Download Magnetic force and magnetic fields Magnetic field Source of

Magnetic field
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Iron filings may be used to show the pattern of
the magnetic field lines.
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A compass can be used to trace the field lines.
The lines outside the magnet point from the
North pole to the South pole.
magnetar
Magnetic force and magnetic
fields
Feb 28, 2012
Source of
magnetic field
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Magnetic fields are associated
with charge in motion and with
elementary charged particle
spin.
If charge moves in a conductor,
for example, a magnetic field is
found to circulate around the
direction of the moving
charge.Details in Chapter 30
Magnetic fields superpose like
electric fields.
The Earth’s
magnetic field
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The source of the Earth’s
magnetic field is likely
convection induced electrical
currents in the Earth’s core.
The direction of the Earth’s
magnetic field wanders and
reverses.
The field shields the Earth from
charged particles emitted by
the Sun.
The north-seeking pole of a compass points to the north
geographic pole.
! This would correspond to the Earth’s south magnetic pole.
The south-seeking pole points to the south geographic pole.
! This would correspond to the Earth’s north magnetic pole.
Pole shifts
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https://en.wikipedia.org/wiki/
File:Earth_Magnetic_Field_Declinat
ion_from_1590_to_1990.gif
During a pole reversal, the
field is reduced by a factor
of ten. The shielding of the
Earth from solar radiation is
reduced.
Magnetic force
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The magnetic field B can be defined by
the magnetic force on charged particles.
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The force on a charge q with velocity v
in a magnetic field B is given by the
“cross product” of velocity and field
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Ferromagnetism
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The magnetic field of a
“permanent magnet” is
associated with alignment of
the spins of charged electrons
in atoms.
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The electrons behave like a
collection of tiny permanent
magnets. When these tiny
magnets are aligned, not
randomly oriented, a net
macroscopic magnetization
and magnetic field is observed.
Strength of
magnetic fields
FB = q v x B
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The magnitude of the magnetic force on
a charged particle is FB = |q| v B sin !.
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Unit T = Wb m-2 = N C-1 m-1 s.
http://solomon.as.utexas.edu/
~duncan/magnetar.html
1 T = 10,000 gauss
Motion in a uniform
magnetic field
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Consider a particle moving in an external
magnetic field with its velocity v
perpendicular to the field B.
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The force is always directed toward the center
of the circular path and does no work so the
KE and speed are constant.
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The magnetic force causes a centripetal
acceleration, changing the direction of the
velocity of the particle.
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Equate the magnetic and centripetal forces:
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Example
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Electrons are observed bending
clockwise in a magnetic field
perpendicular to the page with
radius of curvature r= p/eB.
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From the radius and field, the
momentum p may be
determined.
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Given the momentum per unit
Does B point into or out of the page?
charge created by a known
electric field, the quantity q/m
may be determined.
FB = qvB=ma = mv2/r
Solve for r=mv/(qB) = p/(qB)
Example
Example
r
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An electron moves in a
circle of radius r=1 mm in
a magnetic field B= 1 T.
An electron moves in a circle of
radius r=1 mm in a magnetic
field B= 1 T.
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What is its speed?
What is its speed?
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Assume m =9e-31 kg and
q=-e = -1.6e-19 C.
Assume m =9e-31 kg and q=-e
= -1.6e-19 C.
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(For v~c, there are relativistic
corrections to our formulae.)
-V Volts
Example (cont)
Example (cont)
E
d
0 Volts
v
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What constant electric field
strength E would be required
to accelerate an electron from
rest over a distance d=1 m to a
speed c/2 where c is light
speed?
(Again, for v~c, there are
corrections to this result.)
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For a constant electric field
strength E required to accelerate
an electron from rest over a
distance d=1 m to a speed c/2
where c is light speed…
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If the accelerating field is
achieved with equal and
opposite charges on two
parallel plates separated by d=1
m, a) what is the voltage
between the plates and b) what
is the surface charge density on
the plates?