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Magnetism: Force and Field
General Characteristics
• Like poles repel
• Unlike poles attract
• You can never isolate a north pole from a south pole. N
S
N
SN
S
N
S
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.
N
S
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.
• Magnitude of the force is given by
• Direction of the force is determined by the right-hand rule.
• Units - Wb/m2 or T (1T = 104G)
BvqFB
sinqvBF
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?
Only the perpendicularcomponent of the velocityproduces a magnetic force.
60sin)5.2)(/105.1)(106.1( 819 TsmCF
NF 11102.5
Will move in a helix.
Velocity Selector• Lorentz Force
• When F = 0 and
then
B
EBvqEqF
BEv
B
Ev
p+
Mass Spectrometer
• When the velocity is known, then the mass is known by the charge and radius of curvature in a B field.
p+
E B
qB
mvr
Motion in a Magnetic Field
• component of velocity will cause circular motion.
rqvBFr
vm
2
qB
mvr
Cyclotron Frequency
m
qB
r
v
v
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.
B
E
p+
Force on a Wire• In a uniform magnetic field a straight wire
experiences a force.
• In general for all wires in magnetic fields
• For a uniform magnetic field only the displacement from the starting point to the ending point affects the magnetic force.
BlIF
BsdIFd
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
• For a uniform field to the current
• then for a force arm
to the magnetic force
Fr
BsdIFb
a
BlIF
AIBIBalaIlB )2(2
BAI
2a
F
F
B
Torque on a Dipole
• Remember
• then
Fr
Erq
EqF
2aq
q+
F
F
E
Moments• Magnetic Moment
• Electric Dipole Moment
AI
B
raqp ˆ 2
Ep
r̂ is a unit vector going from thenegative to the positive charge
Electric Energy
• 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?
N SS N NS
Coil Rotates
Biot-Savart Law• Magnetic fields are generated by moving
charge.
2
ˆ
r
rsIdkBd m
mAWbkm /104
70
0 - permeability of free space
I
r̂
r
ds
B Field for a Wire• For a thin straight conductor carrying
current the magnetic field is
• 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
IB
2
0
Ia
Attraction of Wires
• Magnetic Force of one wire interacts with the current in the other wire.
• 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?
a
IIllBIF
2
210211
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.
IsdB 0I
a
B field for a Wire• Chose a closed loop which follows the
magnetic field, which is constant in value.
• Therefore,
• This matches our result from using Biot-Savart Law.
rBdsBsdB 2
IrB 02 r
IB
2
0
Ir
ds
B field for a Toroid
• A toroid is a donut shape with a coil wrapped around it.
• Therefore,
• Get a concentrated field inside the toroid.
ds
rNIrBsdB 02
r
NIB
20
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.
dsl
NIBlsdB 0
nIl
NIB 0
0
Gauss’ Law• Magnetic Flux - Amount of magnetic field
leaving a surface.
• Since magnetic field lines form loops you can never find an isolated magnetic pole.
AdBm
0
surfaceclosed
AdB
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.
Bapplied
Binternal
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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