In a non-magnetic material with no free charges and no free currents, the permittivity ϵ is a function of position. If \(\vec{E}\) represents the electric field and μ0, ϵ0 are free space permeability and permittivity respectively, which one of the following expressions is correct?
1
\(\nabla^2 \vec{E}-μ_0 \frac{\partial^2(ϵ \vec{E})}{\partial t^2}-\frac{1}{ϵ_0} \vec{\nabla}(\vec{E} \cdot \vec{\nabla} ϵ)=0\)
2
\(\nabla^2 \vec{E}-μ_0 \frac{\partial^2(ϵ \vec{E})}{\partial t^2}+\frac{1}{ϵ_0} \vec{\nabla}(\vec{E} \cdot \vec{\nabla} ϵ)=0\)
3
\(\nabla^2 \vec{E}-μ_0 \frac{\partial^2(ϵ \vec{E})}{\partial t^2}+\vec{\nabla}\left(\frac{1}{ϵ} \vec{E} \cdot \vec{\nabla} ϵ\right)=0 \ \)
4
\(\nabla^2 \vec{E}-μ_0 \frac{\partial^2(ϵ \vec{E})}{\partial t^2}-\vec{\nabla}\left(\frac{1}{ϵ} \vec{E} \cdot \vec{\nabla} ϵ\right)=0 \ \)