Problem

1
Problem 14Einstein-de Haas experiment
2
The problem

• When you apply a vertical magnetic field to a
  metallic cylinder suspended by a string it begins
  to rotate. Study this phenomenon.

3
Historical Background

• Experimenteller Nachweis der Ampereschen
  Molekularströme. Naturwissenschaft, 1915, 3,
  237-238
• Experimenteller Nachweis der Ampereschen
  Molekularströme. (Mit W.J. de Haas) Verhadl.
  Dtsch. Phys. Ges., 1915, 17 , 152-170
• (oral report 19.02.1915 article submitted
  10.04.1915)
• Berichtigung zu meiner gemainsam mit Herrn W.J.
  de Haas Veröffenlichen Arbeit Experimenteller
  Nachweis der Ampereschen Molekularströme.
  Verhadl. Dtsch. Phys. Ges., 1915, 17 , 203
• Notiz zu unserer Arbeit Experimenteller
  Nachweis der Ampereschen Molekularströme (Mit
  W.J. de Haas) Verhadl. Dtsch. Phys. Ges., 1915,
  17 , 420
• Ein einfaches Experiment zum Nachweis der
  Ampereschen Molekularströme. Verhadl. Dtsch.
  Phys. Ges., 1916, 18, 173-177.
• (oral report 25.02.1915 article submitted )

Fig.1
4
Nature of magnetism of the elements

• Atoms of the elements contain electrons
• Electrons move in orbits and spin around their
  axises
• They are the currents in the atoms (molecular
  Amperes currents) reason for magnetic
  properties of atoms
• Electrons possess
• Orbital magnetic moment and spin magnetic moment
• Orbital angular momentum and electron spin
  mechanical momentum

5
Moments and Momenta

• Orbital moments
• orbital angular momentum
• L l.
• orbital magnetic moment
• ml - (e/2m).L gl. L
• ml gl. L, where gl gl.e/2m

L
s
v
ms

r

• Spin moments
• Spin mechanical momentum
• s ½.
• Spin magnetic moment
• ms - (e/2m). gs.s
• ms gs.s, where gs gs .e/2m

ml
Gyro magnetic ratio gl
ml/L-(e/2m) 0,88.1011C/kg gs ms/s
-(e/m)1,76.1011C/kg
6
Mixed magnetism
j (l ms). mj gj .j, where gj gj
.e/2m gj 1 j(j1) ms (ms1) l(l1)


2j(j1)
7
Domains

• Magnetic domains are regions in a crystal with
  different directions of the magnetizations
• Ferromagnets

8
Magneto-mechanical phenomena

• The sum of the magnetic moment vectors of the
  domains can be said to be the vector of the
  magnetic moment of the substance.
• Let I be the vector of magnetization, V is the
  volume of the body
• I.VSmd
• Let Q be the total mechanical momentum of the
  domains
• QSLdg.I.V g.Smd

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Magneto-mechanical phenomena

• When the body is not magnetized I0 Q0
• When the body is magnetized I is no more 0
• Then according to the formula Qg.I.V, Q also
  changes
• According to the law of conservation of
  mechanical momentum QtotQD QB
• In the beginning the sum of the mechanical
  momenta of the domains is 0 and the body is not
  moving the total momentum is 0
• QD ? 0 QB ? 0
• So we must observe the spinning of the body

10
Experiment Comparison
Our experiment
Einsteins experiment
Stand
Tungsten wire
Laser
Mirror
Laser beam
Solenoid
Generator
Screen
Picture from Albert Einstein-selected
scientific works, "Nauka", Moscow 1966
11
Experiment Setting
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Laser

• Laser
• Semiconductor laser
• 1.5 euro from the market

13
Wire

• Wire made of Tungsten with thickness of 15 mm
• Connected to a reel
• Frequency measured
• Torsion balance

14
Sample

• The cylinder
• Nail (Fe)
• Two parts of brass (Cu and Zn) up and down
• Weight 7,052 g
• Length 7,44 cm
• Diameter 4mm
• Mirror - aluminum foil

15
Solenoids

• Two solenoids connected in series
• 12000 turns each
• Magnetic field of about 20 G is created
• Alternative current of 6 mA

16
Generator

• Generator of sinusoidal vibrations with changing
  frequency
• Creates resonance to strengthen the effect
• Beating
  effect,
  
  when
  
  slightly
  
  different
  
  frequency
  
  is set

17
Experiment
g
18
Video
19

20
Parameters
I vector of magnetization, its table value is


I1,59155.106
A/m V volume of the sample (only ferromagnetic
part)

• r radius of the cylinder r0.002 m
• h length of the cylinder h0.0744 m

21
Parameters

• j - Angle of declination, experimentally found

• Te experimental time for measuring the angle
  of declination

• f frequency of the torsion balance f0.07Hz

22
Parameters

• Js moment of inertia of the sample
• for cylinder
• for our sample

• mb and rb mass and radius of the brass parts
  mb0,003359 kg and rb0,0015 m
• mf and rf mass and radius of the ferromagnetic
  part mf0,007052 kg and rf0,002 m

23
Parameters

• L decrement of decrease

• jn and jn1 are two consecutive angles of
  declination. The difference is about 0.5 degrees

24
Final Calculation

This will be true if
25
Sources of error

• The torsion balance is not centered
• Brass part Barnetts effect
• Earths magnetic field
• Noises and vibrations
• Domains that do not get remagnetized
• Eddie currents

26
Conclusions

• Einstein - de Haas experiment was successfully
  demonstrated
• The observed magneto-mechanical effect was
  predicted and explained using quantum mechanics
  concepts

27
References

• Albert Einstein-selected scientific works,
  "Nauka", Moscow 1966
• Experimenteller Nachweis der Amperschen
  Molekularstrome,
• Naturwissenschaft, 1915,3,237-238Electricity,
  S.G.Kalashnikov, "Nauka", Moscow, 1977

28
Magnetic Factors

• l, ml - Pure orbital magnetism gl1
• s, ms - Pure spin magnetism gs2
• j, mj - Mixed magnetism gjvaries in terms of l,
  s and j

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Magnetic momentum orbitalIoq/te.f
pomI.Se.f.S
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Different momentums for different materials

• The sum of the spinning and orbital momentums is
  the momentum of the domain j pom psm
• Some materials depend only on their spinning and
  other only on their orbital momentum
• p g.G.h.sqrt(l.(l1))
• g (gyromagnetic factor) for orbitally determined
  is 1 for spinning determined is 2 and for a
  mixture varies between 0 and 2
• Explanation
• Iron is determined by the spinning

g(p/l)/G
31
Applied Magnetic Field
B

• When B is applied, the electron tries to keep
  its previous motion in respect to the axis of its
  orbit
• The vortex of pm draws a circle and creates
  precession
• Its angular speed is W
• W 1/2(e/m).B from theorem of Larmor

W
l
32
Theorem of Larmor
When a magnetic field is applied to a moving in
an orbit electron the precession of the orbit
should move in a circle with an angular velocity
W 1/2(e/m).B in order to keep the motion of the
electron in its orbit the same with respect to
the center of the orbit.

• Three forces
• Fme.v.B Magnetic force
• Fk2.m.v.W Coureolis force
• Fcm. W2.r Centripetal force

• Fm Fk 0
• e.v.B.sin(v, B) 2.m.W.sin(v, B) 0
• W- 1/2(e/m).B

• due to small W, Fc (proportional to W2) is
  negligible in terms of Fk (proportional to W).

33
Collisions between electrons in the atoms of the
substances

• Electrons in the ferromagnetic substances
  collide.
• After each collision when an external magnetic
  field exists the vector of l tries to get closer
  to the vector B
• After a number of collisions the two vectors
  point in one direction.
• The substance obtains a new magnetic momentum or
  it magnetizes. Almost all of the vectors of the
  electrons point in the direction of B.

Collision!!!
Collision!!!
Collision!!!
W
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Momentums

• Magnetic moments
• orbital
• ml gl. l - (e/2m).l
• spinning
• ms -((e/m).½.h)/2. p

• e charge of electron
• f frequency
• S area of the orbit

pom
psm
e

• Mechanical momenta
• orbital
• lm.w.r22.m.f.Sl.h/2p
• w2.p.f
• Spinning
• s n.h/(4. p)

v
ls

r
lo

• Gyro magnetic ratio
• gl ml/l-(e/2m) 0,88.1011C/kg
• gs ms/s -(e/m)1,76.1011C/kg