Lecture 7.1 :!
Electron Current
Lecture Outline:!
More on Capacitors/Dielectrics!
The Electron Current!
Creating Current!
Current and Current Density!
!
Textbook Reading:!
Ch. 29.7 - 30.3
Feb. 24, 2015
1
Announcements
!
•HW6 due next Tue. (March 3) at 9am on Mastering Physics.!
•Quiz #3 in class this Thursday (Feb. 26).
Will cover Ch. 29 material.!
•If you haven’t already done so, please fill out mid-semester
evaluation forms. It’s anonymous, and it’s helpful to me.!
•Exam #1: Average = 66.5 ± 17.01 %!
•Questions?
Concerns? Please feel free to e-mail me or drop by my
office.
2
Last Lecture...
Capacitance is a
geometric property!
VC = Ed
C
Q
VC
1 farad = 1 F ≡ 1 C/V
C
Energy Stored in a
Capacitor.
Q
0A
=
VC
d
Q2
1
2
UC =
= C( VC )
2C
2
3
Last Lecture...
Capacitors in Series
Capacitors in Parallel
1
1
1
1
=
+
+
Ceq
C1
C2
C3
Ceq = C1 + C2 + C3
4
More on Capacitors
What is the equivalent capacitance of this circuit?
5
Clicker Question #1
A capacitor charged to 1.5 V stores 2.0 mJ of energy. If the
capacitor is charged to 3.0 V, it will store
!
A.
B.
C.
D.
E.
1.0 mJ.
2.0 mJ.
4.0 mJ.
6.0 mJ.
8.0 mJ.
UC ∝ (ΔV)2
6
Dielectrics
So far we’ve assumed our parallel-plate capacitors are
filled with vacuum (i.e. - nothing). What if we insert
some other material?
Capacitance = ?
7
Dielectrics
Capacitor with
no dielectric
Dielectric is
polarized.
8
Electric Field is
diminished.
Dielectrics
VC = Ed =
C=
E0
d=
E0
E
Dielectric
Constant
( V C )0
Voltage
diminishes
Q
Q0
Q0
=
=
= C0
VC
( VC ) 0 /
( V C )0
9
Capacitance
Increases
Dielectrics
10
More on Capacitors
Two 5.0 mm x 5.0 mm electrodes with a 0.1mm thick sheet of
Mylar (κ=3.1) between them are attached to a 9.0 V battery.
At some time the Mylar is withdrawn. !
What is the potential energy stored in the capacitor before/
after the Mylar is removed?!
11
The Electron Current
We need to develop an understanding of
how charges can move through systems.
Current = controlled motion of charge.
Wire
Charged Capacitor
Discharged Capacitor
12
The Electron Current
Electrons are the charge carriers in metals!
electron current (ie) = number of electrons per second that pass
through a cross-section of wire.
13
The Electron Current
How long does it take to discharge a Capacitor?
If drift speeds of ~10-4 m/s are
typical, it would take an electron
2000 seconds to travel 20 cm. ????
Discharge doesn’t happen by
moving electrons from one plate
all the way to the other!
14
Creating Current
The fact that current is “flowing” implies
the electrons must be subject to some force.
Electric field inside conductor is due to ends
of conductor being at different potentials.
15
Creating Current
Conduction electrons are like free particles
moving through a metal lattice.
No Electric Field!
With Electric Field!
Average Velocity is Zero
Average Velocity is NonZero
16
Creating Current
Between collisions the acceleration is constant. Magnitude
of the average velocity is called the drift speed, vd
vx
17
Creating Current
Acceleration in E-Field
18
Clicker Question #2
A wire carries a current. If both the wire diameter
and the electron drift speed are doubled, the
electron current increases by a factor of
!
A.
B.
C.
D.
E.
2.
4.
6.
8.
Some other value.
ie ∝ Aνd
19
Current and Current Density
Electrons are the charge carriers in metals!
electron current (ie) = number of electrons per second that pass
through a conductor in a given time.
ie = ne A
d
ne e⇥ A
=
E
m
20
Current and Current Density
Current was known long before electrons were discovered, so
conventional definition of current is in terms of Charge:
I
dQ
dt
1 ampere = 1 A ≡ 1 coulomb per second = 1 C/s
Conventional current and electron current are related:
Q
eNe
I=
=
= eie
t
t
21
Current and Current Density
By convention, current is defined to
flow in the direction in which
positive charges would move! (i.e. in the direction of the Electric Field)
22
Reminders
!
•HW6 due next Tuesday (March 3)!
•Quiz #3 this Thursday (Feb. 26)!
•If you have any questions/concerns, please feel free
to e-mail me or stop by my office. !
!
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