Magnetism

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Magnetism
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MagneticDipole
Magnetic Field (B)
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Magnetic Monopoles

• Do not exist!
• They differ from electric dipoles, which can be
  separated into electric monopoles.

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Magnetic Force on Charged Particle

• magnitude F qvBsin?
• q charge in Coulombs
• v speed in meters/second
• B magnetic field in Tesla
• ? angle between v and B
• direction Right Hand Rule

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Magnetic Force
Calculate the magnitude and direction of the
magnetic force.
v 300,000 m/s
34o
q 3.0mC
B 200 mT
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Magnetic Fields

• Formed by moving charge
• Affect moving charge

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Magnetic Field Visualization
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3D Magnetic Field Visualization
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3D Magnetic Field Visualization
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3D Magnetic Field Visualization
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Magnetic Forces can...

• accelerate charged particles by changing their
  direction
• cause charged particles to move in circular or
  helical paths

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Magnetic Forces cannot...

• change the speed or kinetic energy of charged
  particles
• do work on charged particles

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When v and B are at right angles to each other...

• qvBsin? mv2/r
• qB mv/r
• q/m v/(rB)

x into out
q is
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When v and B are at right angles to each other...
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Practice With Directions
What is the direction of the force F on the
charge in each of the examples described below?
negative q
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Circular Paths in Magnetic Field Fmagnetic
Fcentripetal
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Electron Beam in Magnetic Field
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Electric and Magnetic Fields Together
v E/B
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Magnetic Force on Current-carrying Wire

• F I L B sin?
• I current in Amps
• L length in meters
• B magnetic field in Tesla
• ? angle between current and field

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MAGNETIC FIELD PRODUCED BY CURRENT CARRYING WIRE
A long, straight current carrying wire produces a
magnetic field.
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Magnetic Field forLong Straight Wire

• B µoI/(2pr)
• µo 4p x 10-7Tm/A
• magnetic permeability of free space
• I current (A)
• r radial distance from center of wire (m)

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Hand Rule
i

• Curve your fingers
• Place your thumb in direction of current.
• Curved fingers represent curve of magnetic field.
• Field vector at any point is tangent to field
  line.

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For straight currents
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Principle of Superposition
When there are two or more currents forming a
magnetic field, calculate B due to each current
separately and then add them together using
vector addition.
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Force Between Current Carrying Wires
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Magnetic Field Inside aSolenoid

• B µonI
• µo 4p x 10-7Tm/A
• n number of coils per unit length
• I current (A)

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Lab Magnetic Field Map

• Using a compass, map the magnetic field inside
  and outside your solenoid. Show
• Current through solenoid
• Connection to DC outlet
• Field lines mapped with compass
• Edge effects (What happens to those field lines
  farther away from the solenoid?)
• North and South Poles of solenoid

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Lab EvaluationMagnetic Field MapA) Are field
lines visible in the core of the solenoid?B)
Are the directions of the field lines in the core
consistent with the Right Hand Rule?C) Are the
North and South Poles correctly identified?
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Magnetic Flux

• The product of magnetic field and area.
• Can be thought of as a total magnetic effect on
  a coil of wire of a given area.

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Magnetic flux
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Magnetic Flux

• ?B BAcos?
• ?B magnetic flux in Webers
• (Tesla meters2)
• B magnetic field in Tesla
• A area in meters2.
• ? the angle between the area and the magnetic
  field.

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Magnetic Flux

• A system will respond so as to oppose changes in
  magnetic flux.
• Changing the magnetic flux can generate
  electrical current.

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A Change in Flux
By changing the field strength B going through a
constant loop area A ?F ?B A
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A Change in Flux
By changing the effective area A in a constant
magnetic field B ?F B ?A
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Faradays Law of Induction

• E -N?B/?t
• E induced potential (V)
• N loops
• ?B magnetic flux (Webers, Wb)
• t time (s)

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A closer look

• E -??B/?t
• E -?(BAcos?)/?t
• To generate voltage
• Change B
• Change A
• Change ?

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Lenzs Law

• The current will flow in a direction so as to
  oppose the change in flux.
• Use in combination with hand rule to predict
  current direction.

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(a) As the magnet moves to the right, ?B
increases. (b) To oppose increased ?B , the
induced B must be opposite to that of the bar
magnet. The induced I must be CCW
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When N of magnet is pushed into a loop the ?B?.
Upward B is induced. As viewed from above, the
induced current must flow CCW
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When N of magnet is pulled away from loop the
?B?. Downward B is induced. As viewed from
above, the induced current must flow CW
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Motional emf

• E B L v
• E induced potential
• L length of bar or wire
• V speed of bar or wire

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Induced EMF
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Induced EMF
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2002B5 p.49
A proton of mass mp and charge e is in a box that
contains an electric field E, and the box is
located in Earth's magnetic field B.The proton
moves with an initial velocity vertically upward
from the surface of Earth. Assume gravity is
negligible.
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2002B5 p.49
(a) On the diagram, indicate the direction of the
electric field inside the box so that there is no
change in the trajectory of the proton while it
moves upward in the box. Explain your reasoning.
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2002B5 p.49
(b) Determine the speed v of the proton while in
the box if it continues to move vertically
upward. Express your answer in terms of the
fields and the given quantities.
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2002B5 p.49
The proton now exits the box through the opening
at the top. (c) On the figure, sketch the path of
the proton after it leaves the box.
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2002B5 p.49
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2002B5 p.49
(d) Determine the magnitude of the acceleration a
of the proton just after it leaves the box, in
terms of the given quantities and fundamental
constants.
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1978B4 p.51
Two parallel conducting rails, separated by a
distance L of 2 m, are connected through a
resistance R of 3 O as shown. A uniform magnetic
field with a magnitude B of 2 T points into the
page. A conducting bar with mass m of 4 kg can
slide without friction across the rails.
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1978B4 p.51
(a) Determine at what speed the bar must be
moved, and in what direction, to induce a ccw
current I of 2 A as shown.
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1978B4 p.51
(b) Determine the magnitude and direction of the
external force that must be applied to the bar to
keep it moving at this velocity.
(c) Determine the rate at which heat is being
produced in the resistor and determine the
mechanical power being supplied to the bar.
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1978B4 p.51
(d) Suppose the external force is suddenly
removed from the bar. Determine the energy in J
dissipated in the resistor before the bar comes
to rest.