For the limit R m ≪ 1 {\displaystyle R_{m}\ll 1} , the magnetic diffusion equation ∂ B → ∂ t = 1 μ 0 σ ∇ 2 B → {\displaystyle {\frac {\partial {\vec {B}}}{\partial t}}={\frac {1}{\mu _{0}\sigma }}\nabla ^{2}{\vec {B}}} is just a vector-valued form of the heat equation. For a localized initial magnetic field (e.g. Gaussian distribution) within a conducting material, the maxima and minima will asymptotically decay to a value consistent with Laplace's equation for the given boundary conditions. This behavior is illustrated in the figure below.