1. Electric field Chapter 22
Week-2

2. (22-1)
Electric Fields
In this chapter we will introduce the concept of an electric field As long as charges are stationary Coulomb’s law described adequately the forces among charges. If the charges are not stationary we must use an alternative approach by introducing the electric field (symbol ). In connection with the electric field, the following topics will be covered:
-Calculate the electric field generated by a point charge.
-Using the principle of superposition determine the electric field created by a collection of point charges as well as continuous charge distributions.
-Once the electric field at a point P is known we will be calculate the electric force on any charge placed at P Define the notion of an “electric dipole”. Determine the net force , the net torque, exerted on an electric dipole by a uniform electric field, as well as the dipole potential energy.

3. Fields Imagine an object is placed at a particular point in space.
When placed there, the object experiences a force F.
We may not know WHY there is a force on the object, although we usually will.
Suppose further that if we double some property of the object (mass, charge, …) then the force is found to double as well.
Then the object is said to be in a force field.
The strength of the field (field strength) is defined as the ratio of the force to the property that we are dealing with.

4. Electric Field
If a charge Q is in an electric field E then it will experience a force F.
The Electric Field is defined as the force per unit charge at the point.
Electric fields are caused by charges and consequently we can use Coulombs law to calculate it.
For multiple charges, add the fields as VECTORS.

5. Two Charges

6. to know the Electric Field
Doing it Q
A Charge r F q
The spot where we want
to know the Electric Field

7. General-

8. Force  Field

10. q qo r P
(22-4)

11. O O
(22-5)

12. What is the electric field at the center of the square array?
Superposition and Symmetry

13. d
+ q
- q
(22-6) -q
+q/2

14. << =
(22-7)

15. Kinds of continuously distributed charges
Line of charge
l = the charge per unit length.
dq= lds (ds= differential of length along the line)
Area
s = charge per unit area
dq=sdA
dA = dxdy (rectangular coordinates)
dA= 2prdr for elemental ring of charge
Volume
r=charge per unit volume
dq=rdV
dV=dxdydz or 4pr2dr or some other expressions we will look at later.

16. Continuous Charge Distribution

17. Symmetry

18. Let’s Do it Real Time
Concept – Charge per
unit length 
dq=  ds

19. The math
Why?

20. C A dq
(22-9)

21. The Geometry (the disk)
Define surface charge density
s=charge/unit-area
dq=sdA
(z2+r2)1/2
dA=2prdr
dq=s dA = 2psrdr

22. (z2+r2)1/2 q

23. Final Result
(z2+r2)1/2

24. q q
(22-11)

25. (22-13)

26. Look at the “Field Lines”

27. F+ F-
x-axis
(22-14)

28. A B  U
180˚
(22-15)

29. Fig.a
Fig.b
(22-16)

30. What did we learn in this chapter??
We introduced the concept of the Electric FIELD.
We may not know what causes the field. (The evil Emperor Ming)
If we know where all the charges are we can CALCULATE E.
E is a VECTOR.
The equation for E is the same as for the force on a charge from Coulomb’s Law but divided by the “q of the test charge”.

31. What else did we learn in this chapter?
We introduced continuous distributions of charge rather than individual discrete charges.
Instead of adding the individual charges we must INTEGRATE the (dq)s.
There are three kinds of continuously distributed charges.

32. Kinds of continuously distributed charges
Line of charge
l = the charge per unit length.
dq= lds (ds= differential of length along the line)
Area
s = charge per unit area
dq=sdA
dA = dxdy (rectangular coordinates)
dA= 2prdr for elemental ring of charge
Volume
r=charge per unit volume
dq=rdV
dV=dxdydz or 4pr2dr or some other expressions we will look at later.

33. dq=rdV=r x surface area x thickness
The Sphere dq
thk=dr
dq=rdV=r x surface area x thickness
=r 4pr2 dr

34. Summary (Note: I left off the unit vectors in the last
equation set, but be aware that they should
be there.)

35. To be remembered … REMEMBER THIS !
If the ELECTRIC FIELD at a point is E, then
E=F/q (This is the definition!)
Using some advanced mathematics we can derive from this equation, the fact that:
REMEMBER THIS !