Download Lecture28_Potential

What is the electric field at the very
CENTER of this spherical conductor?
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The electric field at this off-CENTER
point within the spherical conductor
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Nearby charges
create a strong
electric field.
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Much farther away,
individual charges have a much smaller
effect, but there are much more of them!
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All of this balances beautifully and the
electric field even at off-center points
(in fact, EVERYWHERE) within the conductor
is zero!
That’s why fan motors or transformers
(which can produce fluctuating electric fields)
are often shielded from the more sensitive
parts of circuits by “cans” of conducting metal.
Conducting panels when screwed in place provide
a surrounding shield against stray electric fields!
Concept Review
A man lifts a 5 kg
rock 1 meter off
the ground. The
potential energy of
the rock is about
h=1m
A) (5 kg)( 1 m) = 5 J
B) (5 kg)g1m  50 J
C) 2(5 kg)(1 m) =100 J
D) (5 kg)  g2  500 J
Gravitational potential energy =
mgh
About how much work did he do?
A)
5J
C) 50 J
B) 100 J
D) 500 J
E) cannot be determined from
the information given
Concept Review Test
The balls in the figure are identical.
When released from rest, which has
a greater kinetic energy when it gets
to the bottom of its ramp?
A)
B)
C) both the same
Electric Energy
A proton and an electron are
each accelerated by moving the
same distance across a region
of constant electric field, E.
Which experiences the
greater acceleration?
(1)
(2)
(3)
(4)
proton
electron
both have equal acceleration
neither will accelerate at all.
Electric Energy
A proton and an electron are
each accelerated by moving the
same distance across a region
of constant electric field, E.
Which experiences the bigger
increase in Kinetic Energy?
(1) proton
(2) electron
(3) both receive the same
increase in KE
(4) neither -- KE = 0 for both
h
Recall the work done in
elevating a bag of fluids
W = mgh
results in added pressure
P = gh
in this I.V. tube:
Just like
• the work done
mgh in lifting
(pumping water)
• creates added
pressure P = gh
• which can be
exchanged as
fluid kinetic
energy = ½ v2.
voltage is related to the work done
(by a generator or even chemically by a battery)
in separating unlike charge and/or
building concentrations of like charge.
Electric Potential
Difference
Work
V=
q
Electric Potential
Difference
Work
V=
q
PE
=
q
Notice the amount of potential energy
stored by any charge in a potential V is
PE
V
q
PE  qV
charge  voltage = ENERGY
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-- +
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Separating clinging
fabrics is doing work
(W = Fd) against the electric fields
that try to hold them together.
Prying your shoe from
carpet involves a tiny bit
more work than just
lifting the weight
of your foot.
-+++++++++++++++++++++ +
(Favg)(x against
moved )
that force
PE = work required to move an object
against a “restoring” force
g
Work = mgd
m
depends on m, g, d
d
g
Work = mgd
m
depends on m, g, d
d
E Work = Fd
+q
= (qE)d
depends on q, E, d
d
+q
Work
= Ed
q
V = Ed
E
+q
For a uniform E-field
+q
Work = (qE)d
V = Ed
d
But moving toward a
tightly concentrated charge
+q
Q
But for a tightly concentrated charge
Work = (qE)d
V = Ed
Since the E-field keeps changing so fast!
Instead:
qQ
qQ
Work = k
-k
Rstop Rstart
+q
Q
and the voltage
of a concentration of charge Q
build up across the surface of
a spherical conductor of radius, R:
Q
Q
V k
R
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Robert Jamison
Van de Graff
MIT’s
Van de Graff
Generator
1935
Fermi National Laboratory
750 keV =
750,000 eV
1.5 MeV electron accelerator
Basel, Switzerland
Two identical conducting spheres
(with insulated handles) are charged
to different voltages, V1>V2.
The two spheres must be
a. charged with Q1>Q2.
b. charged identically with Q1= Q2.
c. charged with Q1<Q2.
Two identical conducting spheres
(with insulated handles) are charged
to different voltages, V1>V2.
When touched together
a. charge flows from 1 2.
b. all charge stays in place.
c. charge flows from 2  1.
Two identical conducting spheres
(with insulated handles) are charged
to different voltages, V1>V2.
Having been touched together
a. both spheres are now at V1.
b. both spheres are now at V2.
c. both spheres are now at a voltage
in between V1 and V2.
A large conducting sphere of
radius R initially carries an initial charge.
When touched to a smaller, uncharged
conducting sphere of radius r < R
charge flows to the smaller sphere until
1. each sphere carries half the total charge.
2. each sphere carries the same density
of charge.
3. charge is divided between them in
proportion to their radii: q/Q = r/R.
Two conducting spheres (radius R and r),
after touching, are at the same potential.
Q
q
k
=k
R
r
r
q Q
R
or
q r

Q R
But check out a comparison of the
charge DENSITY across the surface of each:
Q
2
4R
r
q Q
R
q
2
4r
q
rQ / R
If
then

2
2
4r
4r
Q

4rR
And how do these compare:
1. >
Q
Q

2. =
2
4rR 4R
3. <
But check out a comparison of the
charge DENSITY across the surface of each:
Q
2
4R
Although Q
>q
q
2
4r
Q
2
4R
q
2
4r
The charge density across the surface
of the smaller sphere is HIGHER!
Charge is crowded together
much more tightly on the smaller sphere!
QUESTION 1
7. is zero
QUESTION 2
7. is zero As argued in slides 4-5!
(B) (5 kg)g1m  50 J
QUESTION 3
As explained in slide 2!
Gravitational potential energy = mgh
QUESTION 4
(C) 50 J
Work done = change in energy it produces
QUESTION 5
(2) electron
qelectron=qproton so since F=qE both proton and
electron experience the same sized force!
However, since melectron<< mproton , they respond
differently! The electron will move with an
acceleration ~2000 greater than the proton
(since the proton is almost 2000 heavier!
QUESTION 6
(3) both receive the same
increase in KE
Both experience the same F=qE and travel the same
distance d under its influence. So the same amount of
work W=Fd is done on each.
QUESTION 7 We’ll discuss this one on Wednesday!