Elementary Vector Analysis

1
(No Transcript)
2
V
3
Gausss Law in differential form
4
(No Transcript)
5
.
6
(No Transcript)
7
(No Transcript)
8
(No Transcript)
9
(No Transcript)
10
(No Transcript)
11

• But this precisely the potential due to q
• At the center of the sphere.
• By the superposition principle for any collection
  of charges outside the sphere the
• Potential at the center of the sphere is equal
• to the their average potential over the
  surface of the sphere.

12
(No Transcript)
13

• Earnshaws theorem follows immediately
• i.e. A charged particle can not be held in
  equilbrium by electrostatic forces alone.

14
(No Transcript)
15
Question 6

16
(No Transcript)
17
Depends only on x
Depends only on y
18
(No Transcript)
19
(No Transcript)
20
Spherical Symmetry
Function of ? only
Function of r only
21
(No Transcript)
22
(No Transcript)
23
(No Transcript)
24

• An uncharged metal sphere of radius R is placed
  in a uniform field EEk. Find the potential in
  the region outside the sphere.

25
(No Transcript)
26
(No Transcript)
27
(No Transcript)
28
(No Transcript)
29

• Earnshaws theorem follows immediately
• i.e. A charged particle can not be held in
  equilbrium by electrostatic forces alone.

30
Electric dipole
31
(No Transcript)
32
(No Transcript)
33
A dipole in an electric field
34
The tendency of the electric field to align the
dipole moment with itself is confirmed by the
potential energy formula. The potential energy is
lowest when the dipole moment is aligned with the
field and highest when the two are anti-aligned.
35
Water is a polar molecule
36
Bonds between atoms

• Different types of bonds between atoms

37
(No Transcript)
38
An insulator

• Suppose we place a pitcher of water in a electric
  field
• As we have seen the water molecule is polar so
  the container looks like a random collection of
  dipoles.
• When the field is applied the dipoles will try to
  align themselves to oppose the field

39

• To do this hydrogen bonds need to be brokenthe
  stronger the field the more the dipoles can align

40
(No Transcript)
41

• Even for amolecule which is not naturally polar.
• The application of an electric field induces a
  polarization.

42
(No Transcript)
43
(No Transcript)
44
(No Transcript)
45

• A material which is not a conductor we will
  describe as a dielectric
• A pure insulator is a dielectric where there is
  no free charges

46
(No Transcript)
47
(No Transcript)
48

• For many materials the polarization is
  proportional to the field

49
(No Transcript)
50

51
Magnetostatics
52
(No Transcript)
53
(No Transcript)
54
(No Transcript)
55
(No Transcript)
56
(No Transcript)
57
(No Transcript)
58
(No Transcript)