chapter 03 part 6 ُem 2015
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Applications on Image TheoryTRANSCRIPT
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Electromagnetic Field Theory
2nd Year EE Students
Prof. Dr. Magdi El-Saadawiwww.saadawi1.net
2014/2015
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Chapter 3
Electrostatic Field Theorems
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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
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3.11. The field of Two Arbitrary (unequal) Point Charges
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• 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
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• 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
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• 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
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3.11. The field of Two Arbitrary (unequal) Point Charges
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3.11. The field of Two Arbitrary (unequal) Point Charges
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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.
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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.
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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.
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For the homogeneous field:
Potential of Two equal point charges in front of an
earthed conducting sphere (Φ = 0), whose radius a.
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For the dipole:
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• 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
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• Example
3.12.1 The consideration of multi-dielectric mediums
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• Example
3.12.1 The consideration of multi-dielectric mediums