Download Magnetic Fields and Forces

Circuits revision
• Here’s the circuit for the
flashing neon bulb.
• What is the period of the
flash in seconds ?
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Magnetic Fields revision
Please try problem 15 in Ch 24 on page 825.
“What is the magnetic field at the center of the
loop….”
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Magnetic Fields and Forces
•
Magnetism
•
Magnetic field shapes and direction
•
Fields near electric currents
•
Magnetic forces
•
Moving charges and magnetism
•
Magnetic machines
•
Magnetic materials
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Magnetism
• Fundamental force of nature
• Related to electricity, but not the same
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Experimental Observations
• Magnetism does not move an electroscope, it
does not act on stationary charges
• Long range force (action over a distance)
• There are 2 poles, north and south, and they
come in pairs
• Like poles repel, unlike poles attract
• Poles attract magnetic materials
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Magnetic Field lines
• Magnetic Fields around
a bar magnet
• Similar to an electric
dipole
• Start at north pole,
terminate at south pole
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Like and unlike poles
Magnetic field lines between poles
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Electric Currents and Magnetic
Fields
Oersted found that a current can move a
magnetic compass
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Direction of Magnetic field
We use the right handed rule to find which
way a magnetic compass would point
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Magnetic field near a loop
• Bend the wire into a loop.
• Dots - field is coming out of the page.
• Crosses - field is going in to the page
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Field near a solenoid
• Many loops will concentrate the field inside
the coil
• Called a solenoid – contains a uniform
magnetic field
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Magnetic field due to a current
Experimentally, the field strength, B, is proportional to
current, I, and inversely proportional to distance, r.
0 I
B
2r
Units of Tesla, where μ0 is the permeability
constant – 1.257x10-6 TmA-1
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Tesla is a large unit
• Magnets in the lab – 0.1 to 1 T
• Kitchen magnets – 5x10-3 T
• Earths magnetic field – 5x10-5 T
• Superconducting magnets – in accelerators
and maglev trains – 10 T
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Magnetic Field at the center of a
current loop
Inside a loop radius R:
B
0 I
2R
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Magnetic Field at the center of a
current loop with N turns
If the loop has N turns,
but its not yet a
solenoid we have:
B
0 NI
2R
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Magnetic field inside a solenoid
The uniform field in a
solenoid is
N
B  0 I
L
For a solenoid with N turns, Length L and current I.
Note: independent of the coil radius. Field is uniform.
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Magnetic Forces
• The magnetic fields
around two wires will
attract or repel, just like
bar magnets.
• A magnetic field exerts a
force on a current, or
moving charge
• Currents in the same
direction attract
• Opposite currents repel
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Direction of Magnetic Force
• The force on a
wire with a
current is
perpendicular to
both the
magnetic field the
direction of the
current.
• We use another
right hand rule
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Magnitude of the Magnetic Force
The force between a magnetic field and a
current along a wire length L perpendicular
to the field is:
F  ILB
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Magnitude of the Magnetic Force
The force between a magnetic field and a current along
a wire length L at an angle, α to the field is:
F  ILB sin 
If the current and B field are parallel – there is no force.
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Force on a moving charge
• A current, I, is a
moving charge.
• The charge q moves
along the wire length
L in time Δt
• The velocity will be
L/Δt
• We find that qv=IL
L
v
t
q qv
I

t L
IL  qv
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Magnitude of the Magnetic Force
The force between a magnetic field and a
charge, q, moving with a velocity, v
perpendicular to the field is:
F  qvB
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Magnitude of the Magnetic Force
The force between a magnetic field and a charge, q,
moving at velocity, v, at an angle, α to the field is:
F  qvB sin 
If the moving charge and B field are parallel – there is no
force.
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Direction of Magnetic Force
• The force on a moving
charge is
perpendicular to both
the magnetic field the
direction of the
charge.
• Note the thumb is now
the direction of the
+ve charge, instead of
the current I.
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Path of charges in a magnetic field
• The force on a
charged particle in a
magnetic field is
perpendicular to its
direction of motion.
• We always get
circular or spiral
paths of charged
paths in a magnetic
field
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Path of charges in a magnetic field
• Centripetal force of
an object in a circle
2
mv
F
 qvB
r
RqB
v
m
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Path of charges in a magnetic field
• If we accelerated the ions
in an electric field V, the
charge to mass ratio can
be measured,
1 2
E  qV  mv
2
q
2V
  2 2
m B R
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Mass spectrometer
• First
measurement of
e/m for the
electron
• Used to
distinguish
different types of
atoms and
isotopes
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Aurora Borealis
• Solar wind from the sun
(protons & electrons)
gets deflected by Earth’s
magnetic field.
• Portion of velocity
perpendicular to the field
lines, curves the ionizing
particles into spirals
• Ionize O2 and N2 in the
ionosphere
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Magnetic forces between currents
• Consider two wires
carrying currents I1 and
I2.
• The field at the top wire
is
I
B2 
0 2
2d
F12  B2 I1 L
 0 LI1 I 2
F12 
2d
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Magnetic forces between currents
From the field from the single wire, we can
deduce the force between 2 wires carrying
currents I1 and I2 is
0 LI1I 2
Fparallel wires 
2d
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Torques and Magnetic Moments
• Torque was defined in chapter 7
• Quantity to measure the force applied near a
pivot
• Useful for calculating rotational motion
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Torque
Torque, τ, measures
the effectiveness of a
force at causing an
object to rotate about
a pivot
  rF sin 
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Torque on a current loop in a B
field
• Current loop in a
uniform field
• The forces on the top
and bottom wires will
rotate the loop
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Torque on a current loop in a B
field
• The total torque, τ, will
be the sum of the
torques on the top and
bottom wires.
• Loop height L, wire
length W
L
  2 F sin 
2
 BIWL sin 
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Torque on a current loop in a B
field
•In general, the torque on
a loop area A will be:
  IAB sin 
The loop is forced to align with
the magnetic field
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Using torque - MRIs
• Magnetic Resonance
Imaging (MRI) uses
the protons magnetic
moment in hydrogen
atoms in high 1T
fields.
• The rate of the emitted
radio waves from the
excited states are
detected
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Using Torque – Electric motor
Using commutators, the loop can be made to
spin, to produce rotational movement
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Permanent Magnets Ferromagnetism
• Ferromagnetism is a property of certain
elements – the ability to maintain a
permanent magnetic field
• Depends on the crystalline structure of the
metal
• Found in alloys of iron, cobalt, nickel,
gadolinium, dysprosium, europium
• Half full electron shells, the magnetic dipole of
the electrons can align
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Periodic Table
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Crystalline structure aligned
• The magnetic
dipoles are grouped
in micron size
crystals, domains
• The dipoles can be
aligned by applying
a magnetic field
• Can be destroyed
by heating (Curie
point) or dropping
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Electromagnets
• An iron core near a
solenoid will align the
domains inside the iron
• This increases the
magnetic field (factor of
100)
• Used to amplify the
magnetic field
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Summary
•
Magnetism
•
Magnetic field shapes and direction
•
Fields near electric currents
•
Magnetic forces
•
Moving charges and magnetism
•
Magnetic machines
•
Magnetic materials
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Homework problems
Chapter 24 Problems
20, 21, 31, 41, 48, 53, 56, 57
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