Fields in homogeneous, isotropic materials

Electric field stress analysis in homogeneous, isotropic materials :

• Consider a parallel conducting plate with infinitely large plates, due to this nullify the field distrortion effect at the edges of the plate and assume uniform field as shown in figure.

• The potential difference between the plates depends on the cross section of the plates,
• Suppose co-ordinates of this cross section are 

         

• We hae

                                                 ... (1)

                                              ... (2)

• Take a laplace of equation (1)

                             ... (3)

• The laplace equation (3) in certain co-ordinates for this are reduces to,

                                                     ... (4)

• Simplification of this equation is,

       

• From the figure,

       

• Now, potential distribution is given by,

                                    ... (5)

• Then, field intensity or electric stress is find by field varying in only one direction.

        

                        ... (6)

• So, the magnitude of electric field stress in the dielectric is constant all over the space in between two conducting plates and the voltage or potential varies linearly in the gap, as shown in figure.