A.1
A.2
A
Derivations in electrodynamics
The Maxwell equations
The four Maxwell equations couple the electric and magnetic fields to their sources, i.e.
electric charges and current densities, and to each other. They are given by
where r and t denote location and time, respectively. D is the electric displacement, E the
electric field, B the magnetic induction and H the magnetic field.
1 ρ F is the free charge
density and J F is the free current density.
The electric displacement and field are related to each other via
where ∈ is the relative permittivity of the medium in which the fields are observed and ∈ 0
= 8.854 × 10
−12
As/(Vm) is the permittivity in vacuo. Similarly, the magnetic field and
induction are related to each other via
where µ is the relative permeability of the medium in which the fields are observed and µ 0
= 4π × 10
−7
Vs/(Am) is the permeability of vacuum. Equations (A.2) are only valid if the
medium is isotropic, i.e. ∈ and µ are independent of the direction. We may assume all the
important materials for solar cells to be non-magnetic, i.e. µ ≡ 1.
Derivation of the electromagnetic wave
equation
We now derive the electromagnetic wave equations in source-free space, ρ F ≡ 0 and j F ≡ 0.
For the derivation of the electromagnetic wave equations we start by applying the rotation
operator ∇ × to the second Maxwell equation, Eq. (A.1b),
A.2
A
Derivations in electrodynamics
The Maxwell equations
The four Maxwell equations couple the electric and magnetic fields to their sources, i.e.
electric charges and current densities, and to each other. They are given by
where r and t denote location and time, respectively. D is the electric displacement, E the
electric field, B the magnetic induction and H the magnetic field.
1 ρ F is the free charge
density and J F is the free current density.
The electric displacement and field are related to each other via
where ∈ is the relative permittivity of the medium in which the fields are observed and ∈ 0
= 8.854 × 10
−12
As/(Vm) is the permittivity in vacuo. Similarly, the magnetic field and
induction are related to each other via
where µ is the relative permeability of the medium in which the fields are observed and µ 0
= 4π × 10
−7
Vs/(Am) is the permeability of vacuum. Equations (A.2) are only valid if the
medium is isotropic, i.e. ∈ and µ are independent of the direction. We may assume all the
important materials for solar cells to be non-magnetic, i.e. µ ≡ 1.
Derivation of the electromagnetic wave
equation
We now derive the electromagnetic wave equations in source-free space, ρ F ≡ 0 and j F ≡ 0.
For the derivation of the electromagnetic wave equations we start by applying the rotation
operator ∇ × to the second Maxwell equation, Eq. (A.1b),