1. ELEC 3105 Lecture 1
Coulomb

3. Applied EM by Ulaby, Michielssen and Ravaioli
4. Electrostatics
Applied EM by Ulaby, Michielssen and Ravaioli

4. Chapter 4 Overview

5. Maxwell’s Equations
God said:
And there was light!

6. Current Density For a surface with any orientation:
J is called the current density

7. ELEC 3105 Lecture 1

8. Coulomb’s Law Electric field at point P due to single charge
Electric force on a test charge placed at P
Electric flux density D

11. Coulomb’s force law (point charges)q1 q2
[F]-force; Newtons {N}
[q]-charge; Coulomb {C}
[r]-distance; meters {m}
[]-permittivity; Farad/meter {F/m}
origin
Property of the medium

12. Coulomb’s force law (permittivity)
For a medium like air
Relative permittivity

13. Coulomb’s force law (permittivity)
FORCE IN MEDIUM SMALLER THAN FORCE IN VACUUM

14. Lecture 1 (ELEC 3105) Basic E&M and Power Engineering
Coulomb's Law
The force exerted by one point charge on another acts along the line joining the charges. It varies inversely as the square of the distance separating the charges and is proportional to the product of the charges. The force is repulsive if the charges have the same sign and attractive if the charges have opposite signs.
Action at a distance

17. Electric Field Due to 2 Charges
Example of (4.18) next

18. Electric Field due to Multiple Charges

19. Electric field (charge distribution)q1 q3 qi z P q2 q4 qN y
Large number N
of point charges x q5

20. PRINCIPLE OF SUPERPOSITION
Given a group of charges we find the net electric field at any point in space by using the principle of superposition. This is a general principle that says a net effect is the sum of the individual effects. Here, the principle means that we first compute the electric field at the point in space due to each of the charges, in turn. We then find the net electric field by adding these electric fields vectorially, as usual.

21. Charge Distributions Volume charge density: Total Charge in a Volume
Surface and Line Charge Densities

22. Electric Field Due to Charge Distributions

23. Electric field (charge distribution)
Charge always occurs in integer multiples of the electric charge e = 1.6X10-19C.
Charged volume q
Charged surface
It is often useful to imagine that there is a continuous distribution of charge
Charged line

24. Electric field (charge distribution)P
Charge volume element dV q
Volume charge density
Units; {C/m3 }
Charged volume
Charge in dV
The electric field at the point P is obtained by summing the electric field contribution from from each volume element dV.
When the volume element
dV--> 0
Sum --> Integral

25. Electric field (charge distribution)P
Field for one element V
Charged volume
With
Integration over
volume V

26. Electric field (charge distribution)
V may be a function of the coordinates
usually a constant
unit vector
function of (x,y,z),….
usually a constant when medium is uniform

27. Electric field (charge distribution)P
Charge surface element dS dS
Surface charge density q
Units; {C/m2}
Charged surface
Charge on dS
The electric field produced at the point P is:

28. Electric field (charge distribution)
s may be a function of the coordinates
usually a constant
unit vector
function of (x,y,z),….
usually a constant when medium is uniform

29. Electric field (charge distribution)P
Charged line element d
Linear charge density q
Units; {C/m}
Charged line
Charge on
The electric field produced at the point P is:

30. Electric field (charge distribution)
may be a function of the coordinates
usually a constant
unit vector
function of (x,y,z),….
usually a constant when medium is uniform

31. Cont.

33. Cont.

34. Example 4-5 cont.