General%20Physics%20(PHY%202140)

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General Physics (PHY 2140)
Lecture 12

• Electricity and Magnetism
• Magnetism
• Magnetic fields and force
• Application of magnetic forces

http//www.physics.wayne.edu/apetrov/PHY2140/
Chapter 19
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Department of Physics and Astronomy announces the
Fall 2003 opening of The Physics Resource
Center on Monday, September 22 in Room 172 of
Physics Research Building.
Hours of operation Mondays, Tuesdays,
Wednesdays 11 AM to 6
PM Thursdays and Fridays 11 AM to 3
PM Undergraduate students taking PHY2130-2140
will be able to get assistance in this Center
with their homework, labwork and other issues
related to their physics course. The Center
will be open Monday, September 22 to Wednesday,
December 10, 2003.
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Lightning Review

• Last lecture
• DC circuits
• Kirchoffs rules
• RC circuit
• Magnetism
• Magnets

Review Problem The three light bulbs in the
circuit all have the same resistance. Given that
brightness is proportional to power dissipated,
the brightness of bulbs B and C together,
compared with the brightness of bulb A, is 1.
twice as much. 2. the same. 3. half as much.
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Last lecture Magnetic Field

• Convenient to describe the interaction at a
  distance between magnets with the notion of
  magnetic field.
• Magnetic objects are surrounded a magnetic field.
• Moving electrical charges are also surrounded by
  a magnetic field (in addition to the electrical
  field).
• A vector quantity magnitude and direction
• The letter B is used to represent magnetic
  fields.

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Magnetic Field Direction

• The magnetic field direction (of a magnet bar)
  can studied with a small compass.

1
S
N
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Magnetic Field Lines
1
S
N
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Applications A bit of history

• IBM introduced the first hard disk in 1957, when
  data usually was stored on tapes. It consisted of
  50 platters, 24 inch diameter, and was twice the
  size of a refrigerator.

It cost 35,000 annually in leasing fees (IBM
would not sell it outright). Its total storage
capacity was 5 MB, a huge number for its time!
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Magnetic Field of the Earth

• A small magnetic bar should be said to have north
  and south seeking poles. The north of the bar
  points towards the North of the Earth.
• The geographic north corresponds to a south
  magnetic pole and the geographic south
  corresponds to a magnetic north.
• The configuration of the Earth magnetic resemble
  that of a (big) magnetic bar one would put in its
  center.

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Magnetic Field of the Earth
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Magnetic Field of the Earth

• Near the ground, the field is NOT parallel to the
  surface of the Earth.
• The angle between the direction of the magnetic
  field and the horizontal is called dip angle.
• The north and south magnetic pole do not exactly
  correspond to the south and north geographic
  north.
• South magnetic pole found (in 1832) to be just
  north of Hudson bay in Canada 1300 miles from
  the north geographical pole.

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More on the Magnetic Field of the Earth

• The difference between the geographical north and
  the direction pointed at by a compass changes
  from point to point and is called the magnetic
  declination.
• Source of the field charge-carrying convection
  currents in the core of the earth.
• In part related to the rotation of the earth
• The orientation of the field flips and changes
  over time every few million years
• Basalt rocks
• Other planets (e.G. Jupiter) are found to have a
  magnetic field.

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Mini-quiz

• You travel to Australia for a business trip and
  bring along your American-made compass. Does the
  compass work correctly in Australia???

• No problem using the compass in Australia.
• North pole of the compass will be attracted to
  the South geographic pole
• The vertical component of the field is different
  (opposite) but that cannot be detected with
  normal operation of the compass.

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19.3 Magnetic Fields

• Stationary charged particles do NOT interact with
  a magnetic field.
• Charge moving through a magnetic field experience
  a magnetic force.
• Value of the force is maximum when the charge
  moves perpendicularly to the field lines.
• Value of the force is zero when the charge moves
  parallel to the field lines.

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Magnetic Fields in analogy with Electric Fields

• Electric Field
• Distribution of charge creates an electric field
  E(r) in the surrounding space.
• Field exerts a force Fq E(r) on a charge q at r
• Magnetic Field
• Moving charge or current creates a magnetic field
  B(r) in the surrounding space.
• Field exerts a force F on a charge moving q at r

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Strength of the Magnetic Field

• Define the magnetic field, B, at a given point in
  space in terms of the magnetic force imparted on
  a moving charge at that point.
• Observations show that the force is proportional
  to
• The field
• The charge
• The velocity of the particle
• The sine of the angle between the field and the
  direction of the particles motion.

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Strength and direction of the Magnetic Force on a
charge in motion
F
B
q
v
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Magnetic Field Magnitude
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Magnetic Field Units

• F newton
• v m/s
• q C
• B tesla (T).
• Also called weber (Wb) per square meter.
• 1 T 1 Wb/m2.
• 1 T 1 N s m-1 C-1.
• 1 T 1 N A-1 m-1.
• CGS unit is the Gauss (G)
• 1 T 104 G.

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Right Hand Rule

• Provides a convenient trick to remember the
  spatial relationship between F, v, and B.
• Consider the motion of positive charge
• Direction of force reversed if negative charge.

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Example Proton traveling in Earths magnetic
field.

• A proton moves with a speed of 1.0 x 105 m/s
  through the Earths magnetic field which has a
  value of 55 mT a particular location. When the
  proton moves eastward, the magnetic force acting
  on it is a maximum, and when it moves northward,
  no magnetic force acts on it. What is the
  strength of the magnetic force? And what is the
  direction of the magnetic field?

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19.4 Magnetic Force on Current-carrying conductor.

• A magnetic force is exerted on a single charge in
  motion through a magnetic field.
• That implies a force should also be exerted on a
  collection of charges in motion through a
  conductor I.e. a current.
• And it does!!!
• The force on a current is the sum of all
  elementary forces exerted on all charge carriers
  in motion.

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19.4 Magnetic Force on Current
x x x x x x x x x x x x x
x x x x x x x x x x x

• If B is directed into the page we use blue
  crosses representing the tail of arrows
  indicating the direction of the field,
• If B is directed out of the page, we use dots.
• If B is in the page, we use lines with arrow
  heads.

. . . . . . . . . . . . .
. . . . . . . . . . .
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• Force on a wire carrying current in a magnetic
  field.

Bin
x x x x x x x x x x x x x
x x x x x x x x x x x
x x x x x x x x x x x x x
x x x x x x x x x x x
x x x x x x x x x x x x x
x x x x x x x x x x x
Bin
Bin
I
I 0
I
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Force on a wire carrying current in a magnetic
field.
x x x x x x x x x x x x
x x x x x x x x x x x x x
x x x x x x x x x x x x x
x x x x
vd
q
A
Magnetic Field and Current at right angle from
each other.
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Force on a wire carrying current in a magnetic
field.

• General Case field at angle q relative to
  current.

B
B sin q
q
I
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Voice Coil
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Mini-Quiz

• In a lightning strike, there is a rapid flow of
  negative charges from a cloud to the ground. In
  what direction is a lightning strike deflected by
  the Earths magnetic field?

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Example Wire in Earths B Field

• A wire carries a current of 22 A from east to
  west. Assume that at this location the magnetic
  field of the earth is horizontal and directed
  from south to north, and has a magnitude of 0.50
  x 10-4 T. Find the magnetic force on a 36-m
  length of wire. What happens if the direction of
  the current is reversed?

B0.50 x 10-4 T. I 22 A l 36 m Fmax BIl
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19.5 Torque on a Current Loop

• Imagine a current loop in a magnetic field as
  follows

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I
F
B
B
F
a/2
b
F
F
a
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In a motor, one has N loops of current
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Example Torque on a circular loop in a magnetic
field
30.0o

• A circular loop of radius 50.0 cm is oriented at
  an angle of 30.0o to a magnetic field of 0.50 T.
  The current in the loop is 2.0 A. Find the
  magnitude of the torque.

B
r 0.500 m q 30o B 0.50 T I 2.0 A N 1
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19.6 Galvanometer/Applications

• Device used in the construction of ammeters and
  voltmeters.

Scale
Current loop or coil
Magnet
Spring
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Galvanometer used as Ammeter

• Typical galvanometer have an internal resistance
  of the order of 60 W - that could significantly
  disturb (reduce) a current measurement.
• Built to have full scale for small current 1 mA
  or less.
• Must therefore be mounted in parallel with a
  small resistor or shunt resistor.

60 W
Galvanometer
Rp
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60 W
Galvanometer
Rp

• Lets convert a 60 W, 1 mA full scale
  galvanometer to an ammeter that can measure up to
  2 A current.
• Rp must be selected such that when 2 A passes
  through the ammeter, only 0.001 A goes through
  the galvanometer.

• Rp is rather small!
• The equivalent resistance of the circuit is also
  small!

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Galvanometer used as Voltmeter

• Finite internal resistance of a galvanometer must
  also addressed if one wishes to use it as
  voltmeter.
• Must mounted a large resistor in series to limit
  the current going though the voltmeter to 1 mA.
• Must also have a large resistance to avoid
  disturbing circuit when measured in parallel.

Rs
60 W
Galvanometer
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Maximum voltage across galvanometer
Suppose one wish to have a voltmeter that can
measure voltage difference up to 100 V
Large resistance
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19.7 Motion of Charged Particle in magnetic field
Bin

• Consider positively charge particle moving in a
  uniform magnetic field.
• Suppose the initial velocity of the particle is
  perpendicular to the direction of the field.
• Then a magnetic force will be exerted on the
  particle and make follow a circular path.

r
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The magnetic force produces a centripetal
acceleration.
The particle travels on a circular trajectory
with a radius
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Example Proton moving in uniform magnetic field

• A proton is moving in a circular orbit of radius
  14 cm in a uniform magnetic field of magnitude
  0.35 T, directed perpendicular to the velocity of
  the proton. Find the orbital speed of the proton.

r 0.14 m B 0.35 T m 1.67x10-27 kg q 1.6
x 10-19 C