1. Electric Forces and Electric Fields
Chapter 15
Electric Forces and
Electric Fields

2. Unfinished business… < 106 < 1012 < 1018 < 1024 < 1030
How many electrons? M=357.2g C12H22O11
< 106
< 1012
< 1018
< 1024
< 1030
< 1036
< 1042

3. Unfinished business… < 1025 < 1026 < 1027 < 1028 < 1029
How many electrons? m=357.2g C12H22O11
< 1025
< 1026
< 1027
< 1028
< 1029
< 1030

4. Unfinished business… How many electrons? M=357.2g C12H22O11
< 1x1026
< 2x1026
< 3x1026
< 4x1026
< 5x1026
< 6x1026
< 7x1026
< 8x1026
< 9x1026
< 1.0x1027

5. Unfinished business… How many electrons? M=357.2g C12H22O11
< 1.1x1026
< 1.2x1026
< 1.3x1026
< 1.4x1026
< 1.5x1026
< 1.6x1026
< 1.7x1026
< 1.8x1026
< 1.9x1026
< 2.0x1026

6. Quiz: Which quantity is not always conserved?
Charge
Energy
Mass
Momentum

7. Review Electric Charge Methods of charging objects Coulomb’s Law
Two types: + (proton), - (electron), same magnitude
SI Unit of charge: Coulomb (huge!) 1C = 1A1s
Charge is conserved (but not mass!)
Charge is quantized in multiples of e = 1.6x10-19 C
Methods of charging objects
Friction, Conduction, Induction, Polarization, Grounding
Coulomb’s Law
Opposite charges attract; like charges repel.
Force proportional to both charges
and the inverse square of separation
Comparison with gravity
Superposition principle

8. Electric Fields Sections 4 – 6

9. Electrical Field
Michael Faraday (1791 – 1867) developed an approach to discussing fields
An electric field is said to exist in the region of space around a charged object
When another charged object enters this electric field, the field exerts a force on the second charged object

10. Action at a Distance Contact forces Field forces
Local: force transmitted by touching
Field forces
Action at a distance – no touching
Eg. Gravity and Electricity
Actually all fundamental forces!
Can think of field as producing a local force
But or course the field is created at a distance

11. Electric Field, cont.
Coulomb’s law is symmetric for the two charges; let’s break it up
A charged particle, with charge Q, produces an electric field in the region of space around it
A small test charge, qo, placed in the field, will experience a force from the electric field
Why must q0 be small?
field
MU28T11-12: Electric Force Field

12. Electric Field Definition
Mathematically,
SI units are N / C
The electric field is a vector quantity
The direction of the field is defined to be the direction of the electric force that would be exerted on a small positive test charge placed at that point

13. Electric Field due to a Positive Spherical or Point Charge
The electric field produced by a positive charge is directed away from the charge
A positive test charge would be repelled from the positive source charge
The magnitude of the electric field produced by the positive charge is

14. Electric Field due to a Negative Spherical or Point Charge
The electric field produced by a negative charge is directed toward the charge
A positive test charge would be attracted to the negative source charge
The magnitude of the electric field produced by the negative charge is
Active Figure: The Small Positive Test Charge

15. More About a Test Charge and The Electric Field
The test charge is required to be a small charge
It can cause no rearrangement of the charges on the source charge
The electric field exists whether or not there is a test charge present
The Superposition Principle can be applied to the electric field if a group of charges is present

16. Are Electric Fields Real?
Why bother with fields instead of just using the force?
The only way to measure it is to putting a test charge in the field
Then you are back to Coulomb’s law!
If a tree falls in the forest, and no one hears it…?
However: the concept of field will be extremely useful in understanding later chapters
Electric fields can generate magnetic fields and vice versa. (not just created by charge)
Electric and Magnetic fields are the medium of light waves (waves are the ripples of E&M fields)

17. Problem Solving Strategy, Electric Fields
Calculate Electric Fields of point charges
Use the equation to find the electric field due to the individual charges
The direction is given by the direction of the force on a positive test charge
The Superposition Principle can be applied if more than one charge is present
EX15.5

18. Electric Field Lines
A convenient aid for visualizing electric field patterns is to draw lines pointing in the direction of the field vector at any point
These are called electric field lines and were introduced by Michael Faraday

19. Electric Field Lines, cont.
The field lines are related to the field in the following manners:
The electric field vector, , is tangent to the electric field lines at each point
The number of lines per unit area through a surface perpendicular to the lines is proportional to the strength of the electric field in a given region
MU28T14: Electric Field Lines

20. Electric Field Line Patterns
Point charge
The lines radiate equally in all directions
For a positive source charge, the lines will radiate outward
For a negative source charge, the lines will point inward

21. Electric Field Line Patterns
An electric dipole consists of two equal and opposite charges
The high density of lines between the charges indicates the strong electric field in this region

22. Electric Field Line Patterns
Two equal but like point charges
The bulging out of the field lines between the charges indicates the repulsion between the charges
The low field lines between the charges indicates a weak field in this region

23. Electric Field Patterns
Unequal and unlike charges
Note that two lines leave the +2q charge for each line that terminates on -q
Active Figure: Electric Field Lines

24. Rules for Drawing Electric Field Lines
The lines for a group of charges must begin on positive charges and end on negative charges
In the case of an excess of charge, some lines will begin or end infinitely far away
The number of lines drawn leaving a positive charge or ending on a negative charge is proportional to the magnitude of the charge
No two field lines can cross each other

25. Atmospheric Electric Fields
The electric field near the surface of the Earth in fair weather is about 100 N/C downward
Under a thundercloud, the electric field can very large, on the order of 20,000 N/C
A device for measuring these fields is called the field mill

26. Conductors in Electrostatic Equilibrium
When no net motion of charge occurs within a conductor, the conductor is said to be in electrostatic equilibrium
An isolated conductor in electrostatic equilibrium has four important properties

27. Property 1
The electric field is zero everywhere inside the conducting material
Consider if this were not true
If there were an electric field inside the conductor, the free charge there would move and there would be a flow of charge
If there were a movement of charge, the conductor would not be in equilibrium

28. Property 2
Any excess charge on an isolated conductor resides entirely on its surface
A direct result of the 1/r2 repulsion between like charges in Coulomb’s Law
If some excess of charge could be placed inside the conductor, the repulsive forces would push them as far apart as possible, causing them to migrate to the surface

29. Property 3
The electric field just outside a charged conductor is perpendicular to the conductor’s surface
Consider what would happen it this was not true
The component along the surface would cause the charge to move
It would not be in equilibrium

30. Quiz: what is the best shape for a lightning rod?.. 1. 2. 3. 4.

31. Property 4
On an irregularly shaped conductor, the charge accumulates at locations where the radius of curvature of the surface is smallest (that is, at sharp points)
Why a lightning rod works

32. Experiment to Verify Properties of Charges
Faraday’s Ice-Pail Experiment
A charged object suspended inside a metal container causes a rearrangement of charge on the container in such a manner that the sign of the charge on the inside surface of the container is opposite the sign of the charge on the suspended object
Any charge transferred to a conductor resides on its surface in electrostatic equilibrium