Physics 122B Electricity and Magnetism

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Physics 122B Electricity and Magnetism
Lecture 8 (Knight 28.1 to 28.5) Review of
Material to be examined in Midterm 1 Current
and Resistance April 11, 2007

• Martin Savage

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Lecture 8 Announcements

• The Midterm examination is this Friday during
  lecture time. You should bring with you to the
  Exam a good calculator, a Scantron sheet, and one
  sheet of 8.5x11 paper on which you have written
  anything you wish on both sides.
• No cell phones or wireless communication allowed.
• Lecture HW Assignment 3 will be been posted on
  Tycho and is due at 10 PM on Wednesday, April 18

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Summaries

• Knight,
• Chapters 25, 26 and 27

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Summary Chapter 25 (1)
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Summary Chapter 25 (2)
Charges
Fields
Not really true semi-conductors
Not always true Only if object is polarizable
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Chapter 26 Summary (1)
The E field exists at each point in
space Non-zero values of the E-field are induced
by electric charges
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Chapter 26 Summary (2)
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Chapter 27 Summary (1)
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Chapter 27 Summary (2)
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Chapter 27 Summary (3)
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The Electron Current
We start with some thought experiments on
a simple system. We have a parallel plate
capacitor that has been charged, e.g. with glass
and plastic rods. Now we connect the plates with
a wire. What happens? The plates quickly
become neutral, and we say that the capacitor has
been discharged. Further study shows that
while the discharge is taking place, the wire
gets warm, a light bulb can be made to glow, and
a compass needle can be deflected. These are
indicators of current flow in the wire.
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Charge Carriers and Inertia
Does the discharge occur because positive
charges are moving to the negative plate, or
because negative charges are moving to the
positive plate?
We have asserted that the current in metals
is caused by the flow of negative electrons.
The first direct evidence that this was the case
was provided in 1916 by the Tolman-Stewart
experiment, which showed that negative charges
go to the bottom of an accelerated conductor.
We model a metallic conductor as a rigid
lattice of positive charges pervaded by a sea
of conduction electrons, 1 per atom, that move
freely in the material.
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The Electron Current
In a metallic conductor in electrostatic
equilibrium, the conduction electrons move around
quite rapidly, but there is no net movement of
charge. This can be changed by pushing on
the sea of electrons with an electric field,
thereby causing the entire sea of electrons to
move in a particular direction, like a gas or
liquid flowing through a pipe. The net
motion, the drift speed vd, is superposed on
the random thermal motions of the individual
electrons, and it is very slow, typically around
10-4 m/s.
We define the electron current i as the
number of electrons Ne that pass through a cross
section of wire or other conductor in a time
interval Dt. In other words Ne i Dt.
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Current and Drift Velocity
If the electrons have an average driftspeed
vd, then on the average in a timeinterval Dt
they would travel a distance Dx in the wire,
where Dx vd Dt. If the wire has cross
sectional area A and there are n electrons per
unit volume in the wire, then the number of
electrons moving through the cross sectional area
in time Dt is Ne n A Dx n A vd Dt i Dt .
Therefore,
This table gives n for various metals.
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Question 1
Which wire has the largest electron current?
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Conservation of Current
Question An electron current iA flows to the
light bulb, passing point A, where it delivers
some energy and makes the bulb glow. How much
electron current iB then passes point B? Answer
All of it! iAiB. Reason the electrons dont
have anywhere else to go. What goes to the bulb
must return from the bulb. The bulb cannot use
up the electrons. Plumbers Analogy 1 If water
flows into a constant diameter pipe at 2.0 m/s,
it must flow out of the pipe at the same speed.
It cannot pile up in the pipe.
This principle is called Conservation of
Current.
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A Puzzle
We discharge a capacitor that has been
given a charge of Q 16 nC, using a copper wire
that is 2 mm in diameter and has a length of L
20 cm. Assume that the electron drift speed is
vd 10-4 m/s. How long does it take to
discharge the capacitor? (Note that L/vd
0.2m/10-4 m/s 2000 s 33.3 min.)

• Points to consider
• The wire is already full of electrons.
• The wire contains about 5x1022conduction
  electrons.
• Q 16 nC requires about 1011 electrons.
• A length L of wire that holds 16 nCof
  conduction electrons is 4x10-13 m.
• L/vd 4x10-9 s 4 ns. That is roughly the
  discharge time.

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Creating a CurrentNon-Static Situation
Suppose you want to slide a book across a
table. If you give it a quick push, it moves but
slows due to friction as soon as you remove your
hand, and its kinetic energy becomes heat. The
only way to make the book move at a constant
speed is to continue pushing it.
The sea of conduction electrons is similar
to the book. If you push the electrons, you
create a current, but they are not moving in
vacuum, and collisions with other electrons and
atoms soon dissipates their kinetic energy as
heat. The only way to maintain the current of
electrons is to push them, using an electric
field.
An electron current is a non-equilibrium motion
in an E field.
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Establishing theElectric Field in a Wire (1)
The figure shows two metal wires attached to
the plates of a parallel plate capacitor, with
their ends close together but not touching. The
wires are conductors, so some of the charge from
the capacitor plates spreads out along the wires
as surface charge. E0 inside all
conductors..plates and wires.
Now we connect the wires. What happens?
The surface electrons can move, and do so. In
10-9 s the sea of electrons shifts slightly, and
the surface charges are rearranged into a
non-uniform distribution of charges, as shown.
Surface charges near the and plates reflect
these charges, but surface charges become
near-neutral half-way along the wire
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Establishing theElectric Field in a Wire (2)

• The figure shows the region of the wire near the
  neutral midpoint. The surface charge rings
  become more positive to the left and more
  negative to the right.
• In Chapter 26, we found that a ring of charge
  makes an on-axis E field that
• Points away from a positive ring and toward a
  negative ring
• Is proportional to the net charge of the ring
• Decreases with distance from the ring.

The non-uniform surface charge distribution
creates an E field inside the wire. This pushes
the electron current through the wire
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Example The Surface Charge on a
Current-Carrying Wire
Two 2.0 mm diameter charged rings, with
charges Q, are 2.0 mm apart. What value of
Q causes the electric field at the midpoint to be
E0.010 N/C?
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Turning the Corner
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Question 2
Which surface charge distribution will
produce the largest electron current?
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A Model of Conduction (1)
Now turn on an E field. The straight-line
trajectories become parabolic, and because of the
curvature, the electrons begin to drift in the
direction opposite E, i.e., downhill.
axF/meE/m so vxvix axDt vix Dt eE/m
This acceleration increases an electrons kinetic
energy until the next collision, a friction
that heats the wire.energy is imparted to the
atoms of the lattice.
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A Model of Conduction (2)
One Collision
Time-History over many Collisions
Collision is independent of E
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Example The Electron Current in a Copper Wire
The mean time between collisions for
electrons in room-temperature copper is t
2.5x10-14 s. What is the electron current
in 2.0 mm diameter copper wire where the internal
field strength is E 0.010 N/C?
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Batteries and Current
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Electrical Current
D
D
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Example The Current in a Copper Wire
From the previous example,
What is the current I?
How much charge passes through the wire in an
hour?
D
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Current and Electrons
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The Current Density in a Wire
Example A current of 1.0 A passes through a 1.0
mm diameter aluminum wire. What is the drift
speed of the electrons in the wire?
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End of Lecture 8

• Before the next lecture, read Knight 29.1 to
  29.4.
• Exam Friday.study everything in chaps
  25,26,27
• Will NOT cover material on currents and
  non-static situations.