Harmonics

Chapter 6

 Harmonics

The Sound of the Big Bang

Even when all Earthly and astronomical sources of radio waves are screened out, some static remains on the most sensitive radios. This static is caused by radiation left over from the big bang, the explosion that created the universe.

© Microsoft Corporation. All Rights Reserved./NASA/WMAP Science Team

Microsoft ® Encarta ® 2006. © 1993-2005 Microsoft Corporation. All rights reserved.

Frequency

We perceive frequency as “higher” or “lower” sounds. The frequency of a sound is the number of cycles, or oscillations, a sound wave completes in a given time. Frequency is measured in hertz, or cycles per second. In these examples, the frequency of each higher wave is double that of the one below, producing the same note at different frequencies, from 110.00 Hz to 880.00 Hz. Waves propagate at both higher and lower frequencies, but humans are unable to hear them outside of a relatively narrow range.

© Microsoft Corporation. All Rights Reserved.

Microsoft ® Encarta ® 2006. © 1993-2005 Microsoft Corporation. All rights reserved.

The masks of God, Oriental mythology 1976 by Joseph Campbell “ For the inaudible music of the spheres, which is the hum of the cosmos, in being becomes audible, through music it is the harmony, the meaning of social order, the harmony of the soul, itself discovers therein its accord.”

Period of audible sound waves 1 x 10^-3

Speed of sound V=√B/P in a solid V_A1=√V/P

A molecule travels at 401 m/s

Sound travels at 1,000 feet per second

Sound intensity level β=10 log (1/10) decibels

Sound waves speed 330 m/s in air 343 m/s at 20^oc

Fundamental frequency Hz ƒ₁ = V/2L = 200m/s / 2(1.0m) = 100 Hz

Ultra sound PR = (P₁-P_e/P₁-P₂)² x 100

Harmonic motion ( Kinematics)  χ = A cos (wt+φ)k/m χ= 4π²χ/T²

            Beats ƒ₂T –ƒ₁T=1  T=2π√m/k   ƒ_beat 1/T = ƒ₂-ƒ₁

Diatomic music scale

            Hz.                   Note

256                                    C

288                                    D

320                                    E

341                                    F

384                                    G

427                                    A

480                                    B

512                                    C

Resonant frequency reaches a maximum when the frequency of the driving force equals the natural frequency. The forced vibration wave length of emitted sound wave equals the circumference.

Bulk/density/temperature

V= √B/P          V=(331m/s)√1 +T/273

Spherical wave                         Intensities

I₁=Pav/4πrf      I₂=Pav/4πrg      I₁/I₂ = rg/rf

Wave varies I/r²

V=Δx/ΔT         V=ƒλ

Intensity of a wave

1≡ 1/A ΔE/ΔT

Heat capacity – systems of coupled oscillators Cp∫^wmax_o N(w) C_E(w)dw

            N(w) = frequency spectrum      C_E(w) = heat capacity of frequency W

            W_max = high frequency cut off. In wave motion the phase and group velocities

            Vp= w/k, Vg = dw/dk, k=2π/λ.

Acoustic and optical modes

Acoustic and optical modes in two or more different types of atoms m₁u_s=c₁(υ_s+1/2+υ_s-1/2 – 2u_s) m₂u_s+1/2 =c₁(u_s+1+u₂-2υ_s+1/2) w²=c₁(m₁+m₂/m₁m₂)±[cf(m₁+m₂/m₁m₂)²-4cf/m₁m₂ sin =1/2ka]

Work and energy (joule) j

ƒ₁/ƒ₂ = m₁a₁/m₂a₂  N-m =kg –m²/s²

Renaissance energy

ƒ_o =1/2π √LC

Thermionic emissions

1ƒ≈ BV²_E –K/V

Line integral in closed loop

∫cV x dl or φV x dl  annulus π(R²-r²) between 2 concentric circles

Truncated icosahedrons

Truncated icosahedrons – the use of light metrics harmonics to form a closed cage model, shrink-wrapped around metal ions. Second harmonics is used to make Bucky balls ~30mJ of Q – switched (Nd x YAG). The only plausible structure to satisfy all sp ² valences is only a spheroid structure. All valences are satisfied and the molecules appear to be aromatic. A singularity is a perfect combination of energy flowing together in harmony and is not dependant on speed or mass. Pythagorean concept of harmonicas as a grand unified theory of the universe has been obscured for more than two millennia. Technically this is called the spiral of fifths. The seventh octaves and the twelve fifths differ by 1.0136 called the comma of Pythagoras. Mathematically the ratio 2 to 1 doubled seven times gives a frequency 128 times higher, but if you proceed on this basis of the ratio of 2 to 3 which is 1.5 and you go up the twelve fifths. These give you 129.75 and if you divide 129.75 by 128 you get the decimal 1.0136. In the text Katatome Kanonos (Division of the Canan) says the number 531.441 is greater than twice 262,144. The explanatory statement is six sequioctave intervals (multiple 262,144 by two to get 524,288, divide 531,144 by that number gives 1.013643265) this proves that melodic space is irrational (pure notes). In 1584 the Chinese invented a special system to cope with it known as “Equal temperament” (flat notes).

Spherical harmononics

Spherical harmononics may be used to describe the normal modes of oscillation of spherically shaped objects. Each harmonic has two identifying indices that distinguish it from other spherical harmonic waveforms. On the surface of a vibrating sphere certain nodal circles appear where the surface is at rest. The number of these nodal circles for a given spherical harmonics is called its order n;n is one of the indices used to identify the normal mode. . The second identification index corresponds to the number of nodal circles, which pass through the poles of the vibrating sphere. A general property of a nodal circle does not pass through the poles of the sphere, and then it must lie in a plane parallel to the spheres’ equator, parallel 1=6 m=0, both 1=6 m=3, vertical 1=6 m=6 P=(r,Θ,φ) (Cartesian coordinates). A boundary condition is when a region of infinite compression occurs, the boundary layer under continuous changing pressure, will accelerate at an infinite rate under the action of the force. The impedance in sound waves stress  P and the velocity of displacement  δξ /δt have a relationship to the waveform ξ =ξ₀ exp {i(wt – kx)} (applied to induced, voltage to current). Complex impedance is when voltage and current are oscillating (not in phase) there is power transferred ½ (V1* + V*1) = ½ 11*(z+z*). Matching phase is when trying to maximize the power transfer, access a boundary or a series of boundaries. The source of impedance Z _i feeding a load of impedance Z₂, electric-circuit theory shows the power developed in the load p=1/2 11*(Z₂ + Z*₂) = 1/2V V* (Z₂ +Z*₂) { 1/Z₁+Z₂  + 1/Z*₁ + Z*₂}² Maximum is when Z*₁ = Z₂. Sub harmonic oscillations are oscillations of a non-linear system with periods that are integral multiples of the period of the driving force The oscillator changes with a frequency of w/n, with n=an integer. A non-linear oscillator undampened the equation of motion is w^2¨q +q + єq³ =ƒ cos 3τ A harmonic (non-linear) perturbation theory (Lindstedt – Poincare) undampend driven a harmonic oscillator ƒ=1, є = 1/10, w= 1. Standing waves occur when ever oscillations are confined to a finite space

Harmonics        # integration      q₀                     q₁                     q₂                     sum

1                      2.3555             2.37126           -0.01389          C₁                    2.35737 +C₁

3                      0.04563           -                       0.04167           .00366             .04533

5                      0.00083           -                       -                       .00073             .00073

>5(sum)           1.17x10^-5         -                       -                       -                       -

Coupled oscillations are bringing into unison, the “Kuramoto model.” Experiments on the math shows with a large number of electronic oscillations on a microchip the coupled oscillation would bring them into unison in two neat phase transitions. The Coulomb field φ = φ₀ +φ₁ + φ₂ + …  The quantities which depend only on the polar angles are called generalized spherical harmonics. For every index  n there are in all 2n+1 independent spherical harmonics. Yn  Arbitrary parameters can be determined from the charge distribution producing the field φ(r) = ^∞_n=0∑ 1/rⁿ +1  Yn(0,α) φ(r) =∫ p(r¹)/‌‌│r-r¹│ dv¹ and/or = ∑ ei/│r-r₁│ it has the potential of a given distribution of a charge. A field of rotationally symmetric quadrupole, the angular dependence is given by the second zonal spherical harmonic.P₂ (cosΘ)=(3 cos² Θ-1)/2 (in a uniform quadruple electric field there is neither a force nor a torque)  Coulombs’ law is the force of electrical attraction and is proportional to the product of the electrical charge and inversely proportional to the square of the distance between them.

Fourier’s theorem

Any periodic function ƒ(x) can be expressed as the sum of a series of sinusoidal functions which have wavelengths which are integral submultiples of the wavelength λ of ƒ(x)

ƒ(x) = C₀+C₁ cos (2πx/λ + α₁) + C₂ cos (2πx/λ² + α₂) + … + C_n cos (2πx/λn + α_n) + … the n’s are called the order of the terms which are harmonics, amplitude C_n and phase angle α_n.

Sound

Humans hear 16 Hz to 20,000 Hz or 20 KHz.

-         tolerable 1.0 x 10¹² decibel

-         pain 120 (dB)

-         deafening 100 (dB)

-         damage 140 (dB)

The maximum safe levels for different exposures;

-         15 min 100 (dBa)

-         2 min 109 (dBa)

-         28 second 115 (dBa)

-         0.11 seconds 139 (dBa)

-         30 min 97 (dBa)

-         24 hours 80 ma level in (dBa)

-         8 hours 85 (dBa)

-         4 hours 88 (dBa)

-         1 hour 94 (dBa)

Thermodynamics

Chapter 7.

Thermodynamics

Heat, radiation, the temperature of space of light, sound, aether, calorific rays, is it a wave or a particle? A current is a consequence of a difference of temperature between two opposite faces.

Friction

The force of static friction between any two surfaces f z≤ µ_s n. Thermal expansion (all dimensions increase) Δr=αr₀ΔT, r= radius, T= temperature the average coefficient of area expansion ΔA=A-A₀=γA₀ΔT, γ=2α the increase in volume ΔV =βV₀ΔT, β=3α average coefficient of volume expansion. Quantity Q of heat is transferred to m kg of a substance, thereby changing its temperature by ΔT st the specific heat c of the substance is defined as C ≡ Q/mΔT heat transferred between a system  of mass m and its surroundings  for a temperature change of ΔT as Q=mcΔT is called phase change the heat required to change the phase of a given mass m of a pure substance is Q=mL L= latent heat, T= temperature, condition H = Q/ΔT = KA(₂-T₁/L) k = thermal conductivity A= area, L=thickness.. Stefan’s law says the rate at which an object emits radiant energy is P=δA _e T⁴ , δ=5.6696 x 10^-8 w/m² x k⁴ and e is a constant called emissivity. All objects radiate and absorb energy in the form of electromagnetic waves hotter than its surrounding, radiates more energy, if it is cooler than its surroundings it absorbs more energy. The 1^st law of thermodynamics is when a system under goes a change from one state to another the change in its internal energy Δu is Δu=u_F –u₁ = Q-w, Q= heat transferred, w=work done + heat enters – heat leaves. Max force is static friction, fsmax between an objet and a surface is proportional to the normal force acting on the object. This max force occurs when the object is on the verge of slipping fs≤u_sn, u_s is the coefficient of static friction. When a body slides over a surface the direction of force of kinetic friction f_k is opposite the direction of the motion and the magnitude is proportional to that of the normal force. The second law of thermodynamics says heat will not flow from cold to a hot object. No heat engine operating in a cycle can absorb thermal energy from a reservoir and just perform an equal amount of work (change in entropy). The heat capacities at constant pressure is 1 atm, near 25 ⁰ c. C (diamond 510 (jk ^-1 kg ^-1 ) specific heat capacity. Entropy is related to the  hardness of the element; hard solids are more ordered and have lower entropies than soft solids. Carbon (diamond) 2.4 jk^-1 hard, Carbon (graphite) 5.7 jk^-1 soft, Density C(diamond) 3.51 (g cm^-3) C(graphite) 2.25 (g cm^-3). Molar volumes C(graphite) 5.33 ¯v(cm³ mol^-1) pressure to C(graphite) → C(diamond) 15.000 atm. Gold has a high charge on the atomic nucleus, the electrons move at speeds approaching that of light, giving gold its color (the theory of relativity). At standard temperature and pressure(70⁰F/20⁰c, 14 psi) an average molecule shimmies at 10 billion times per second. A common place chemical reaction is one million billionth of a second.

Black Body Radiation

Rayleigh-Jeans classical theory of black body radiation predicts that a body will emit more and more radiation the higher the frequencies, this is a contradiction with observations. The “ultra-violet catastrophe” clearly shows that there is an error in the classical approach. The way to avert the ultra-violet catastrophe was discovered by Planck in 1901, by the quantization of the electromagnetic radiation, the photon. The Bose-Einstein distribution law (quantum statistic) for photon and applies to other particles like bosons, alpha-particles, pi mesons etc.

T/K                  P_tot                               λ_max/μm

50                    0.354 w/m²                  57.955

370                  1.063 Kw/m²               7.832

2060                1.021 Mw/m²               1.407

Yoshida et all, 1995. The differential spectrum multiplied by energy cubed.

Every particle of matter in the universe attracts every other particle with a force which diminishes as the square of the distance is increased. The force which holds every respective pair of masses together being the integrated force of their component parts. With gravity there is no selection, no particular atoms, the attraction of gravitation is proportional simply to the quantity of the attracting matter, regardless of its quality. In quantum physics this is reversed.

Gravity is measured by the amount of motion which it can generate in a certain time (earth is 32 feet per second)

Chemical affinity is said to convert heat into light and then again into magnetism and electricity but gravity refuses to be converted, it is a force maintaining itself under all circumstances. By the exertion of a certain pull (gravity) through a certain space, a body is caused to clash with a certain definite velocity, heat is thereby developed, and this is the only sense in which gravity can be said to be converted into heat. In no case is the force which produces the motion annihilates or changes into anything else.

Light

Chapter 8

Light

Diffraction and Interference of Light

When light passes through a slit with a size that is close to the light’s wavelength, the light will diffract, or spread out in waves. When light passes through two slits, the waves from one slit will interfere with the waves from the other. Constructive interference occurs when a wave front, or crest, from one wave coincides with a wave front from another, forming a wave with a larger crest. Destructive interference occurs when a wave front of one wave coincides with a trough of another, cancelling each other to produce a smaller wave or no wave at all.

© Microsoft Corporation. All Rights Reserved.

Microsoft ® Encarta ® 2006. © 1993-2005 Microsoft Corporation. All rights reserved.

Constants

Period of visible light wave 2 x 10^-15

Speed of light c≈3 x 10⁸ m/s

Refraction of light sin ө 2/sin ө1 = V₂/V₁ = constant

Diamond refraction λ⁰ = 589nm 2.419

Infused quartz refraction V= 0/n = 3.00 x 10 ⁸ m/s/1.458

Deep violet .000039 cm

Dark red .000076 cm

Blue .00005 cm

Green .000055 cm

Red ↓ (.003 cm to 25 km) heat/radio

x-ray – ultraviolet’s - .00000004 cm

gamma – ultraviolet’s – one ten-millionth of violet

Braggs reflection is ΔK=-G geometry conditions for nλ=2d_nki sin ө, n=order of diffraction.

Equitant wave lengths corresponding to the root = mean- sq, velocities of a neutron gas at 0⁰c and 100⁰c are 1.55Å and 1.33Å respectively.

Particle/Wave

In 1924 deBroglies hypothesis states the light exhibits both wave like and particle like properties P=h/λ the moving particles P=mu would have an associated wavelength λ given by λ=h/p = h/mu. Electrons, protons, neutrons and simple atoms and molecules all agree with deBroglie formula. Light and matter have dual natures. This schizophrenic behavior of matter and radiation shows that neither the particle model nor the wave model is strictly correct. They are not mutually exclusive but rather they are complementary description. This means that we can not know the instantaneous values of both the position and the momentum to an arbitrary degree of accuracy.

friction

If a continuous spectrum of light is subjected to repeated reflection from an ionic crystal the light eventually becomes a narrow band of frequencies. Reflected light is known as “residual rays.”

Three unexplained effects of photoelectric; Kinetic energy of the ejected electrons is independent of the intensity of the light. Electrons are only ejected if the frequency of light exceeds a certain threshold. The kinetic energy of the ejected electron is proportional to the frequency of the incident light. Maxwell equations made the physical prediction that “light travels with the same speed, in all directions. A spherical pulse of light will appear spherical. Galileo’s the speed of an object is a private relative concept. If the speed of light is infinite there is no conflict between Galileo’s space-time and Maxwell’s laws of electromagnetism and optics.

Cerenkov radiation states that electromagnetic radiation, usually bluish light, emitted by a beam of high energy charged particles at a speed greater than light. The effect is similar to that of a sonic boom causing a shock wave set up in the electromagnetic field.

A rainbow can be seen as a natural example of refraction, a bending of light, reflection is light bounced off mirrors. Light is a particle and a wave. All waves have crests, troughs, wave length, amplitude, and frequency. A wave length is the distance between crests. Frequency is the number of waves in a fixed time and point. Amplitude is the distance between crest and trough.

Young, Thomas made the comparison between sound waves produced by a tuning fork and waves of light. Young used the modulus of elasticity-stress applied to a body to the strain produced. The bulk modulus is the ratio of the pressure on a body to its fractional decreases in volume. The shear (or rigidity) is the tangential force per unit area divided by the angular deformation in radians. Young interference is the interaction of two or more wave motions affecting the same part of a medium so that the instantaneous disturbances in the resultant waves are the vector sum of the instantaneous disturbances in the interfering is when to waves coincide.

Destructive interference is the maxima of one wave hitting the minima of another wave.

Lasers produce coherent radiation and produce interference effects like holography and measuring. Superluminal (faster than light) tachyons are the link between Polari ability and refractive Lorentz transformation, α=(3/4 π n)[ (N ² -1/n ² +2)] x ¹ =β (x- V ^t ), Y ¹ =y  z ¹ =z  t ¹  = β (τ –vx/c ² ) transforming the position and motion parameters.

Lasers are electromagnetic force traveling as a wave and electromagnetic waves that have two components, an electric field, and a magnetic field that vibrate at right angles to one another. Electromagnetic energy of the proper wave length can excite the electrons until one or more of them leave the atom altogether, called an ion, positively charged. The key is not the wattage but wavelength. Lasers produce light that is precisely spaced and lined up. The quality of laser light is called coherent. Stimulated emission is an atom already in an excited state and it is struck by another photon, the electron will drop back to a lower energy orbit and give off a photon. Moreover the incoming photon will not be absorbed at all. So there will be two photons leaving the atom. A resonator cavity reflects electromagnetic waves back and forth (usually a box) getting atoms or molecules into the excited state and then holding them there, is called population inversion. The Meta stable state of the atom is only partly stable; in this state a few photons will be emitted. The photon strikes other atoms producing stimulated emissions. The more tightly bunched its waves are the more information can be carried. Light can exert a minuscule amount of pressure. The light pressure is determined by hv=mc², when a bean of circularly polarized light is perfectly reflecting then the pressure is twice the value, P=1/c namely 21/c. This is because a photon on being reflected back, undergoes a change of momentum of P-(-P) = 2P. Each photon transfers twice as much momentum to the surface; this momentum causes torque on the surface. The magnitude of the torque per unit area is J=1/2πv = 1/w or T=Nh/2π. This implies that the photons carry angular momentum as well as linear momentum. A total internal reflection is mirror surfaces “spherical” reflecting the light to the interior. Lasers can be classified either by the material that is used to produce laser action or by the method used to excite the active atoms. The material can be solid, liquid, or gas. The method of exciting the material can be optical “light” electrical or chemical. The differential equations completely replace the Newtonian theory of motion, provided the masses are represented as singularities of the field. They contain the laws of force and motion while eliminating inertial systems. The fact that masses appear as singularities indicates that these masses can not be explained by symmetrical fields or gravitational fields. Not even the fact that only positive gravitating masses exist can be deduced. Gravity has 10 differential equations. The principle of general relativity implies the number of functions to be determined by the differential equations is 10-4=6. Six differential equations that is independent of one another. The remaining four equations are relations (identities). The most natural theoretical system must replace symmetrical tensor fields with non-symmetrical tensors bring the differential equations up to 16 independent components, which still doesn’t satisfy all the laws and parameters of gravity. Everything is a particle and a field at the same time, and you can not give one up or the other, but still we do not know how to combine them as one equation.

Light Quanta/ Thermal Radiation

Electromagnetic energy that is emitted from a surface is called thermal radiation. Radiation consists of a continuous spectrum of frequencies extended over a wide range. The spectral distribution and the amount of energy radiated depend on the temperature of the emitted surface. The spectral distribution has a definite frequency (or wave length) at which the radiation power is maximized and varies in direct proportion to the absolute temperature. This is known as Wien’s law. At 500^o C and above, the body glows visibly. Measurements indicate that the total power increases s the forth power of the absolute temperature, known as Stefan-Boltzmann law. In a hollow cavity inside a single body thermally insulated from the cavity walls. If the cavity walls are maintained at a constant temperature, the radiation then fills the cavity and some of it is absorbed by the body. The body also emits radiation and equilibrium is attained when the body emits at the same rate that it absorbs. Irradiance of the radiation within the cavity;  I is the total power per unit area incident on the body, b is the fraction of incident power that the body absorbs and H is the radiance or power per unit area that it emits for equilibrium H=bI. In the case of several bodies within a cavity the equilibrium of each body is I=H₁/b₁=H₂/b_{2 =} ... at a given temperature the ratio of the emitted power to the fraction of power absorbed is the same for all bodies and is equal to the irradiance within the cavity, known as Kirchhoff’s law.  The perfect absorber is called blackbody, b=1 and the corresponding value of H is the maximum possible H_max = 1  this is also known as Hohlraumstralung.

Photon

One photon can start an avalanche of 10,000 or more reactions. Light causes changes in matter and matter causes changes in light. Light waves can be used as a finger print for all materials. Ultra violet light causes movement of electrons from orbital to orbital. Microwave radiation can stimulate rotational motion. Infrared light stimulates vibrations, dipoles caused by vibrations, then there is no field to which oscillating electromagnetic field can interact. All living things are physico-chemical machines.

Physiology is the physical and chemical processes in the body. Hemoglobin is made up of several thousand atoms, a 3 dimensional subjected to intermolecular force. Many biochemical systems, heart, lungs, endocrine systems are non-linear oscillating systems.

Fechner’s Law – the more you have the more it takes to notice a difference. Fenchners oscillating reaction is a heterogeneous system, it takes place in two phases, solid-phase, and electrode and liquid phase solution.

Oscillations is glycolyis, it is the reaction in the body in which sugar is broken down for energy. Belousov-Zhabolinsky  or BZ reactions is a reaction solution, periodically cycles between rich red, deep blue and new leaf green in a series of sudden and dramatic colors. When applied to the oscillations of glycolyis form pulses of color. The nature of the human cell is an impressive, entropy-defying, energy-utilizing, self-assembling, self repairing, environment responding nanobot. Nanotubes pound per pound are stronger than steel and pound per volume are 1/6 the weight.   

Non-linear interaction between light and matter allows the frequency of light to be doubled or tripled.

Sound and light are mutually helpful, the conceptions being explained and strengthened and defined by the other. Pitch is dependent of wave length, which answers to the color of light. The range of the visible spectrum is about an octave.

 The transference of a wave from one tuning fork to another, it is the motion of each wave hitting the other tuning fork. These impulses are added to themselves, wave after wave. In 5 seconds that equal to 1,280 waves hitting the other tuning fork. This is called The influence of synchronism.

Gravity

Chapter 9

Gravity 

Gravitational Lens

A gravitational lens occurs when the gravitational pull of a very massive object, such as a galaxy, bends the light of an object behind it. In this photo, the bright yellowish object in the center of the image is a massive galaxy. Another galaxy is hidden behind it. The nearer, visible galaxy bends the light of the hidden galaxy and makes its light appear as blue streaks around the central galaxy.

Photo Researchers, Inc./Space Telescope Science Institute/NASA/Science Photo Library

Microsoft ® Encarta ® 2006. © 1993-2005 Microsoft Corporation. All rights reserved.

One arc second equals 1/3600^th of a degree. One milli-arc second is 1000 times smaller than that.

Constant force (Newton) N

W= (ƒ cos ө)s kg-m/s²

Work – energy theorem w_net = KEƒ ^– KEI

Gravitational potential energy PE ≡ mgy

Average power/force on moving α  =w/Δt    =F¯V

Average angular speed ≡ө₂-ө₁/t₂-t₁ = Δө/Δt

Centripetal force fc=m_ac=m V_E²/R

Law of gravitation F=G m₁m₂/r₂

The gravitation force exerted by a spherical mass on a particle outside the sphere F=G m_Em/R_E²

The second condition for equilibrium asserts in an object is in rotational equilibrium, external torque ∑T=0, ∑F=0 (external force) ∑r=0, ∑F=0, ∑Fx=0, ∑Fy=0,∑Fz=0, up to 7 fields

The center of gravity Yeg = ∑m_iy₁/∑m_i

Angular momentum τ=1α=1(w-w_e/Δt)=1w-1w_e/Δt

Mass-energy equivalence E=m₀C²/√1-v²/c²

Kinetic energy KE= mc²-m₀c²

Average centripetal acceleration a_c=v²/r

Centripetal force a_c=v_t²/r, FC=ma_c=v_t²/r

Gravitational force g=G m_e/r²

Keplers third law, the ratio of the square of each (planet) T²=(4π²/Gm_s)r³=ksr³

Rotational kinetic energy ½ 1 w²

Gravitational potential energy PE_g

Translational kinetic energy KE_t

Rotational kinetic energy KE_r (KE₁+KE_r+PE_g)I = (KE_t+KE_r+PE_g)g

Change in entropy Δs≡ΔQr/T, Δs=change between two equilibrium states, ΔQr = heat transferred, T = absolute temperature.

Gravitational force (Newton’s law) Fg=G m_em_p/r², Inertia F_net=∑F = ma

Acceleration due to gravity g 09.81 ms^-2

Gravity fields can bend light.

The factors of gravity are; Constant force, work energy theorem, gravitational potential energy, average force on moving wave, average angular speed, centripetal force and the laws of gravitation. The gravitational force exerted by a spherical mass on a particle out side the sphere is F=gMeM/Re². The second condition for equilibrium asserts that an object is in rotational equilibrium, external torque up to 7 fields. Plus considering the center of gravity, angular momentum, the mass-energy equilance, the kinetic energy, keeping in mind Kepler’s third law which is based on the ratio of the square of each object. Also the translational kinetic energy, change in entropy, inertia and the acceleration due to the gravity have to be considered.

The impulse-momentum theorem states that the impulse of the force acting on an object equals the change in momentum of that object. The center of gravity of an object is the point where all the weight of the object can be considered to be concentrated.

Chandrasekhar limit is the maximum possible mass of an object that is prevented from collapsing under its own gravity by the degeneracy pressure of either electrons or neutrons. Spin- speed-pressure = gravity. The faster the spin, the faster the collapse, the faster it spins, the conservation of angular momentum.

Inverse square law force for short distance V(r) =-Gmm^1/r - a Gmm^1/r e^-r/l. a = s strength of the Yukawa potential relative to the 1/r potential, for smaller the r = l, v(r) = -Gmm^1/r (1+a). (1+a)G= gravitation constant. The strength of the Yukawa potential is restricted to 1a1< 10^-6 for l =10^-9cm. Gravitational mass distribution in a spherical p(r) =density. M(r) = mass enclosed within the radius r then g=Gm(r)/r² and dg/dr=-2G M(r)/r³+G/r² dm/dr = 2g/r+G/r² 4p r ²p(r). The value of G can be calculated from the measured values g and dg/dr provided we know the density p. g varies with depth for uniform-density sphere, g would decrease linearly with depth. Gravitation effects can not propagate with infinite speed; we expect that gravitational effects propagate in the form of waves at the speed of light.

There are two forces; 1- gravitational mg by the mass, 2 – centrifugal pseudo-force ma produced by rotation, g=acceleration of gravity, a=centrifugal acceleration. For a known field strength E(r) the force and torques on a system (per unit charge) a system point charges e₁,e₂,e₃…en located in a vacuum at position r₁, r₂,r₃… r_n the energy to bring the individual charges to their locations. No work is required to bring the first system into place. Now bring e₂ to its place, distance r₁-r₂ = r₁₂ from e, and because of Coulomb repulsion, work e ₁e₂/r₁₂ is required. Next bring e₃ for this we have to expend energy e₁e₃/r₁₃ +e ²e³/r²³ continues this way until all charges are in place. The total work of assembling w=e ₁e₂/r₁₂ + e ₁e₃/r₁₃ +e ₂e₃/r₂₃ + …

Maxwell’s field theory = every volume – element dv in empty space, if the region of an electric field contains the energy udv, the energy density u=1/8pE² accordingly an extended region of space should contain energy. U=1/8p∫ E² dv the assemblage of h point charges, the expended work w is identical with the increase of field energy u. In a dipole electrostatic field fixed moment p in an electrostatic field E. Set e = e and e₂=-e and r₁=r+s, r₂=r with es=p the E field produces placed point charges. We obtain energy contribution – pe when orient dipole parallel to the field, we must expend the work pe with the potential energy u of the dipole depends upon the angle q between the dipole and the field direction. The torque T=δu/δθ=-pe sinθ must exist, against which we must do work increases with θ for this turning moment. In a non uniform field to torque the field gradient is positive on T minimum is when it is perpendicular to the direction of the field.

Universal gravitation – every particle of matter in the universe attracts every other particle with a force which is directly proportional to the product of their masses and inversely proportional to the square of their distances apart. Gravitational force “attraction” exerted at an external point by a sphere of uniform density or a sphere composed of uniform concentric shells was the same as if it’s whole mass were concentrated at its centre. As for the space curvature, matter and energy and the pressure involved. The mass grips space-time telling it how to curve, space-time grips mass telling it how to move. Increases in gravity by shrinking will cause a release of energy, causing it to be hotter, causing it to expand; decreases in gravity by expanding will cause a reduction in gravity causing it to cool causing it to shrink.

Lorentz-Fitzgerald contraction – An electron has radius when at rest, its radius when moving at a speed is given by its radius. Since the velocity is bound to be less than the speed of light the ratio must be less than 1; the radius is less than the initial radius corresponding to a contraction. The mass of a particle (electron) would be inversely proportional to its radius, its mass when moving with the speed 99% of the speed of light the effective mass is 7.1 times the rest mass. If the rest mass is 99.9% the speed of light the effective mass is 22.4 times the rest mass.

M-Theory – The number of dimensions required for each of the gauge groups u(1) – represented by motions around a circle, su(2) epitomized by rotations along a spherical surface, su(3) exemplified by transformation in a space with several complex variables requires 4 dimensions adding 1,2,4=7. Combining this with the 4 dimensions of space-time produce the value of 11 for the minimum number, precisely the dimensionality of super gravity. Taken to the power of two (duality) to account for chirality distinctions. S-duality involves exchanging a week coupling constant for a strong one. T- Duality pertains to the replacement of a small complification radius with an enormous one. Gravitation limited to one-millimeter π radius bulk. Lowering the universal temperature would precipitate a phase transition. Infinite is relative and possible. Spherical!

Different forms of energy as a source of gravity. The types are the rest mass of protons and neutrons, the rest mass of electrons, electric fields in the nucleus, magnetic fields in a nucleus, strong fields in a nucleus, a weak field in nucleus, and the gravitational energy in the earth. Gravity gravitates, earths gravitational self-energy is 4.6 x 10^-10 times its rest mass. If gravitational self-energy does not contribute in the normal way to the gravitational mass. Gravitational interactions of anti-matter inertial masses for particles and anti-particles correspond. The observed equality of gravitational and inertia for all forms of energy means that any system containing any combination of the different kinds of energy will have equal gravitational and inertial masses. Gravitational quadrupole radiation is electromagnetic dipole radiation.

Flight factors

There are four forces of flight: the drag, lift, thrust and gravity. The center of pressure is the line of balance between the 4 forces. An up angle of 5 degrees will create 25% lift; an up angle of 10% will create 30% lift, etc. The pressure differential is 2.5 ounces per square inch, which will produce a lift force of 20lbs per square foot.

Viscosity and Kinematic viscosity of air;

Viscosity: V=μ/p   μ- (Pas x 10⁵), Kinematic Viscosity V – (m^2/5 x10⁶)

Reynolds number (Re)

Average velocity u, diameter d, density p, viscosity μ, kinematic viscosity V.

Re = pud/μ = ud/V, compression Δp/p

Decreases in diameter; area A1 & A2, velocities u₁ & u₂, densities p₁ & p₂

P₁A₁u₁=p₂A₂u₂ the flow velocity is inversely proportional to the cross sectional area. When diameter is reduced flow velocity increase.

At speeds 2 times the speed of sound produces 400 degrees F on a ships exterior.

Propagation of a sonic wave is a change in pressure (sound) that propagates at sonic velocity (a) from the source in all directions known as calm, subsonic(m<1), sonic(m=1) and supersonic(m>1), mach cone(2ά) sin ά=a/u=1/m called a mach angle. Sonic velocity is proportional to the square root of absolute temperature. A sudden change in pressure is adiabatic (a=√ΚRT) 5 times the speed of sound is hypersonic. Mach numbers are the ratio of flow velocity to sonic velocity, a pressure increase brings about an increase in density (Δρ=Δρ/a²).

Shock waves are created when air undergoes large and rapid compression. A thin wave of large pressure change is produced. The wave face at the rear of the compression wave, being at a higher temperature propagates faster than the wave at the front. The rear wave gradually catches up with the front wave increasing the pressure discontinuously, which is called a shock wave. The shock wave is only associated with an increase in pressure in the flow direction. Since a shock wave is different from a sound wave, because of a large change in pressure the propagation velocity of a shock is larger the larger the pressure rise, the greater the propagation velocity. A Rankine-Hugoniont equation shows the relationships between the pressure, density, and temperature ahead and behind a shock wave.

Turbine flow is descried as follows; If a turbine is placed in the course of a flow (air/water) the turbine rotation is owing to the velocity of energy. The flow velocity is obtainable from the rotational velocity of the turbine, while the integrated volume is calculated by the number of revolutions.

Thrust is the mass and time rather than density speed cross section, we can express thrust at the rate which it inserts momentum into the flow. Thrust happens when V₂ is greater than V₁. The trust time, distance and power is worked per time power becomes force times velocity. The efficiency is called Froude propulsion efficiency moving the largest possible mass-per-time (m/t)

The tension is T=Δpt and the stress is σn=Δpr/t. Photon power is propulsion derived from light.

Electric propulsion is charged particles discharged backwards to give forward thrust. 1 electro thermal, arc jets, and resistojet. 2 electrostatic, ion accelerators, 3 electromagnetic, coaxial magnetic plasma. Electric propulsion has a low thrust but a very low flow rate giving a 1sp of some 4000s (specific impulse) Stockes law for drag for a sphere is D=6πμau, a= the radius of the sphere. For terminal velocities mass equal gravity mg, sphere densities po, and fluid medium pf.

V=mg/6πua = 2a²g (po-pf)/qu. The mass of 1 kilogram exerts a force of 9.8 newtons at the surface. The acceleration due to gravity is 9.8m-². F=ma F= force in the product of mass m and the acceleration a.

The required escape velocity Ve for vertical flight is Ve=√2go re where go is the acceleration of gravity at the earths surface 32.174 ft/s² and re is the radius of earth 3959 miles or 6371km. Escape velocity is around 36,700ft/s or 25,000mi/h or 11.2km/s.

Space hazards are cosmic radiation, meteorites, weightlessness, light deprivation, and temperature which is -69.7ºF and -56.5ºC.

Time is taken as 10km/second =36,000km/hr = mach30 or 30 times the speed of sound, 1/30,000 of the speed of light. 1 parsecs = 3,262 light years or 3.086 x 10¹³km. Light travels 300 million meters a second or 300,000 km a second. 1 light year = 10¹³km. The moon is 1.3 light seconds away; the sun is 8 light minutes away.

Gravity

Humans tolerate 15 g gravity for a few minutes – when perpendicular, but only 6 g when in the direction of acceleration.

Humans can take 1 g (32' per second per second the speed of light)

Acceleration due to gravity

g/cm/s²=9.780356(1+0.0052885 sin² ø – 0.0000059 sin^z Zø)

            ^-0.003086 H     ø latitude          H height

Ø         H=0                 H=1Km           H=5Km           H=10Km

0          9.78036           9.77727           9.76493           9.74950

5          9.78075           9.77760           9.76532           9.74989

10        9.78191           9.77882           9.76648           9.75105

15        9.78381           9.78072           9.76838           9.75295

20        9.78638           9.78330           9.77095           9.7552

25        9.78956           9.78647           9.77413           9.75870

30        9.79324           9.79016           9.77781           9.76238

35        9.79732           9.79424           9.78189           9.76646

40        9.80167           9.79858           9.78624           9.77081

45        9.80616           9.80307           9.79073           9.77530

50        9.81065           9.80757           9.79522           9.77979

55        9.81501           9.81193           9.79958           9.78415

60        9.81911           9.81602           9.80368           9.78825

65        9.82281           9.81972           9.80738           9.79195

70        9.82601           9.82292           9.81058           9.79515

75        9.82860           9.82551           9.81317           9.79774

80        9.83051           9.82743           9.81508           9.79965

85        9.83168           9.82860           9.81625           9.80082

90        9.83208           9.82899           9.81665           9.80122

           

Magnetics

Chapter 10

Magnetics

Magnetic Field of a Permanent Magnet

Iron filings arrange themselves along the lines of a magnetic force, making the lines visible. Magnets are surrounded by a magnetic field, and the magnetic lines of force run from one pole of the magnet to the other.

Orion Press Photo Library

Microsoft ® Encarta ® 2006. © 1993-2005 Microsoft Corporation. All rights reserved.

Magnetic field strength 20T, B:10^-15 to 50T (10^-11 to 500kg)

Lorentz force F=-e(E+v x B)

High magnetic field >50T duration of 10^-5s

Flux density = 100T (1MG)

Magnetic pressure 4 x 10¹⁰ PA

Electric field strength E:<5 x 10⁸ Vm^-1

Each electron with a charge 1.6 x 10^-19 c, circles the atom once in 10^-16 s, if we divided the electronic charge by this time interval. We see the orbiting electron is equivalent to a current of 1.6 x 10^-3 A. Such a current produces a magnetic field on the order of 20T at the center of the circular path. Magnetic field lines always form closed loops, they don’t begin or end any where.

A varying magnetic field induces an EMF and hence an electric field. “Faraday’s law” The charge required to deposit or liberate a mass=m, F=Faraday’s constant, z= charge of ion, M=relative ionic mass. Magnetic fields are generated by moving charges “Ampere’s Law.” Where dB is the infinitesimal element of the magnitude of the magnetic flux density, at the distance r at point p from the element length dl of a conductor, the magnetic permeability of free space, 1 is the current flowing through the conductor and the angle between the direction of he current and the line joining the element of the conductor and P. Electromagnetic waves carry energy as they travel through space with an average power per unit area is where Em and Bm are the max values of the electric and magnetic fields. Electromagnetic waves transport momentum as well as energy. The speed of light, the frequency f and wave are related by c=fλ. The ratio of the electric field to the magnetic field in an electromagnetic wave equals the speed of light. Electromagnetic waves flow forward and backwards in time. Mutual induction uses oscillating magnetic fields.

Gauss’ Law the total electric flux normal to a closed surface in an electric field is proportional to the algebraic sum of the electric charges within the surface. Cooperative phenomenon – phase transition. Maxwell’s theory showed that magnetism and electricity are one and the same. Force and light itself is a manifestation of the electromagnetic force. Maxwell realized that if the charging electric field could produce a changing magnetic field and the changing magnetic field could produce a changing electric field, the two components of the single unified electromagnetic field could get along quite nicely together without any need for electric currents or magnetic’s at all. The equations say that a self-reinforcing electromagnetic field with the electricity producing the magnetism and the magnetism producing the electricity could set off through space on its own once it was given a push to start.

Isothermal renanence

Ti = poor titanomagnetities Ti = poor ilmenohaematites. The two commonest magnetic minerals in most terrestrial rocks. They form solid solutions at temperatures above 900 degrees c but have a rhombohedral structure. Silica rich rocks (acidic) have compositions approaching that of the ilmenohaematite series. Ultra basic rocks (silica poor) titanomagnetite. Quench-cooling is fairly rare under most geological conditions. More normal cooling rates result in the high temperature solid solutions resolving to form intergrowths between titanomagnetite (cubic) series and ilmenohaematite (rhombohedral).

Shape anisotropy, the magnetic field within a magnetic grain is uniform, the magneto static force due to the magnetic poles at the surface depend on their separation. In spherical grains the separation of the surface poles is constant in all directions, so spheres have zero shape anisotropy. Magnetic properties depending on the actual composition. The unit cell size increases with increased Ti content and Curie temperature decreasing.

Magnetic units, the force between two poles, of strength in a vacuum given the distance between them and the constant of the permeability of free space with a sI value. The magnetic field of a material and its intensity of magnetization are both measured in amperes per meter (Am^-1) and are related to the magnetic induction in a magnetized medium, which is measured in tesla (T). In a three axis system cause anhysteretic magnation rotations, because gyro magnetic magnetization which dominate the natural remanence with a tendency to become “noisy” at fields over 50mT. A three dimensional statistical analyses, distribution vector points on a sphere would have a probability density, the angular distance between an individual point and the true mean of the vector population and the precision parameter, varying from zero if all vector points are uniformly distributed, to infinity if they are all identical to the mean. In the Fisher distribution the precision, is for the absolute total population of the vector points on a sphere. K precision parameters can be estimated for the values greater than 7 and for K greater than 3. In the analyses of unit vectors of values of K greater than 10 indicate that the observed mean is close to the true mean of the total population. Uniformly magnetized spheres. Taniclination = 2 tan (latitude) the variation in total intensity according to latitude. The formula for the magnetization on the surface of a uniformly magnetized sphere with the total magnetic moment. Spherical harmonic analysis of the field show that virtually all the field (greater than 99.5%) is of a internal origin with the balance attributable to the effects of electrical currents in the upper mantle. 80% of the geomagnetic field is described in terms of the first harmonics (based on 8 internal fields). If electrical currents being maintained as a result of convective motion in the outer core, it will create a uniform magnetization in the inner (solid) core. Magnetization as a fundamental property of rotating matter is generally accepted,  the field is generally accepted that the field is generated by electrical currents circulating in the core.

Nuclear Magnetic resonance is the magnetic movement along an axis and the nuclear gyro magnetic ratio of the energy of that spin. The magnetic field is expressed in tesla (T) it is the energy level between the two states. The frequency for the transition of protons is 11.7T 500 x 10⁶ Hz and 18.1T 800 x 10⁶ Hz. Black Body radiation – the electromagnetic radiation density in an evacuated enclosure is brought to a temperature radiation is produced. The spectral distribution of the radiation energy is denoted by the angular frequency and is not dependent on material it is determined solely by temperature. On the elements surface energy is propagated with the velocity of light and all points contribute radiation. A fraction of the radiation present in the volume will restrict the wave. The isotropic radiation is suspended by the surface. The radiation incident is obtained by integrating the volume of the cone contained in the hemisphere. The total radiation incident is obtained over the complete hemisphere. The energy radiated per unit time and unit area corresponds to the total energy in the enclosure and includes the total energy for each spectral component. Since radiation and momentum differ by a factor of 1/c the momentum is transferred to the walls and is the radiation pressure. If the wall is the ideal reflector, the radiation will be reflected and the momentum is transferred. The energy emitted per second per square centimeter of the black body are  the non-degenerative energy levels of an atom, the latter reacts with the black body radiation by emitting or absorbing light quanta of a magnitude dependent on the state and the density of the spectral energy and the radiation field absorbed from the field. A 3 dimensional oscillator is 2π ²e²/m u (w).

Earth’s Geomagnetic fields

North pole is at 73⁰ N 100⁰W South pole is at 68⁰ S 143⁰ E

The total intensity which varies from 30μT near the equator to 60μT near the poles. The total magnetic moment being at present 8.01 x 10²²Am². A 80% geomagnetic field can be described in terms of first harmonics, corresponding to a single geocentric dipole inclined at 11 ½⁰ from earths arc of rotation with magnetic poles at 78.5⁰N 70⁰W and 78.5⁰S 110⁰E. This is an average tendency for the total magnetic field strength to decrease by about 18nT year^-1. This would result in a lost of the geomagnetic field in 200 years time.

The field has a distinct westward drift of a non-dipole component at 0.2⁰ year^-1. 20,000 km is the limit that distant gravitational forces disrupt planetary bodies. The possibility that universal gravitational constant G may not be constant, but could vary on a long time scale. Which could be major important in the evaluating the significance of the red shift of the light from distant galaxies.

On a parochial scale it has been suggested that many terrestrial features result from changes in the constant increases in earth’s radius is during a 1/3 during the last 200 million years. G has changed by more than ± 1% during the 4.5 billion years. The equator is where earth’s rotational surface speed is the highest, the higher the elevation the less work required. Delta – Vn is the horizontal velocity to take orbit speed at earth equator the payload would start with a Vn of 1,000 mph with 11 tons per person – life support supplies for 2 years. Orbital speeds 17,500 mph to 24,000 mph. Total atmospheric pressure 14.7 psi oxygen make up to 21% of atmospheric pressure at sea level 3.09 psi. Space suits 3.5 psi. Spacecraft 5 psi.

At 64,800 mph revolving around the sun it’s not speed that harms the body. Positive G force – head to foot, Negative G force – foot to head. 4 G positive force on 150lb = 600 pounds, 5 G is blackout.

Biological aspects of Magnetations

Corn grows faster in a magnetic field strength stronger than earths. Many animals (insects, invertebrates, bacteria) have magnetic particles in their brains or necks that appear to have an influence on their behavior. There are other similar direct effects of geomagnetic fields on animals, such as high incidence of heart attacks during magnetic storms. Micro- organisms form new species at time close to polarity transitions and other species become extinct. There is a 50:50 probability occurring at the time, The cause thought to be related to decreases in strength of the field which would cause a restriction in the height of the ionosphere and allow a greater penetration of cosmic and solar radiation. This also causing mutation rates to increase. The increase in radiation is calculated to be less than 10%, even for a total loss of the geomagnetic field. Out planet in a 24,000 year orbit passes through a photon belt of light twice, each passage lasting about 2,000 years, causing disruptions in magnetic fields.

Magnetic Levitation above a Superconductor

A small cylindrical magnet floats above a high temperature superconductor. The vapor is from boiling liquid nitrogen, which keeps the superconductor in a zero-resistance state. As the magnet is lowered toward the superconductor, it induces an electric current, which creates an opposing magnetic field in accordance with Ampere’s law. Because the superconductor has no electrical resistance, this induced current continues to flow, keeping the magnet suspended indefinitely.

Photo Researchers, Inc./David Parker/IMI/Science Source

Microsoft ® Encarta ® 2006. © 1993-2005 Microsoft Corporation. All rights reserved.

Organic Superconductors

Elliot theory

According to the model where torsional oscillations of the ET Molecule can life symmetry restrictions and enable introchain and interchain spin relaxation to cause broaden line widths, higher pressure, should stiffen the crystal lattice which should reduce the oscillations and thereby sharpen the ESR line width. An empirical formula for describing this situation has been proposed.

Fundamental interactions:

1.      Gravitational interactions are 10⁴⁰ times weaker than electromagnetic interaction.

1. A gravitational interactions are long-range atomic-negligibly weak.

2.      Weak interactions are 10¹⁰ times weaker than electromagnetic interactions.

3.      Electromagnetic interactions are the exchange of virtual photons.

4.      Strong interactions are 10² times stronger than electromagnetic interactions and are the exchange of virtual mesons.

Superconductors

The critical temperature at which electrical resistance drops to zero, subjected to magnetic field (the temperature always drop to a lower temperature in a magnetic field.) high temperatures means anything above 23K. The Meissner effects is a phenomenon relates to the ability to exclude a magnetic field – a permanent magnet will float above a superconducting material at its critical temperature (the higher the magnetic field the lower the temperature). Magnetic susceptibility is measured by the degree to which magnetic fields are distorted by the material. Evidently oxygen had to be present in the atmosphere for the creation of superconductivity when mixing and baking small amounts of material.

Super molecular machines

Supramolecular machines are organized systems of cooperating molecules, where the individual molecules constitute the functional components. Such systems have a great potential as sensors and actuators, information processing devices, memories with high storage capacity tailored catalyst for complex “chemical” reactions and energy conversion systems. The most intricate devices of the kind are living systems. Tools and machines are functional units, systems where different components interact to perform tasks that cannot be done by any component. In bio-systems, most intricate supramolecular machines – for example; machines transforming “light” energy into chemical energy by electron or proton pumping are present. The energy is by self-assembly from molecular components of complicated structures able to interlock in a distinct manner. Supramolecular engineering are involved in the programmed environment changes. The critical point is to find appropriate conclusions leading to the evaluation of a life like system at the end of a long sequence of consistent steps.

Magnetic bubble memory

This consists of materials, such as magnetic garnets, that are easily magnetized. A thin film on a non-magnetic substrate constitutes a bubble – memory chip. When a magnetic field is applied to a chip, by placing it between two permanent, garnets, cylindrical domains are formed. The bubble constitutes a magnetic region of one polarity surrounded by a magnetic region of the opposite polarity. Information is represented as the presence or absence of a bubble at a specified storage location and is retrieved by means of a rotating magnetic field. A chip measures 15mm² or 25mm² in closed in two permanent magnets and two rotating field coils; each chip can store up to 1 million bits.