Transcript Lecture 3 - Purdue University

Chapter 15
Matter and Electric
Fields
Question 1 (Chap. 14)
What is the direction of the electric field at location X,
due to the dipole?
+
C
B
D
A
E
X
Question 2 (Chap. 14)
Locations 1 and 2 are equidistant from the center of the
dipole. At which location is the magnitude of the electric
field larger?
d
+
1
d
A. at location 1
B. at location 2
C. magnitudes are the same
2
Net Charge
Matter is made out of atoms.
Atom contains charged particles: electrons (-e), protons (+e)
Neutral atom: number of electrons and protons is equal:
Example: Hydrogen atom: 1 proton, 1 electron
net charge = (+e) + (-e)=0
Sodium atom: 11 protons, 11 electrons
Sodium atom (Na) can lose an electron:
Sodium ion (Na+): (+11e) + (-10e) = +e
Ordinary matter is electrically neutral.
However, can be charged by adding/removing charged particles
Can we create an excess charge inside a sample?
Conservation of Charge
The net charge of a system and
its surroundings cannot change
If one object gets charged positively, there must be an object
which gets charged negatively.
The net electric charge is conserved in any physical process.
Charge can be transferred from one object to another.
Annihilation : e+ + e- = g + g
Induced Dipole
An applied electric field creates induced dipoles!
E
• it is not a permanent dipole
• an induced dipole is created when a neutral object is polarized
by an applied electric field
Polarization
Amount of polarization p in most materials is proportional to the
magnitude of the applied electric field:
p = aE
- “polarizability” of a material
In an induced dipole, is the distance between the charges fixed?
The distance is proportional to the strength of the applied field.
A Neutral Atom and a Point Charge
1. Charge q1 creates field E1 at the location of the atom
q1
E1 =
rˆ
2
4pe 0 r
1
A Neutral Atom and a Point Charge
1) E1 =
q1
rˆ
2
4pe 0 r
1
2. Field E1 polarizes the atom creating a dipole
1 aq1
p = aE1 =
rˆ
2
4pe 0 r
A Neutral Atom and a Point Charge
1) E1 =
q1
rˆ
2
4pe 0 r
2) p =
1 aq1
rˆ
2
4pe 0 r
1
3. Dipole creates field E2 at the location of q1
æ 1 ö 2aq1
1 2p
1 2a
ˆ
E2 =
=
E
=
r
ç
÷
1
5
4 pe 0 r 3 4 pe 0 r 3
4
pe
r
è
0ø
2
A Neutral Atom and a Point Charge
q1
E
=
1) 1 4pe r 2 rˆ
0
2
1
2) p =
3)
1 aq1
rˆ
2
4pe 0 r
4. Induced dipole exerts force F1 on the charge:
2
æ 1 ö 2aq12
÷÷
F1 = q1E2 = çç
rˆ
5
è 4pe 0 ø r
æ 1 ö 2aq1
÷÷
E2 = çç
rˆ
5
è 4pe 0 ø r
A Neutral Atom and a Point Charge
q1
E
=
1) 1 4pe r 2 rˆ
0
2
1
1 aq1
p
=
rˆ
2)
2
4pe 0 r
3)
æ 1 ö 2aq1
÷÷
E2 = çç
rˆ
5
è 4pe 0 ø r
4)
æ 1 ö 2aq12
÷÷
F1 = çç
rˆ
5
è 4pe 0 ø r
2
5. The charge q1 exerts force F2 on the dipole (reciprocity):
2
æ 1 ö 2aq12
÷÷
F2 = - F1 = -çç
rˆ
5
è 4pe 0 ø r
A Neutral Atom and a Point Charge
1) E1 =
q1
rˆ
2
4pe 0 r
2) p =
1 aq1
rˆ
2
4pe 0 r
1
2
3)
æ 1 ö 2aq1
÷÷
E2 = çç
rˆ
5
è 4pe 0 ø r
4)
æ 1 ö 2aq12
÷÷
F1 = çç
rˆ
5
è 4pe 0 ø r
5)
æ 1 ö 2aq12
÷÷
F2 = -çç
rˆ
5
è 4pe 0 ø r
2
2
Neutral atoms are attracted by charges!
Interaction strength ~ 1/r5
Exercise
Atom A is easier to polarize than atom B. Which atom would
experience a greater attraction to a point charge a distance r away?
A
B
-
FA
+
-
+
FB
2
æ 1 ö 2aq12
÷÷
F2 = çç
~a
5
è 4pe 0 ø r
Conductors and Insulators
Different materials respond differently to electric field
Conductor: contains mobile charges that can move through material
Insulator: contains no mobile charges
Polarization of Insulators
Insulator: Electrons are bound to the atoms or molecules.
Electrons can shift slightly (<1 Å), but
remain bound to the molecule.
Individual atoms or molecules can be
polarized by external electric field.
There are a lot of molecules – the net
effect produced by the induced dipoles
can be very large.
Polarization of Insulators
Diagram showing polarization of an insulator:
Dipoles: exaggerated in size; stretch: degree of polarization
No mobile charges: excess charges stay where they are
Low Density Approximation
p = aE ¹ aEapplied
Field E at a location of a molecule is a
superposition of the external applied field
and the field created by other induced
dipoles:
(
p = a Eapplied + Edipoles
Simplifying assumption:
)
Eapplied >> Edipoles
p » a Eapplied
Conductors
There are charges which can move freely throughout the material
E
In contrast to an insulator, where electrons and nuclei can move
only very small distances, the charged particles in a conductor are
free to move large distances.
Polarization of conductors differs from that of insulators.
Ionic Solutions are Conductors (home)
Salt water:
Na+ and ClH+ and OH-
Apply external
electric field
Enet = Eapplied + Ech arg es
When an electric filed is applied to a conductor, the mobile charged particles begin
to move in the direction of the force exerted on them by the field.
As the charges move, they begin to pile up in one location, creating a concentration
of charge  creates electric field.
The net electric field is the superposition of the applied field and field created by the
relocated charges.
Ionic Solutions are Conductors (home)
Assumption: charges will move until Enet=0
(static equilibrium)
Proof: by contradiction: Assume Enet≠0
Mobile ions will move
This is not equilibrium
Enet = Eapplied + Echarges
Assumption Enet≠0 is wrong
Enet=0
It is not a shielding effect, but a consequence of superposition!
A Model of a Metal
Metal lattice
Positive atomic cores
and mobile-electron sea
Electrons are not completely free – they are bound to the
metal as a whole.
There is no net interaction between mobile electrons
Drude Model of Electron Motion in a
Metal

E


p 
 Fnet  (e) Enet
t
-
No net interaction between mobile electrons
Forget previous velocity after collision
p  p  0  eEnet t
v
v
p eEnet t

me
me
et
Enet
me

et
me
(mobility)
Later we will show that
conductivity ()  μ
Some important sources of collision:
- impurities
- thermal motion of atoms
(more motion at higher temperature T
 shorter t  lower 
[common feature of metals])
Metal in Electric Field
Enet inside the conductor will be:
A. Uniform positive
B. Uniform negative
C. Zero
D. will have complex pattern
Metal in Electric Field
Simplified diagram
of polarized metal
Note: It is
not charged!
Net charge is
still zero
Electric Field inside Metal
In static equilibrium:
Enet = Eapp + E pol = 0
Enet= 0 everywhere inside the metal!
Mobile charges on surface rearrange to achieve Enet=
Actual arrangement might be very complex!
It is a consequence of 1/r2 distance dependence
Enet= 0 only in static equilibrium!
0
Excess Charge on Conductors
Excess charges in any conductor
are always found on an inner or
outer surface!
Conductors versus Insulators
Conductor
Insulator
yes
no
Polarization
entire sea of mobile charges
moves
individual atoms/molecules
polarize
Static
equilibrium
Enet= 0 inside
Enet nonzero inside
Excess charges
only on surface
anywhere on or inside
material
Distribution of
excess charges
Spread over entire surface
located in patches
Mobile charges