Question

State the general solution of Maxwell's equations for the scalar potential V(n,t) and vektorpotential A(r,t) in terms of sources, and include the source-freeterms.

Answer 1

The general solution of Maxwell's equations for the scalar potential V(n,t) and vector potential A(r,t) in terms of sources is expressed using appropriate Green's functions. The solution includes the source-free terms where there are no charges or currents present.

Step-by-step explanation:

To obtain the general solution of Maxwell's equations for the scalar potential V(n,t) and vector potential A(r,t) in terms of sources, we use the appropriate Green's function that relates the sources to the potentials. The solution can be expressed as:

V(n,t) = ∫G(n,n',t')ρ(n',t')d³n'

A(r,t) = ∫G(r,r',t')(J(r',t')/c)d³r'

Here, ρ(n',t') is the charge density, J(r',t') is the current density, G(n,n',t') and G(r,r',t') are the Green's functions for the scalar and vector potentials, respectively, and c is the speed of light.

The source-free terms correspond to the case when there are no charges or currents present, and are given by V(n,t) = 0 and A(r,t) = 0 respectively.