Physics 1010:
The Physics of Everyday Life
TODAY
• Electrostatics
• Magnetostatics
1
Admin Stuff
• If you need grade verification for your
scholarship, see me after class
• Prof. Finkelstein will give lecture on
Tuesday (circuits)
• HW 7 is due by midnight Monday
• Some HW grades have been mixed up, Jing
is looking into it
2
“Kinds” of Forces
(forces that we talked about in class)
•
•
•
•
•
•
spring force
normal force: force perpendicular to a surface
Gravity
Friction
Force due to pressure
Centripidal
3
“Kinds” of Forces
(forces that we talked about in class)
•
•
•
•
•
•
•
person’s force (pushing or pulling)
gravity
spring force
normal force: force perpendicular to a surface
friction: force tangent, or parallel, to a surface
fluid pressure (times area)
tension (of a rope)
4
“Kinds” of Forces
(forces that we talked about in class)
•
•
•
•
•
•
•
person’s force (pushing or pulling)
gravity
spring force
normal force: force perpendicular to a surface
friction: force tangent, or parallel, to a surface
fluid pressure (times area)
tension (of a rope)
However: this is not a very insightful or even useful classification of
forces; it merely summarizes some of the forces we’ve dealt with.
5
The Four Fundamental Forces
}
}
and Unifications Leading Thereto and Therefrom
}
Electric force Electromagnetic
Magnetic force}
(the) Weak force
Interplanetary
Gravitational
Apples on earth
(the) Strong force
}
today’s subject
Electroweak
interaction
GUT ?
(grand
unified
theory)
Theory of Everything ?: BIG GUT = GUT + Gravity,
explains all forces as aspects of a single
interaction theory
6
Frictions is
A)
B)
C)
D)
Gravity
Electromagnetic
The Weak Force
The Strong Force
7
Frictions is
A)
B)
C)
D)
Gravity
Electromagnetic
The Weak Force
The Strong Force
8
Pulling on a string is
A)
B)
C)
D)
Gravity
Electromagnetic
The Weak Force
The Strong Force
9
Pulling on a string is
A)
B)
C)
D)
Gravity
Electromagnetic
The Weak Force
The Strong Force
10
The spring force is
A)
B)
C)
D)
Gravity
Electromagnetic
The Weak Force
The Strong Force
11
The spring force is
A)
B)
C)
D)
Gravity
Electromagnetic
The Weak Force
The Strong Force
12
The buoyancy force is
A)
B)
C)
D)
Gravity
Electromagnetic
The Weak Force
The Strong Force
13
The buoyancy force is
A)
B)
C)
D)
Gravity
Electromagnetic
The Weak Force
The Strong Force
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• Except for gravity, all of the “kinds” of forces we
draw in force diagrams are due to the
 Electromagnetic force (mostly electric)
•
•
•
•
•
•
friction
tension
fluid pressure
normal force
“pushing” force
spring force
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Lennard-Jones Potential
Force ~ - slope
V
All “contact” forces
(spring force, friction,
water pressure, etc)
are a result of molecules
“pushing” or “pulling”
against each other. They
are all due to the
Lennard-Jones potential.
r
This force is
ELECTROSTATIC
r
16
The electric force
Electric charge comes in two “flavors”: it can be positive
or negative. Pick the statement that best characterizes
the “direction” of the electric force:
A.
B.
C.
D.
Like charges attract (each other); opposites attract
Like charges repel; opposite charges attract
Like charges attract; opposite charges repel
Like charges repel; opposite charges repel
17
The electric force
Electric charge comes in two “flavors”: it can be positive
or negative. Pick the statement that best characterizes
the “direction” of the electric force:
A.
B.
C.
D.
Like charges attract (each other); opposites attract
Like charges repel; opposite charges attract
Like charges attract; opposite charges repel
Like charges repel; opposite charges repel
Answer: B. For example, two electrons would
accelerate away from each other, and two protons
would accelerate away from other, but an electron and
a proton would accelerate toward each other (electrons
have negative charge, protons are positive).
+
+
-
-
+
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Elementary Charge
• Animal hair (wool, fur) likes to acquire a positive
charge from (or give up a negative charge to)
rubber
• Silk likes to acquire a negative charge from (or
give up a positive charge to) glass
• Where do the charges come from?
All macroscopic charges are integer multiples of the electron
(negative) or proton (positive) charge.
Amounts of charge are measured in Coulombs (C).
A proton has a charge 1.60 x 10-19 C; an electron has a charge
-1.60 x 10-19 C. That is, 6.25 x 1018 protons make 1 C of
charge; 1 C is a lot of charge.
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Charge Conservation
• Although neither electrons nor protons are
conserved (both can be created and destroyed) the
TOTAL CHARGE IS ALWAYS CONSERVED.
• Just as energy and momentum conservation allow us
to solve otherwise difficult problems, so charge
conservation will allow us to solve some tough
problems.
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Calculating gravitational and electric forces
• Gravitational force between two masses,
m1 and m2, separated by distance r:
m2
m1
r
F1on 2,g
m1m2
=G 2
r
“Newton’s Law of Gravitation”
G = 6.67 x 10-11 N m2/kg2
• Electric force between two charges, q1 and
q2, separated by distance r:
!
q2
q1
r
+
+
-
-
+
-
F1on 2,e
q1q2
=k 2
r
“Coulomb’s Law”
k = 8.99 x 109 N m2/C2
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Aside: Inverse-Square Laws
Both the electric and gravitational forces obey inverse-square
laws:
F∝1/r2 -- the force (of one mass or charge on another) is
proportional to the inverse square of the distance (between
them).
Most important: the force diminishes with distance
Second most important: doubling the distance quarters the
force
Inverse-square laws reflect the three-dimensionality of our
universe: the area of a 3D sphere of radius r is A = 4πr2 ∝ r2 .
“Stuff” spreading out in 3 dimensions obeys an inverse-square
law.
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Inverse-Square Laws
A special spray-paint nozzle sprays
equally in all directions. In 1 min., it
paints a 1mm thick coat on the inside
surface of a sphere of radius 1 m.
How thick would the paint be if the
sphere had a 2 m radius?
2
Area
of
sphere
=
4πr
A. 1/8 mm
B. 1/4 mm
C. 1/2 mm
D. 1 mm
E. 2 mm
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Inverse-Square Laws
A special spray-paint nozzle sprays
equally in all directions. In 1 min., it
paints a 1mm thick coat on the inside
surface of a sphere of radius 1 m.
How thick would the paint be if the
sphere had a 2 m radius?
2
Area
of
sphere
=
4πr
A. 1/8 mm
B. 1/4 mm B. The 2 m sphere has 4 times the area (A ∝ r2) of the
1 m sphere, but receives the same TOTAL amount of
C. 1/2 mm paint in the same time; therefore, the paint must be 1/4
D. 1 mm
as thick. After 1 min. of spraying, the thickness of
2 -- an inversepaint
on
a
sphere
of
radius
r
varies
as
1/r
E. 2 mm
square law. “Stuff” spreading out in 3 dimensions obeys
an inverse-square law (e.g., light and sound intensity).
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Calculating gravitational and electric forces
between two protons: Clicker Question
m1m2
F1on 2,g = G 2
G = 6.67 x 10-11 N m2/kg2
r
• Electric force: F1on 2,e = k q1q2 2
k = 8.99 x 109 N m2/C2
r
1
2
Each proton (shown left) has
!
F1on 2,g
F1on 2,e
mass m = 1.67 x 10-27 kg and
q,m
q,m
-19 C.
charge
q
=
1.60
x
10
!
Considering the electric force Fe and
r=1 mm
gravity Fg, will two protons separated
!
!
by r = 1mm be attracted or repelled?
• Gravitational:
What is the ratio of strengths, Fe/Fg ?
kqq
Fe
r2
=
Gmm
Fg
r2
kq2
(8.99 "109 Nm2 /C2 )(1.60 "10#19 C)2
=
=
= 1.24 "1036
2
#11
2
2
#27
2
Gm
(6.67 "10 Nm /kg )(1.67 "10 kg)
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The Electric Force is much, much stronger
than Gravity (comparing protons). Why then,
is gravity so much more noticeable?
A gravity deals with much larger bodies
B depends on difference in charge
C gravity does not have a positive and negative
D
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The Electric Force is much, much stronger
than Gravity (comparing protons). Why then,
is gravity so much more noticeable?
The attraction between positive and negative charges
is so strong that positive and negative charges tend to
clump together, canceling each other out. For example,
atoms:
-
+
+
+ +
++
-
-
A carbon atom:
A nucleus with 6 protons
(and 6 neutrons), with
6 electrons.
Net charge: zero
Nature abhors a charge imbalance
(because net charges produce strong forces on each other)
Note: the Strong Force holds the nucleus together; over very short distances, the
Strong Force is stronger than the electric force.
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Charge “clumping” reduces electric force
A positive and negative charge close together
constitute an electric “dipole”; single charges are
“monopoles”.
Dipoles do not obey the inverse square law; the
force a dipole exerts on a charge (or on another
dipole) falls off with distance much faster than
1/r2
This will be important in magnetostatics, because
there are no magnetic “monopoles”; only dipoles.
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Dipole forces fall off much faster than 1/r2
An insulator does not allow charges to move
within it; in an insulator, charges cannot move.
+
+
-
An insulator (above, right) has equal and opposite charges
placed on each end. A positive charge (above, left) is
placed at a large distance from the insulator:
A. The insulator will be attracted to the charge.
B. The insulator will be repelled by the charge.
C. Neither of the above
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Dipole forces fall off much faster than 1/r2
+
+
-
An insulator (above, right) has equal and opposite charges
placed on each end. A positive charge (above, left) is
placed at a large distance from the insulator:
A. The insulator will be attracted to the charge.
B. The insulator will be repelled by the charge.
C. Neither of the above
Answer: C. Because the charge on the left is far from the dipole,
forces of the external charge on the positive and negative parts
of the insulator are almost equal and opposite.
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What does “far away” mean?
How far away do you have to be for the
force to be negligible?
•
•
•
•
A inverse square
B REALLY far
C much farther than the size of the dipole
D
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Dipole forces fall off much faster than 1/r2
+
+
-
An insulator (above, right) has equal and opposite charges
placed on each end. A positive charge (above, left) is
placed at a large distance from the insulator:
A. The insulator will be attracted to the charge.
B. The insulator will be repelled by the charge.
C. Neither of the above
Answer: C. Because the charge on the left is far from the dipole
COMPARED TO THE SIZE OF THE DIPOLE, forces of the
external charge on the positive and negative parts of the insulator
are almost equal and opposite.
32
Clicker Question
A conductor allows charges to move freely
within it; in a conductor, charges move freely.
+
+-
Suppose a conductor has two equal and opposite charges;
they can move freely, so they attract each other until
they’re almost in the same place.
When a positive charge is brought close to the conductor
from the left:
A. The conductor will be attracted to the charge.
B. The conductor will be repelled by the charge.
C. Neither of the above
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Clicker Question
A conductor allows charges to move freely
within it; in a conductor, charges move freely.
+
+-
Suppose a conductor has two equal and opposite charges;
they can move freely, so they attract each other until
they’re almost in the same place. When a positive charge
is brought close to the conductor from the left:
A. The conductor will be attracted to the charge.
B. The conductor will be repelled by the charge.
C. Neither of the above
The external charge
-+
+
“polarizes” the conductor:
Answer: A. Because the conductor has zero net charge, the net force on it will be small;
however, since the charges are free to move within the conductor, the positive charge will
be repelled slightly, while the negative charge will be attracted. Since the distance
between the negative charge and the external charge is less than that between the positive
charge and the external charge, the negative charge is attracted more strongly than the
positive charge is repulsed (c.f. Coulomb’s Law). Therefore, the conductor experiences a
net force toward the left.
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Magnetostatics
Magnetic poles are like electric charges
a) Attract
b) Repel
c) Have no effect on each
other
N
S
N
If they are close together,
the two magnets to the
right will
S
•
The correct answer is (b), like poles repel each other,
and the two south poles are closest, so their forces
are the most important
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Many similarities with electric forces
• Like poles repel
• Opposite poles attract
• Force grows weaker at greater
distances
• Some choice of sign: + pole =
north pole = pole that seeks
the north
N
S
Exception: magnetic poles always come in pairs!
Cut a magnet, get two magnets, each with a
north and south pole.
THERE IS NO MAGNETIC MONOPOLE
N
N
S
S
N
S
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The earth is one big magnet
Is the north pole of the earth a magnetic
a) North pole
b) South pole
c) Neither
The correct answer is (b), north poles of magnets are
attracted to the north of the earth, so the north pole of
the earth is the south pole of the magnet earth.
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Magnetic poles are like electric charges
HOWEVER:
•
•
There is no magnetic “monopole”. All magnets
come with both poles.
Forces between magnets are therefore very
small, unless magnets are “close” together
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What do we mean by “close”?
How close do magnets have to be for the
magnetic force to be significant.
•
•
•
•
A REALLY close
B closer than 1/r2
C as close as the magnet is big
D
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At large distances, magnetic forces
decrease more rapidly than inverse square
• On left: Upper north pole
really close to lower south
pole. Feels only that force.
• On right: Upper north pole
and upper south pole about
same distance from lower
south pole, so 1/r2 forces
cancel, force less than 1/r2
S
N
S
N
S
N
THAT’S BECAUSE MAGNETIC POLES ALWAYS COME IN PAIRS
S
N
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Magnetic materials: poles “move” by
attractive force (like charges in conductors)
• Iron, nickle,
cobalt, other
elements (rareearth ceramics)
• Extends the
magnet
S
S
N
N
N
N
S
S
Neutral bar
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Why are some magnets made in the shape
of a horseshoe?
a) Because that shape is
known to give good luck
b) Gives extra pickup power
S
N
because poles move around
S
N
in the item to pick up
c) Bringing the poles of the b) The north pole attracts
the south poles in the
horseshoe together
intensifies the magnetic medium, but it also helps
repel more north poles to
field
the other end where they
are attracted by the south
pole of the horseshoe
magnet
42
Currents produce magnetic fields in
direction per right-hand rule
• Wrap fingers
around in direction
of coil current
• Your thumb is the
north pole
North pole
Current
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Permanent magnets: the spinning
electrons line up
N
N
N
N
N
N
N
N
N
N
N
N
• Electrons have negative
charge, so opposite of
right-hand rule
• Ferromagnetic material:
spinning electrons line
up
• Non magnetic material:
other forces prevent
alignment
44
The earth has a magnetic south pole at its
geographic north pole
The currents flowing inside
the earth flow
a) from west to east
b) from east to west
c) from north to south
d) from south to north
N
(b) From east to west so that the right hand
rule gives the thumb going out the south pole
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Motors can use permanent magnets and
electromagnets
• Linear motor
N
• Turn on attraction in
front
• Turn on repulsion behindS
• After moves, change
coils to keep going
• Usual motor: put into
circle
S
N
S
N
SN
SN
S
N
S
S
N
N
S
N
46
Electromagnetic induction - moving
magnets (or changing magnetic fields)
cause currents to flow, magnetization
• Moving electric charges cause
magnetic fields (Oersted,
Ampere, 1820)
• Moving magnetic poles cause
electric fields (Faraday, 1831)
= Induction
Induction is how we produce all
our electricity (except batteries)
Rising current, counter
clockwise from top
Metal block
Causes current in metal
that is clockwise from top
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Lenz’s law: Current induced by a changing
magnetic field always produces a magnetic
field that opposes the change
• Produces opposite
current
• Opposite magnetic
fields
• NOT magnetization
North pole
Current
S
N
Current
Induced current
North pole
Induced north pole48
Summary
• Electric and magnetic forces similar
• Electric charge comes in monopoles,
magnetic poles only in dipoles
• Currents produce magnetic fields
• Changing magnetic fields produce currents
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