0\) (since \(b_0 = 0\)), \(\nabla \times B = 0\). Combined with \(\nabla \cdot B = 0\) and the torus axiom that curl-free div-free fields are harmonic (hence constant): \(\exists B_0,\, \forall x,\, B(x) = B_0\).