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Tuesday, 19 July 2016
Why does the light in a room come on instantly when you flip a switch several meters away?
A. Electrons travel at the speed of light through the wire.
B. Because the wire between the switch and the bulb is already full of electrons, a flow of electrons from the switch into the wire immediately causes electrons to flow from the other end of the wire into the light bulb.
C. The switch sends a radio signal which is received by a receiver in the light which tells it to turn on.
D. Optical fibers connect the switch with the light, so the signal travels from switch to the light at the speed of light in an optical fiber.
Why does the light in a room come on instantly when you flip a switch several meters away?
A. Electrons travel at the speed of light through the wire.
B. Because the wire between the switch and the bulb is already full of electrons, a flow of electrons from the switch into the wire immediately causes electrons to flow from the other end of the wire into the light bulb.
C. The switch sends a radio signal which is received by a receiver in the light which tells it to turn on.
D. Optical fibers connect the switch with the light, so the signal travels from switch to the light at the speed of light in an optical fiber.
Current
• How do we know it is there?
• What is it?
• What effect does current have?
Current: How do we know it is there?
Charge Carriers
 The outer electrons of metal atoms
are only weakly bound to the nuclei.
 In a metal, the outer electrons
become detached from their parent
nuclei to form a fluid-like sea of
electrons that can move through the
solid.
 Electrons are the charge carriers
in metals.
Slide 30-22
Microscopic scale: Field in conductor
makes electrons move!
In a metal, electrons are the charge
carriers of current.
The Electron Current
 If the number density of
conduction electrons is
ne, then the total
number of electrons in
the shaded cylinder is
Ne  neAvdt
 So the electron current
is:
Slide 30-24
The Electron Current
 If the number density of
conduction electrons is
ne, then the total
number of electrons in
the shaded cylinder is
Ne  neAvdt
 So the electron current
is:
Slide 30-24
Microscopic scale: Field in conductor
makes electrons move!
In a metal, electrons are the charge
carriers of current.
What creates current?
• An electron current is a nonequilibrium motion of
charges sustained by an internal electric field.
Electric fields
Fields move at
speed of light!!!
Establishing the Electric Field in a Wire
 This is an electrostatic situation.
 What will happen if we connect the
bottom ends of the wires together?
 Within a very brief interval of time
(109 s) of connecting the wires, the sea of electrons
shifts slightly.
 The surface charge is rearranged into a nonuniform
distribution, as shown in the figure.
• We know there is a potential difference => electric field
inside, but lets look at the details:
• A non-uniform surface charge distribution
Recall:
(Ex. 26.4 in bk)
Electric field of ring
Easy on axis!
(s=R,θ,z=0)
R
KQzP
Ez  2
( z P  R 2 )3 / 2
Rank the electric field in the center
from largest to smallest.
• Rank the electric field in the center
from largest to smallest.
• Establishing the Electric Field in a Wire
 The nonuniform distribution of surface charges along a
wire creates a net electric field inside the wire that
points from the more positive end toward the more
negative end of the wire.
 This is the internal electric field that pushes the electron
current through the wire.
Slide 30-34
Surface charge is distributed on a
wire as shown. Electrons in the wire
A.
B.
C.
D.
E.
Drift to the right.
Drift to the left.
Move upward.
Move downward.
On average, remain at
rest.
QuickCheck 30.2
Surface charge is distributed on a wire as shown.
Electrons in the wire
A.
B.
C.
D.
E.
Drift to the right.
Drift to the left.
Move upward.
Move downward.
On average, remain at rest.
Electric field from
nonuniform surface
charges is to the right.
Force on negative
electrons is to the left.
Slide 30-36
A Model of Conduction
 Within a conductor
in electrostatic
equilibrium, there is
no electric field.
 In this case, an
electron bounces
back and forth
between collisions,
but its average
velocity is zero.
Slide 30-37
A Model of Conduction
 In the presence of an
electric field, the
electric force causes
electrons to move
along parabolic
trajectories between
collisions.
 Because of the
curvature of the
trajectories, there is a
slow net motion in the
“downhill” direction.
Slide 30-38
A model of current:
Average speed between collisions:
v x  v x , 0  at
F eE
a 
m m
Average time between collisions: τ
eE
vd  v x  v x , 0  at 
m
0m/s
Current: How do we know it is there?
A model of current:
Average speed between collisions:
v x  v x , 0  at
F eE
a 
m m
Average time between collisions: τ
eE
vd  v x  v x , 0  at 
m
Microscopic perspective of current:
A
vdτ
N e  ne vdA
Ne
ie 

Electron current = the number of electrons per second that pass through a
cross section of wire in a conductor.
Electric current
Units: Amperes, Coulombs per
second
eE
I  ene
A
m
What is current?
• Broadly: motion of charges
• Specifically:
dQ
I
dt
• Units: Ampere (A), ‘amp’
1Coulomb
1Ampere 
1second
• The direction of conventional current is arbitrarily defined
as the same direction as positive charges flow.
Direction of current
• The direction of conventional current is arbitrarily
defined as the same direction as positive charges flow.
• The direction of current I in a metal is opposite the
direction of the motion of electrons.
QuickCheck 30.3
Every minute, 120 C of charge flow through this cross section of the wire.
The wire’s current is
A.
B.
C.
D.
E.
240 A.
120 A.
60 A.
2 A.
Some other value.
Slide 30-44
QuickCheck 30.3
Every minute, 120 C of charge flow through this cross section of the wire.
The wire’s current is
A.
B.
C.
D.
E.
240 A.
120 A.
60 A.
2 A.
Some other value.
Slide 30-45
Current
Note that the direction of the
current I in a metal is opposite
to the direction of the electron
current ie.
Slide 30-47
The Current Density in a Wire
Thecurrent
Current
Density
a Wire
The
density
J in in
a wire
is the current per square meter of
cross section:
The current density has units of A/m2.
Slide 30-48
No net charge in a conductor
Current density: J=I/A
ne e 
J
E
m
2
QuickCheck 30.4
The current density in this wire is
A.
B.
C.
D.
E.
4  106 A/m2.
2  106 A/m2.
4  103 A/m2.
2  103 A/m2.
Some other value.
Slide 30-49
QuickCheck 30.4
The current density in this wire is
A) 4  106 A/m2.
B) 2  106 A/m2.
C) 4  103 A/m2
D) 2  103 A/m2.
E) Some other value.
Slide 30-50
No charge accumulation
 
J

d
A

0

Currents are conserved
• Conservation of charge!
Equate with the volume of water in a pipe.
Currents are conserved.
No charge accumulation.
I
=
I
I
=
Currents are conserved.
No charge accumulation.
I
=
I
=
I
What are the magnitude and the
direction of the current in the
fifth wire?
A. 15 A into the junction
B. 15 A out of the junction
C. 1 A into the junction
D. 1 A out of the junction
E. Not enough data to
determine
What are the
magnitude and the
direction of the
current in the fifth
wire?
A.
B.
C.
D.
E.
15 A into the junction
15 A out of the junction
1 A into the junction
1 A out of the junction
Not enough data to determine
Conductivity
Current density: J=I/A


J  E
2
ne e 

m
τ dependent
Non-uniform charge density
A wire with radius R has charge density J(r)=C(R-r). What is
the total current through the wire?