### Solved Example:

#### 9993-01

The Maxwell’s equation, $\nabla \times \overline{H} = \overline{J} + \dfrac{\partial \overline{D}}{\partial t}$ is based on: (GATE ECE 1998)

Solution:

Ampere’s law states that the magneto motive force around a closed path is equal to the current enclosed by the path,

For steady electric fields, $\oint \overline{H} \cdot \overline{dl} = I = \int \bar{J} \cdot \bar{da}$

$\overline{J} = \bar{\sigma E}$ is the conduction Current density (amp/m$^2$)

For time – varying electric fields:

$\oint \overline{H} \cdot \overline{dl} = \int ({\overline{J} + \overline{J_d}}) \cdot \overline{d_a}$

Where $\overline{J_d}$ is the displacement current density $\dfrac{\partial \overline{D}}{\partial t}$

By Stroke’s theorem $\oint \overline{H} \cdot \overline{dl} = \iint (\nabla \times \overline{H}) \cdot \overline{da}$

So $\nabla \times \overline{H} = \overline{J} + \dfrac{\partial \overline{D}}{\partial t}$

$\overline{J} + \dfrac{\partial \overline{D}}{\partial t}$ is the total current density (Conduction current density + displacement current density)

### Solved Example:

#### 9993-02

Maxwell's equation in ______ form gives information at points of discontinuity is electromagnetic field. (UPPSC Polytechnic Lecturer Electrical Nov 2021 Paper I)