# Solved Problem-1

Problem-1

Two extensive homogeneous isotropic dielectrics meet on the plane

(a) for

(b) The angles between electric field intensity and the normal to the boundary surface in both media

(c) The energy densities in J/m

(d) The energy within a cube of 2 m side centred at (3, 4, -5)

*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/m

^{3}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,

(c) The energy densities are given as,

(d) At the centre (3, 4, -5) of the cube of side 2 m,
Hence, the energy within the cube is,

(1)

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

**Note:**The relation is satisfied.(c) The energy densities are given as,

*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.