where ρ ρ is the charge density, which is a function of time and position, ε ε 0 is the vacuum permittivity, μ μ 0 is the vacuum permeability, and J is the current density vector, also a function of time and position. Inside a linear material, Maxwell's equations change by switching the permeability and permittivity of free space with the permeability and permittivity of the linear material in question. Inside other materials which possess more complex responses to electromagnetic fields, these terms are often represented by complex numbers, or tensors.