Question

For static electric and magnetic fields in an inhomogeneous source-free medium, which of the following represents the correct form of two of Maxwell's equations?

• A. $\nabla \cdot \overrightarrow{E}=0$ $\nabla \times \overrightarrow{B}=0$
• B. $\nabla \cdot \overrightarrow{E}=0$ $\nabla \cdot \overrightarrow{B}=0$
• C. $\nabla \times \overrightarrow{E}=0$ $\nabla \times \overrightarrow{B}=0$
• D. $\nabla \times \overrightarrow{E}=0$ $\nabla \cdot \overrightarrow{B}=0$

Answer 1

The correct option is D

$\nabla \times \overrightarrow{E}=0$

$\nabla \cdot \overrightarrow{B}=0$

Ans : (d)
This is order of understanding Maxwell's equations.
For any material

$\nabla \times E=\frac{\partial B}{\partial t}\nabla \cdot B=0$

$\nabla \times H=J+\frac{\partial D}{\partial t}\nabla \cdot D={\rho }_v$
For source free like charge or current free conditions

$\nabla \times E=0\nabla \cdot B=0$

$\nabla \times H=0\nabla \cdot D=0$

If $D=\in EandB=\mu Hand\in or\mu$ are constant with distance or direction then

$\nabla \cdot (\in E)=0\nabla \times \frac{B}{\mu }=0$

$\nabla \cdot E=0\nabla \times B=0$

These are called as homogeneous/isotropic medium.
For non-homogeneous material. However they are not valid.