16-115sp13-elect3.pdf

Physics 115
General Physics II
Session 16
Electric Fields
Conductors & Shielding
Charging by Induction
Electric flux & Gauss’s Law
• R. J. Wilkes
• Email: ph115a13@u.washington.edu
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Lecture Schedule
(up to exam 2)
Today
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Example: acceleration under E
An electron and proton are initially held a distance d = 1 m apart.
When released, what is the velocity of each after 1 nanosecond?
Find the force on each, then apply what you learned in PHYS 114:
F E
= k q 1 q 2
r 2
= ke2
r 2
= (8.99×109 N ⋅ m 2 /C 2 )(1.60×10 −19 C) 2
(1m) 2
=1.44×10 −9 N
Tiny F – but tinier masses!
Result: huge acceleration
Notice: F is independent of m
but kinematics depends on m
This is the
point,
however
v = at = F E
m t
v p
= F E
m p
t =
= 8.62×10 8 m/s
v e
= F E
m e
t =
=1.58×10 12 m/s
Did you see the
flaw in this?
To simplify
discussion, I
ignored the fact
that positions
(so: r, and F E )
would change
rapidly; in fact at
these speeds
they would
collide long
before 1 ns
1.44×10−9 N
(
(1.67×10 −27 kg) 10−9 s)
1.44×10−9 N
(
(9.11×10 −31 kg) 10−9 s)
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Dipole E Field Maps
Dipole = +q / –q pair with fixed separation, often encountered in physics]
Two varieties of field map for a dipole:
Field Map
Arrows show the
E field vectors for
location at dots
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Field Lines
4
4

Two Positive Charges
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Field Map
Density Field of lines Lines ~ |E|
Notice: E=0 halfway between
5
5

E field of a sheet of charge
• If a thin sheet carries uniformly distributed charge the
E field will be uniform and perpendicular to the sheet
– For a sheet in the y-z plane,
consider E field at a point on
the x axis:
For contributions to E from Δq’s
symmetrically located at + y
• x components add
• y components cancel
• Result: uniform E pointing out (if +q)
– Except near edges: symmetry ends there!
– “infinite sheet” approximation...
– NOTICE: E does not diminish with distance!
• Field lines are parallel – same density everywhere
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Parallel oppositely charged plates = “capacitor”
• Consider 2 parallel (infinite) conducting plates,
separation d, one has +q and the other has –q
• In the gap, E field is uniform (constant magnitude
and direction) and perpendicular to plates
– Capacitors have useful properties
• important in physics and technology
– We’ll come back to study them later
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Quiz 10
For an infinite sheet of
charge:
How does the
magnitude of the E
field compare at the
points shown?
(A) All points have different field magnitudes
(B) Field at a is larger, but other points are equal
(C) All points have equal field magnitudes
(D) Point a is smallest, but other points are equal
(E) Cannot answer without more information.
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Charge and E on a conductor
Charge mobility in conductors à charges separate easily
Like charges push each other away à end up on outer surface
1. If excess charge is placed on a conductor, it is all on the exterior
2. If all charge is at rest, interior of conductor must have E=0
(or charges would be moving)
Also:
3. Exterior E field must be perpendicular to surface
(or charges would be moving on surface)
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Shielding effect in a conducting shell
We know that, due to mobility of electrons in conducting materials
1. E inside a conductor must be zero
2. All excess charge resides on surface
3. External field lines stop (and start again) at right angles
4. A cavity inside the conductor will be shielded against external fields
• External field may cause separation of charge on surfaces, but
net Q = 0, so E inside cavity is 0 also
• Internal charge is not the same!
– Induced Q extends E field outside: Shielding only works one-way
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Lightning rods
E fields are more intense around sharp features on a conductor
(we’ll soon see why this must be)
• Intense fields may exceed insulating ability
of air : breakdown = sparks
– Lightning = air breakdown and discharge, caused
by q separation between rain clouds and objects
on ground
– “St. Elmo’s Fire” = “ball lightning” (air discharges
localized around pointy objects like ship masts)
• Another Ben Franklin idea (1749):
lightning rods
– Pointed rod on rooftop, connected by heavy wire
to rod driven into earth
• Recall: earth = “ground” = infinite q reservoir
– Rod’s high E field breaks down air nearby,
discharges excess q buildup on house
– If discharge is too slow and lightning does strike,
cable provides a path for lightning charge to
bypass house into ground
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Charging by induction
Charge separation by induction:
• Hold charged rod near metal
object
– (not in contact – no direct
transfer of q)
• Rod’s q attracts opposite charge
within conductor
• same-sign charge is repelled –
and left behind
• Conductor’s net charge is still
zero but E field of rod has caused
charge separation
• Field set up between separated q
inside conductor cancels external
field from rod
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