14. – Faraday Generator
Construct a homopolar electric generator. Investigate the electrical properties of the device and find its
efficiency.
Problem
– Rotating magnets
– Stationary magnets
• Interpretation
• Basic explanation
p
• Theory
• Measurements description
• Results
• Conclusion
– Rotating magnets
– Stationary magnets
• Construction
C
i
Contents
Faraday’s
y experiment
p
Disk
Rotating
Rotating
St ti
Stationary
Magnets
g
Stationary
Rotating
R t ti
Rotating
N
No
Yes
Yes
Voltage
g induced
• In later experiments with cyllindrical magnets the following results were achieved:
Interpretation
p
Lorentz force acting on electrons rotating inside the disk
Velocity of the disk relative to the magnets = 0
→ Explanation somewhat questionable
→ Understanding the nature of U d t di th t f magnetism and Lorentz force
o
2. Magnets rotating with the disk
o
1. Stationary magnets
y
g
Basic explanation
p
(
)
Ei – intensity
i t
it off electric
l t i fifield
ld
ω – angular velocity
r – inner radius
R – outer radius
r
r
r FL r r
r r
FL = q v × B ⇒ Ei = = v × B
q
R r
2
2
r
r
R −r
B – magnetic induction
Ui = ∫ Ei ⋅ d r = B ω
v – velocity
2
r
• Lorentz force
St ti
Stationary
magnets
t
Theory
• Magnetic field is a consequence of moving charged particles
→Electric and magnetic fields in different frames of refference connected by transformations
• Magnets modeled by an inductor producing a h
homogenous magnetic field of magnetic i fi ld f i induction B
Moving magnets
Theory
Coulomb force acting on the left
• In the frame reference of the electron we obtain a
v
ωr
• Currents of charged particles
• Velocity of negative particles in the reference frame of the moving electron larger on the right side then on the left side → larger length contraction v → larger density of positive particles
• Analogous observation → larger d it f iti ti l th density of positive particles on the left side
Moving magnets
Theory
x’
x
B
r
P
y yy’
ω’r’
ω
r
γ=
(ω' r' )2
1− 2
c
1
β=
c
ω' r'
ω' – angular velocity of rotating l
l
f
system
rr’=r –
r distance of P from the center
ω’r’ – linear velocity of point P
B – magnetic field of the rotating g
g
inductor
S – frame of refference of point P
S’ – laboratory frame of refference
Moving magnets
Theory
(ω ' r ' ) 2
1−
c2
R2 − r2
= ∫ E y dr = B ω
2
r
[1] Edward M. Purcell: Elecromagnetism, McGraw-Hill
Ey =
Uy
′
′
ω 'r'
Ez = 0
′
Bz = B
Ey = 0
R
′
Ez = 0
′
Ez = γ (Ez − βcBy )
Bx = 0
By = 0
B
′
Ex = 0
′
E y = γβ cB
′
E x = Ex
′
Ey = γ (Ey + βcBz )
E x= 0
S’
S
Transformations [1]
Fields acting in point P
Moving magnets
Theory
• In both variations the same disk and axle are used
• Diameter of disk ‐ 40 mm, axle ‐ 5 mm
– Large range of velocities
– Simple assembly
Si l bl
• 2 variants –
2 variants stationary magnets and magnets rotating with the disk
• The generator is powered by a machine lathe
Construction
• The disk and the axle are turned from one piece of aluminium
• The brushes are made from curved aluminium to the same curvature as the axle and the disk
Construction
• Magnets are attached to the disk using an double sided sealing tape and are also connected by their own magnetic force
Construction rotatingg magnets
g
• Magnets attached with double sided sealing tape to polycarbonate housing which separates the disk and magnets The housing is not in the disk and magnets. The housing is not in contact with the disk
Stationary magnets
Construction
• Open load voltage and the short circut current are measured using a digital multimeter
Measurements
– 0.0032N for each variant (same system of brushes)
• Moment of torque – dinamometer
– 0.22 T for the distance of the rotationg magnets
T f th di t
f th t ti
t
– 0.15 T for the distance of the stationary magnets
• Rotation frequency –
Rotation frequency stroboscope • Magnetic induction – hall probe
Measurements
Results
0
2
4
6
8
0
50
150
Angular velocity [m/s]
100
200
Measured voltage
Calculated voltage
Comparisson of theroetical and experimental induced voltage for rotating magnets
Voltage [mV]
Voltage [m
mV]
0
1
2
3
4
5
0
20
40
80
100
Angular velocity [rad/s]
60
120
140
160
Measured voltage
Calculated voltage
Comparisson of theroetical and experimental induced voltage for stationary
magnets
Results
Current [mA]
0.00
0.02
0.04
0.06
0.08
0
20
40
60
100
120
Angular velocity [rad/s]
80
140
Rotating magnets
160
• Short circut voltage
Sh t i t lt
180
200
0 00
0.00
0.01
0.02
0.03
0.04
0
20
Results
Current [mA]
40
80
100
Angular velocity [rad/s]
60
120
Stationary magnets
140
160
• Input mechanical power
– Calculated from angular momentum of friction and angular velocity
– P = ωM
• Output power
O t t – Calculated from voltage on load and short circut
i t current t – Maximal output power: P = UI/2
• Efficiency – ratio of output and input power η =
Efficiencyy
Pt
Pu
Efficien
ncy
5.0e-8
1.0e-7
15 7
1.5e-7
2.0e-7
2.5e-7
3.0e-7
3.5e-7
4.0e-7
4.5e-7
20
40
60
100
120
140
Angular velocity [rad/s]
80
Rotating magnets
Efficiencyy
160
180
200
Efficiency
2.0e-8
4.0e-8
6 0e 8
6.0e-8
8.0e-8
1.0e-7
1.2e-7
1.4e-7
1.6e-7
20
40
60
100
Angular velocity [rad/s]
80
Stationary magnets
Efficiencyy
120
140
160
• Two variations of the homopolar generator were constructed
• In‐depth explanation comparring two d h
l
interpretations (magnetism and special relativity)
l
• The difference between the induced voltages between the stationary and rotating construction arises only because of different distances between the magnets
Summaryy and conclusion
• Measured and calculated open load voltage are in very good agreement
• The resistance in the stationary system very small, but when the disk is rotating the y
resistance increases dramatically because of the irregularities on the surface → very small efficiency • The construction leaves a lot of space for improvement which would increase the effeciency by large amounts.
ff i
b l
Summaryy and conclusion
1. Edward M. Purcell: Electromagnetism, McGraw‐Hill
g
2. The homopolar motor: A true relativistic engine
Jorge Guala‐Valverde, Pedro Mazzoni, and Ricardo Achilles Am. J. Phys. 70, 1052 (2002)
3. Serway, Jewett, Physics for Scientists and Engineers, 7th edition, Thomson 2007.
4. Layton, Simon, A different twist on the Lorentz force and L t Si
A diff
t t i t th L
t f
d Faraday's law, Phys. Teach. 36, 474 (1998)
5. http://www.physics.umd.edu/lecdem/outreach/QOTW/arch
11/q218unipolar.pdf
6. http://www.stardrivedevice.com/over‐unity.html
7 ttp://www.rexresearch.com/trombly/trombly.htm
7.
ttp://www rexresearch com/trombly/trombly htm
References
Thank you for your attention!
Bx = 0
Bz = B
By = 0
′
Bx = Bx
β
′
By = γ (By − Ez )
c
β
′
Bz = γ (Bz + Ey )
c
′
Ez = γ (Ez − βcBy )
′
E x = Ex
′
Ey = γ (Ey + βcBz )
Transformations [1]
Ez = 0
Ey = 0
E x= 0
S
Fields acting in point P
S’
′
B z = γB z
′
Ez = 0
′
Bx = 0
′
By = 0
′
Ex = 0
′
E y = γβ cB z
Moving magnets
Theory