Question

An inhomogeneous medium is the one where the permittivity (ϵ) depends on the position (x,y,z). Obtain ∇⋅ E for such a medium with a volume charge density rho(x,y,z).

Answer 1

To obtain ∇⋅E for an inhomogeneous medium with a volume charge density ρ(x,y,z), use Gauss's Law in differential form: ∇⋅E = ρ/ε, where ε is the permittivity that depends on the position.

Step-by-step explanation:

To obtain ∇⋅E for an inhomogeneous medium with a volume charge density ρ(x,y,z), we can use Gauss's Law in differential form:

∇⋅E = ρ/ε

Where ∇⋅E is the divergence of the electric field, ρ is the volume charge density, and ε is the permittivity.

In this case, since the permittivity ε depends on the position (x,y,z), we can write it as ε(x,y,z).

Therefore, the final expression for ∇⋅E is:

∇⋅E = ρ(x,y,z)/ε(x,y,z)