1. Chapter 18: Electric Forces and Fields
Charges
The electric force
The electric field
Electric flux and Gauss’s Law

2. Charges
Thales of Miletus, ~ 600 B.C.: a piece of amber, rubbed against fur, attracted bits of straw
“elektron” – Greek for “amber”

3. Charges electric charge: an intrinsic property of matter
two kinds: positive and negative
net charge: more of one kind than the other
neutral: equal amounts of both kinds

4. Charges
charge is quantized: comes in integer multiples of a fundamental (“elementary”) charge
SI unit of charge: the coulomb
symbol: C
Size of elementary charge: 1.60×10-19 C
Elementary charge: often written as “e”

5. Charges Charge is a conserved quantity.
If a system is isolated, its net charge is constant.
Charges exert forces on each other, without touching.
Attraction if charges are unlike (opposite sign)
Repulsion if charges are like (same sign)

6. Charges Motion of charges Conductors: Insulators:
Charges can move freely on the surface or through the material – loosely bound valence electrons
Typically: metals
Insulators:
Little movement of charge on or through the material
Electrons are tightly bound
Typically: rubber, plastic, glass, etc.

7. Charges Separation of charges
Sometimes possible by mechanical work (friction)
Example: friction between hard rubber and fur or hair
electrons leave the fur and go to the rubber
rubber acquires a net negative charge
fur acquires a net positive charge
net charge of total system remains zero

8. Charges Transfer of charge By contact By induction
Objects touch – net charge moves from one to the other
By induction
Charged object brought near to another object
Like charges driven from second object through path to earth
Path to earth taken away
Original charged object withdrawn: opposite net charge remains on second object

9. The Electric Force Studied systematically by Charles-Augustin Coulomb
French natural philosopher,

10. The Electric Force: Coulomb’s Law
Attractive or repulsive – like or unlike charges
Magnitude:
Constant of proportionality:
magnitudes of charges
constant of proportionality
distance between charges

11. The Electric Force: Coulomb’s Law
Coulomb’s Law (electric force)
Newton’s Law of Universal Gravitation (gravitational force)

12. The Electric Field
Field: the mapping of a physical quantity onto points in space
Example: the earth’s gravitational field maps a force per unit mass (acceleration) onto every point
Electric field: maps a force per unit charge onto points in the vicinity of a charge or charge distribution

13. The Electric Field
Place a test charge q0 at a point a distance r from a charge q

14. The Electric Field
Use Coulomb’s Law to calculate the force exerted on the test charge:

15. The Electric Field
Divide the electric force by the magnitude of the test charge:

16. The Electric Field
Take away the test charge and define the quantity E as the ratio F/q0:

17. The Electric Field
We calculated the magnitude of E, in terms of the magnitude of F :
Both E and F are vectors. For a positive test charge, E points in the same direction as F.
E always has the same direction as the electric force on a positive charge (opposite direction from the force on a negative charge).

18. The Electric Field
The electric field is “set up” in space by a charge or distribution of charges
The electric field produces an electric force on a net charge q1 :
If more than one charge is present, each charge produces an electric field vector at a given point in space. These vectors add according to the usual vector rules.

19. The Electric Field Parallel-Plate Capacitor two conducting plates
each has area A
each has net charge q (one +, one -)
electric field magnitude between plates:
(where e0 is the permittivity of free space)
field points from + plate to - plate

20. The Electric Field: Field Lines
Electric Field Lines
Directed lines (curves, in general) that start at a positively-charged object and end at a negatively-charged one
Field lines are drawn so that the electric field vector is locally tangent to the field line

21. The Electric Field in Conductors
A net charge in a conducting object will move to the surface and spread out uniformly
mutual repulsive forces make the charges “want” to get as far from each other as possible
In the steady state, the electric field inside a conducting object is zero
because the charges in a conductor are free to move, if there is an electric field, the charges will move to a distribution in which the electric field is reduced to zero

22. The Electric Field in Conductors
Example: a conducting sphere is placed in a region where there is an electric field
Initially, the field is present inside the sphere

23. The Electric Field in Conductors
The field causes the charges to separate, and
the separated charges produce their own field.

24. The Electric Field in Conductors
The motion continues until the “internal” field
is equal and opposite to the “external” one …

25. The Electric Field in Conductors
… and their sum is zero.

26. Electric Flux We define a quantity associated with the electric field:
SI unit of electric flux: Nm2/C
electric flux
area
angle between electric field vector and surface normal

27. Electric Flux
Consider a positive charge q … what is the electric field at a spherical surface centered on the charge and a distance r from it?

28. Electric Flux Rearrange and substitute for the area of a sphere:
Note that the left side is the electric flux through the spherical surface. Since the field vectors are radial, f = 0° everywhere.

29. Electric Flux: Gauss’ Law
Johann Carl Friedrich Gauss
German mathematician – 1855
Mathematics, astronomy, electricity and magnetism

30. Electric Flux: Gauss’ Law
Our result for the sphere enclosing the charge q :
is a statement of Gauss’ Law for a spherical surface, where f is everywhere zero (the electric field vector is everywhere perpendicular to the surface).
The sphere is an example of a Gaussian (closed) surface.

31. Electric Flux: Gauss’ Law
In general, a Gaussian surface is any surface that continuously encloses a volume of space. Such a closed surface wraps continuously around the volume.
Think of a water balloon, hanging over your palm, assuming some strange, arbitrary shape.

32. Electric Flux: Gauss’ Law
Here is an arbitrary Gaussian surface, containing an arbitrarily-distributed net charge Q :
This is the general form of Gauss’ Law.

33. Gauss’ Law: Application
Calculating the electric field inside a parallel-plate capacitor
charge q, spread uniformly over
plate area A
Gaussian cylinder radius = r
Flux through surfaces 1 and 2 zero

34. Gauss’ Law: Application
Calculating the electric field inside a parallel-plate capacitor
Flux through surface 3:
Net charge enclosed in cylinder:
Flux according to Gauss’ Law:

35. Gauss’ Law: Application
Calculating the electric field inside a parallel-plate capacitor
Equate the two expressions for
and solve for E :
Sometimes is defined as a
“charge density”:
Then: