# Solved Problem-1

Problem-1
Two extensive homogeneous isotropic dielectrics meet on the plane z = 0. For z â‰¥ 0,  and for z â‰¤ 0,  A uniform electric field,  kV/m exists for z â‰¥ 0. Find
(a)  for z â‰¤ 0
(b) The angles between electric field intensity and the normal to the boundary surface in both media
(c) The energy densities in J/m3 in both dielectrics
(d) The energy within a cube of 2 m side centred at (3, 4, -5)

Solution
(a) Since,  is the normal to the boundary plane, the normal component is,

Arrangement of dielectrics

By boundary conditions,
(1)

and,

(2)

So, the field in the second medium is given as,

(b) Let  and  be the angles  and  make with the interface while  and  are the angles they make with the normal to the interface.

Similarly,

Hence, the angles between electric field intensity and the normal to the boundary surface in both media are given as,

Note: The relation  is satisfied.

(c) The energy densities are given as,

(d) At the centre (3, 4, -5) of the cube of side 2 m, z = -5 < 0; i.e., the cube is in the region 2 with 2 â‰¤ x â‰¤ 4, 3 â‰¤ y â‰¤ 5, -6 â‰¤ z â‰¤ -4.

Hence, the energy within the cube is,