Electromagnetic Field Theory

2nd Year EE Students

Prof. Dr. Magdi El-Saadawiwww.saadawi1.net

saadawi1@gmail.com

2014/2015

Chapter 3

Electrostatic Field Theorems

Chapter 3

Electrostatic Field Theorems 3.1. Introduction 3.2. Electric Field Intensity3.3. The Scalar Potential3.4. The electric flux density (Displacement flux density)3.5. Poisson and Laplace Equations3.6. Capacitance3.7. The Point Charge (Coulomb-and Superposition Law)3.8. The Dipole3.9. The Method of Images 3.10. The Homogeneous Field 3.11. The field of Two Arbitrary Point Charges 3.12. Applications on Image Theory3.13. Generalization of the Capacitance Conception 3.14. Energy in Electrostatic Fields3.15. Electrostatic Forces

3.11. The field of Two Arbitrary (unequal) Point Charges

• The equipotential surface Φ = 0 occurs when:

• This surface is found to be a sphere as follows:

3.11. The field of Two Arbitrary (unequal) Point Charges

• The general equation of a sphere of radius a and its

center at (x1, y1, z1) is:

3.11. The field of Two Arbitrary (unequal) Point Charges

• Thus

• The general equation of a sphere of radius a and its

center at (x1, y1, z1) is:

3.11. The field of Two Arbitrary (unequal) Point Charges

• Thus

3.11. The field of Two Arbitrary (unequal) Point Charges

3.11. The field of Two Arbitrary (unequal) Point Charges

Thus we got also with the help of image principle the

potential of a point charge q at a distance ζ from the

middle point of a conducting earthed sphere (Φ = 0),

whose radius a.

lf there is a forgiven charge of the sphere (the potential is not zero i.e. Φ = V ,

thus another point charge q" must be placed in the centre of the sphere which will produce the forgiven potential,

Potential of a point charge q at a distance ζ from the

middle point of a conducting sphere (Φ = V), whose

radius a.

we set two image charges + q' and - q‘, and replace the arrangement with the four charges to find Φ & E

Potential of Two equal point charges in front of an

earthed conducting sphere (Φ = 0), whose radius a.

For the homogeneous field:

Potential of Two equal point charges in front of an

earthed conducting sphere (Φ = 0), whose radius a.

For the dipole:

• Other than conductors in electric fields where an equipotential surface as a boundary condition is undertaken; the conditions to be fulfilled at the boundaries of multi-dielectric mediums are:

Et1 = Et2Dn1 = Dn2 ......... for ρs= 0

Φ1= Φ2.

3.12.1 The consideration of multi-dielectric mediums

• Example

3.12.1 The consideration of multi-dielectric mediums

• Example

3.12.1 The consideration of multi-dielectric mediums