Download Magnetic Fields

Magnetism: Force and Field
General Characteristics
• Like poles repel
• Unlike poles attract
N
S
• You can never isolate a
north pole from a south
pole.
N
S
N
S
S
N
Earth’s Magnetic
Field
• North pole of compass is attracted to the north. Therefore,
the north pole is a magnetic south pole.
• Measurements have indicated that the earth’s magnetic
field is decreasing.
• There is evidence of pole reversal at the mid-Atlantic
ridge.
S
N
Earth’s Magnetic
Field
• Barnes noticed a 5%
reduction in the earth’s
magnetic field in 130
yrs.
• Reversing Magnetic
Field recorded in the
earth’s crust.
• Humphreys proposes
rapid reversals due to
the flood.
Unique Earth
• Stable sun
• Nearly circular
orbit
• Water present in 3
phases
• Magnetic field
• Ozone
• Nitrogen
atmosphere
• Probability
– 1069 to 1
Magnetic Force
• Magnetic fields exert forces on moving
charges.



FB  qv  B
• Magnitude of the force is given by
F  qvB sin 
• Direction of the force is determined by the
right-hand rule.
• Units - Wb/m2 or T
(1T = 104G)
Force on a proton
• Ex. What is the force on a proton traveling
60° with respect to a uniform magnetic field
of 2.5 tesla at half the speed of light?
19
F  (1.6 10 C )(1.5 10 m / s)(2.5T ) sin 60
F  5.2 10 11 N
8
Only the perpendicular
component of the velocity
produces a magnetic force.
Will move in a helix.
Velocity Selector
• Lorentz
 Force



F  qE  qv  B
E
• When F = 0 and
  
v EB
p+
then
E
v
B
B
Mass Spectrometer
• When the velocity is known, then the mass
is known by the charge and radius of
mv
r
curvature in a B field.
qB
p+
E
B
Motion in a
Magnetic Field
•  component of velocity
will cause circular motion.
v
2
v
m  F  qvB
r
mv
r
qB
Cyclotron Frequency
v qB
 
r m
r
B
Cyclotron
• 2 sets of D magnets are set up
to bend charged particles into a
circular path.
• An alternating electric field
between the D magnets causes
the particles to speed up.
• The particles spiral outward
with increasing speed.
E
p+
B
Force on a Wire
• In a uniform magnetic field a straight wire
experiences a force.
 

F  I l  B
• In general for all wires in magnetic
fields


dF  I  ds  B
• For a uniform magnetic field only the
displacement from the starting point to the
ending point affects the magnetic force.
Force on a Loop
• Ex. What is the force on a
semicircle shaped loop, if
the straight portion has a
force of 8 N on it?
• What is the current in the
loop if the radius of
curvature is 0.75m and the
magnetic field is 2 T?
Torque on a Loop
• Remember
  
  r F


b 
F  I   ds  B
a
• For a uniform field  to the current
F  I l  B
• then for a force arm 
to the magnetic force
  2aIlB  (2al ) IB  AIB
 
  IA  B

B
F
2a
F
Torque on a Dipole
• Remember
  
  r F


F  qE
• then 
 
  qr  E
q+
q
F
F
2a
E
Moments
• Magnetic Moment

 IA


  B


• Electric Dipole Moment

p  2aq rˆ
r̂
 
  p E

is a unit vector going from the
negative to the positive charge
Electric Energy
Coil Rotates
S
N N
S S
N
• Ex. What is the torque on a
circular loop with radius of 5 cm
rotating at 0.25 Hz if it has a
current of 1A and is in a uniform
magnetic field of 0.2 T?
Biot-Savart Law
• Magnetic fields are generated by moving
I
charge.


Ids  rˆ
dB  k m
2
r
0
7
km 
 10 Wb / A  m
4
0 - permeability of free space
ds
^r
r
B Field for a Wire
• For a thin straight conductor carrying
current the magnetic field is
0 I
B
2a
• Use the right hand rule to determine the
direction. (Place thumb in direction of
current and B Field is in direction of
fingers grabbing the wire.)
• Effect of moving charges is transmitted
at the speed of light. Magnetism is the
result of moving charges.
a
I
Attraction of Wires
• Magnetic Force of one wire interacts with
the current in the other wire.
l 0 I 1 I 2
F1  I1lB2 
2a
• This concept is used to define the Ampere
and the Coulomb.
• Find the attraction between two wires
carrying 10 A each that are 1 mm apart?
Ampere’s Law
• The line integral of B·ds around any closed
path equals 0I, where I is the total steady
current flowing through the surface
bounded by the closed path.
 
B

d
s


I
0

a
I
B field for a Wire
• Chose a closed loop which follows the
magnetic field, which is constant in value.
 
B

d
s

B
ds

B
2

r


• Therefore,
0 I
B 2r   0 I  B 
2r
r
I
ds
• This matches our result from using BiotSavart Law.
B field for a Toroid
• A toroid is a donut shape with a coil
ds
wrapped around it.
 
 B  ds B2r  0 NI
r
 0 NI
• Therefore, B 
2r
• Get a concentrated field inside the toroid.
B field in a Solenoid
• A long wire is wound in
the form of a helix.
• Let a solenoid consist of N
turns over a distance of l.
 
 B  ds Bl  0 NI
B
 0 NI
l
  0 nI
ds
l
Gauss’ Law
• Magnetic Flux - Amount of magnetic field
leaving a surface.
 
 m   B  dA
• Since magnetic field lines form loops you
can never find an isolated magnetic pole.
 
B

d
A

0

closed surface
Magnetism
• Sources
– Orbital magnetic moment of an electron.
– Spin magnetic moment of an electron.
• Types of Magnetism
– Ferromagnetic
– Paramagnetic
– Diamagnetic
Ferromagnetism
• Consists of small regions
(called domains) where the
magnetic moments are
aligned.
• Using an external magnetic
field you can align the
domains.
Hysteresis
• A remnant magnetic field
remains when an external
field is removed.
• To remove a magnetic field
a oscillating magnetic field
with decreasing amplitude
needs to be used.
Binternal
Bapplied
Magnetic Recording
• Iron embedded on a
surface can store
direction of a magnetic
field.
Paramagnetism
• Weak interaction between magnetic
moments within the material.
• Magnetic moments will align in the
presence of an external magnetic field.
• If the material is lowered below the Curie
temperature, it will maintain its magnetic
alignment.
Diamagnetism
• Has no permanent magnetic moment.
• The presence of an external magnetic field
causes a weak opposing magnetic moment
in the material.
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