Transcript Electrical forces

electrical forces,
magnetic forces,
action-at-a-distance
Fields
+
-
Mico-world Macro-world
Lecture 8
Benjamin Franklin
Ben Franklin
Matter is filled with a mysterious
Fluid-like substance called “electricity.”
When an object has its “normal amount”
of electricity, it is electrically “neutral”
And doesn’t feel electrical forces.
When an object has more than its normal
amount of electricity, it is “positively
charged.”
When it has less than its normal amount
it is “negatively charged.”
Charged objects feel electrical forces.
Friction can move “electricity”
from one object to another
Franklin hypothesized that rubbing a comb through hair
moved some “electricity” from the comb to the hair
Comb has an “electricity”
deficit & thus becomes
negatively charged
Hair has a surplus
& becomes
positively charged
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_
_
_
+
+
+
+
Opposite charges attract
Like-sign charges repel
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_
Modern picture of “electricity”
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_
+
++
++
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_
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_
Negatively charged electrons
orbit around a positively
charged nucleus
Electrical attraction
between minus electrons
& plus nucleus keeps
electrons in orbit
Positive Ion
An atom with one or more
electrons removed
_
_
_
+
++
++
_
_
_
”net” charge is positive
“electricity” flow
“electricity” doesn’t flow from comb to hair, some
electrons from hair atoms get stuck on the comb
Comb has an excess of
of electrons & is thus
negatively charged
The removal of
each electron
leaves a positive
ions in the hair
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_
_
_
+
+
+
+
Atomic electrons play the role of
“fluid-like electricity”
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+
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++
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+
Electrical
Conductors
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_
_+ _
_
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_
_
_
_
positive ion
(fixed in crystal)
Conduction electron
free to move around
_
_
+ _ + _ + _ + _ + _ + _ + _ +_
+ _ + _ +_ + _ +_ +_ +_ +_ +
+ _+ _ + _ + _ + _+ _+ _ + _+
_
_+ _ + _ + _ + _ + _ + _ + _ + _ +
+ + + + + + + + +
Charging by induction
Charging by induction (2)
Electroscope
Electrical Force
Charles Coulomb 1736-1806
Coulomb’s Law
The electrical force between two
charged objects is proportional to the
charge of each object and inversely
proportional to the square of the distance
between them.
Coulomb’s law
q1
proportional to the
charge of each object
Inversely proportional
to the square of the
distance between them
combine:
r
q2
Fc  q1
Fc  q2
1
Fc  2
r
q1 q2
Fc  2
r
Proportionality constant:
“Coulomb’s Constant”
q 1 q2
Fc = k r2
Units & Coulomb’s constant
q 1 q2
Fc = k r2
Unit of charge = “Coulomb”(C)
Unit of distance = m
k = 9.0 x 109 Nm2/C2
This is a big number
Hydrogen atom
electron
qe = -1.6x10
qp = +1.6x10
5x10–11 m
proton
–19
C
–19
C
qe qp
Fc = k r2
=9x109Nm2/C2
(1.6x10-19C)2
(5x10-11m)2
=9.2x10-8N
Gravitational force in an atom
electron
5x10–11 m
proton
me = 9.1x10
mp = 1.7x10
–31
kg
–27
kg
memp
FN = G r2
-31kgx1.7x10-27kg
9.1x10
=6.7x10-11Nm2/kg2
(5x10-11m)2
=4.1x10-47N
Electrical vs gravitation at atomic
scales
FC=9.2x10-8N
_
FN=4.1x10-47N
5x10–11 m
+
FC
FN
=
9.2x10-8N
+39
=
2.2x10
4.1x10-47N
Electrical force is >1039x the gravitational force!!
Fc = 22,000,000,000,000,000,000,000,000,000,000,000,000,000 x F N
Magnetism
another “invisible” force
N-poles & S-poles
S
N
Unlike poles attract
N-poles & S-poles
S
N
like poles repel
N-poles & S-poles can never be
isolated
S
N
Break a magnet into two pieces:
S
N
S
N
A new N-pole & S-pole are formed
Compass needles
If left to its own accord, the N-pole of a
magnet will try to point towards the North
The Earth is a magnet
Earth’s geographic
North pole is a
Magnetic S-pole
geographic
South pole is a
magnetic N-pole
Action at a Distance
+
-
q1
M1
r
q2
M2
Coulomb’s law
q1 q2
Fc = k r2
Newton’s law of Gravitation
M 1 M2
FN = G
r2
Moon-earth
MMME
FN=G
r2
How does the Moon
know that the Earth
is where it is
(& what ME is)?
Electroscope
How do the electrons
in the foil know that
someone is moving a
charged object up here?
& that it’s negatively
charged?
& how much it is
charged by?
Ball on an empty trampoline
surface
The ball feels
no net force
Ball on a “loaded” trampoline surface
The ball is “attracted” to the girl’s force
Luminiferous aether & E-Fields
+
Faraday’s method for computing
E fields
Ftest=coulomb force
on test charge
Imaginary small positive
“test” charge qtest
+
Ftest
+
x
E = Ftest/qtest
Example
+
+
E-field from 2 plus charges
+
+
E-field from 2 plus charges
E-Field is the dir of force on +
charge
+
-
E-Field for opposite charges
Better picture
+
-
Rules
E-field lines start on + charges and end on - charges
Direction of E-field lines = direction of force on a +
charge placed at that point (opposite for – charge)
Where E-field lines are close together, the E field is
large; where they are far apart, the E-field is small.
The bigger the charge, the more E-field lines start (or
stop) on it.
E-field lines never cross
Magnetic Fields
Imagine a small
N-pole is placed
at the point
S
N
x
B-field is in
the direction
of the net
force
Determine the
magnetic force
on the imaginary
N-pole
B-field from a bar magnet
S
N
Rules
S
N
B-field lines come out of N-poles
& go into S-poles
B-field lines never end
Density of B-field strength of the field
The stronger the pole, the more B-field
exit (or enter)
Arrays of magnets
,arrays of magnets
Earth’s magnetic field
Which ones are N? Which are S?
E-field? or B-field?
1. Which is +?
2. Which is -?
3. Which is bigger?
+
_
Gravitational Fields
force on test particle
test particle
m
g
Fm
Fm
g=
m
mass of test particle
Rules:
•g-field lines start at infinity
& end on mass
•The more dense the lines,
the stronger the g-field
•The bigger the mass, the more
g-field lines end on it
•At any point in space, g is the
acceleration due to gravity there.
(On the surface of the earth,
g = 10 m/s2.)
E-field Rules
E-field lines start on + charges and end on - charges
Direction of E-field lines = direction of force on a +
charge placed at that point (opposite for – charge)
Where E-field lines are close together, the E field is
large; where they are far apart, the E-field is small.
The bigger the charge, the more E-field lines start (or
stop) on it.
E-field lines never cross
B-field
Rules
S
N
B-field lines come out of N-poles
& go into S-poles
B-field lines never end
Density of B-field strength of the field
The stronger the pole, the more B-field
exit (or enter)