1. Physics 014
Electric fields 1

2. Topics Electric Field Electric Field Lines
Electric Fields due to points, dipoles, etc.

3. Electric Field
How do we deal with action at a distance?

4. Electric Field
Using a vector field, we can describe action at a distance near a charged object:

6. Electric Field
We define the electric field, at point P due to the charged object as

7. Electric Field
The force on a test charge q0 DUE to an external field is

8. Electric Field
Using a vector field, we can describe action at a distance near a charged object:
Place a positive test charge q0 near the object at point P
Measure the electrostatic force acting on the charge:

9. Electric Field The magnitude of the electric field is E=F/q0
The SI unit for electric field is newton per coulomb (N/C)

10. Electric Field Lines
Electric field lines are a useful visual way of picturing electric fields

11. Electric Field Lines
At any point, the direction of a straight field line gives the direction of the electric field at that point

13. Electric Field Lines
At any point, the direction of the tangent to curved lines gives the direction of the electric field at that point.

15. Electric Field Lines
Electric field lines extend away from positive charge (where they originate) and toward negative charges (where they terminate)

17. Electric Field Lines The electric field is:
large where field lines are close together
small where they are apart

19. E due to a point charge
The magnitude of the electric field due to a point charge is

20. E due to a point charge F is from Coulomb’s law
The vector points away from the point charge, q, if q is positive
The vector points toward the point charge, q, if q is negative

22. E due to a point charge
For a test charge near n point charges, the net electric field at the position of the test charge is

23. ???
For a proton p and an electron e on an x axis, what is the direction of the electric field due to the electron at (a) point S and (b) point R? What is the direction of the net electric field at (c) point R and (d) point S?

24. E due to a point charge
Example: The diagram shows three particles with charges q1=+2Q, q2=2Q, and q3=-4Q, each a distance d from the origin. What net electric field is produced at the origin?

26. Given: Eqn:
q1=+2Q
q2=-2Q
q3=-4Q
= ?

27. Calc:
First we will find the fields due to the individual charges, the we will do a vector sum to find the net electric field.

29. Calc:
Now we do a vector sum for the net electric field

30. Calc:
There is an easy way to do the vector sum. Use symmetry. Notice that E1 +E2 equals the magnitude E3. In addition, from the diagram we see that and are symmetric about the x axis; their y components cancel

32. Calc:
By symmetry,