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1Electrostatics: Dielectric Breakdown, Electrostatic Boundary Conditions 2Dielectric BreakdownIf a dielectric material is placed in a very strong electric field, electrons can be torn from their corresponding nuclei causing large currents to flow and damaging the material. This phenomenon is called dielectric breakdown.3Dielectric Breakdown (Contd)The value of the electric field at which dielectric breakdown occurs is called the dielectric strength of the material.The dielectric strength of a material is denoted by the symbol EBR.4Fundamental Laws of Electrostatics in Integral Form

Conservative fieldGausss lawConstitutive relation5Fundamental Laws of Electrostatics in Differential Form

Conservative fieldGausss lawConstitutive relation6Fundamental Laws of ElectrostaticsThe integral forms of the fundamental laws are more general because they apply over regions of space. The differential forms are only valid at a point.From the integral forms of the fundamental laws both the differential equations governing the field within a medium and the boundary conditions at the interface between two media can be derived.7Boundary ConditionsWithin a homogeneous medium, there are no abrupt changes in E or D. However, at the interface between two different media (having two different values of e), it is obvious that one or both of these must change abruptly.8Boundary Conditions (Contd)To derive the boundary conditions on the normal and tangential field conditions, we shall apply the integral form of the two fundamental laws to an infinitesimally small region that lies partially in one medium and partially in the other.9Boundary Conditions (Contd)Consider two semi-infinite media separated by a boundary. A surface charge may exist at the interface.Medium 1Medium 2xxxxrs10Boundary Conditions (Contd)Locally, the boundary will look planar

x x x x x xrs11Boundary Condition on Normal Component of D Consider an infinitesimal cylinder (pillbox) with cross-sectional area Ds and height Dh lying half in medium 1 and half in medium 2:

DsDh/2Dh/2x x x x x xrs

12Boundary Condition on Normal Component of D (Contd)Applying Gausss law to the pillbox, we have

013Boundary Condition on Normal Component of D (Contd)The boundary condition is

If there is no surface charge

For non-conductingmaterials, rs = 0 unlessan impressed source ispresent.14Boundary Condition on Tangential Component of E Consider an infinitesimal path abcd with width Dw and height Dh lying half in medium 1 and half in medium 2:

Dh/2Dh/2Dwabcd15Boundary Condition on Tangential Component of E (Contd)

abcd

16Boundary Condition on Tangential Component of E (Contd)Applying conservative law to the path, we have

17The boundary condition is

Boundary Condition on Tangential Component of E (Contd)Boundary condition for tangential component of E : perform a line integral ( ). (fig. 3-16)

The tangential component of an E field is continuous across an interface.

Boundary conditions for electrostatic fields

Boundary condition for normal component of D : Apply Gausss law ( ).

The normal component of D field is discontinuous across an interface where a surface charge exists-the amount of discontinuity being equal to the surface charge density.

Boundary conditions for electrostatic fields

If medium 2 is a conductor, D2=0 and

When no free charges at the interface,

Boundary conditions for electrostatic fields

Normal component:Tangential component:

Electric flux density inside the lucite sheet : boundary condition at the left interface(no free charges).

Electric field intensity inside the lucite sheet :

Polarization vector inside the sheet :

ExampleA lucite sheet (r=3.2) is introduced perpendicularly in a uniform electric field E0 =axE0 in free space. Determine Ei, Di, and Pi inside the lucite.

ExampleTwo dielectric media with permittivities 1 and 2 are separated by a charge free boundary. The electric field intensity in medium 1 at the point P1 has a magnitude E1 and makes an angle a1 with the normal. Determine the magnitude and direction of the electric field intensity at point P2 in medium 2. Boundary conditions at the interface between two dielectric media :

Direction :

Magnitude :

and