3-8. Electric flux density and dielectric constant

1

• 3-8. Electric flux density and dielectric
  constant
• Where the electric flux density (displacement)

Electric susceptibility
Relative permittivity (dielectric constant)
Absolute permittivity
2

• Example 3-12. Dielectric shell. Find and .
• Solution
• Make Gaussian surface
• rltri
• riltrltro
• rgtro
• The electric flux
• Regardless of r is in i or ii or iii
• However the E-field expressions are

rltri or rgtro
riltrltro
3

• 3-8.1 Dielectric strength
• Breakdown
• Transformer oil with air bubbles.
• Example 3-13 Two spherical conductors.
• Solution.
• a). From equal potential condition,
• or

4

• That
• b) The electric field at the sphere surfaces

5

• 3-9. Boundary conditions for electrostatic
  fields
• The tangential component of the E-field is
  continuous across the boundary
• E1tE2t
• Show.
• Apply
• In the integral form
• Where L is a narrow frame abcd.
• So that
• and

6

• The normal component of field is continuous
  across the interface, provided no surface charge
  exists.
• Show. Make a flat disk Gaussian surface
• Hence
• Special cases

7

• Example. Given a charge-free flat dielectric
  interface separating e15eo and e22eo. If
  find
• Solution
• Using boundary conditions
• Hence
• and

E2