Nikiya Anton Bettey 2021: 09-22-2021-1654 - magnetic flux magnetic reluctance permeance Dielectric complex reluctance properties of magnetic materials Air Permeance of Building Materials ferrofluid

Wednesday, September 22, 2021

09-22-2021-1654 - magnetic flux magnetic reluctance permeance Dielectric complex reluctance properties of magnetic materials Air Permeance of Building Materials ferrofluid

In physics, specifically electromagnetism, the magnetic flux through a surface is the surface integral of the normal component of the magnetic field B over that surface. It is usually denoted $Φ$ or $Φ B$ . The SI unit of magnetic flux is the weber (Wb; in derived units, volt–seconds), and the CGS unit is the maxwell. Magnetic flux is usually measured with a fluxmeter, which contains measuring coils and electronics, that evaluates the change of voltage in the measuring coils to calculate the measurement of magnetic flux.

https://en.wikipedia.org/wiki/Magnetic_flux

Magnetic reluctance, or magnetic resistance, is a concept used in the analysis of magnetic circuits. It is defined as the ratio of magnetomotive force (mmf) to magnetic flux. It represents the opposition to magnetic flux, and depends on the geometry and composition of an object.

Magnetic reluctance in a magnetic circuit is analogous to electrical resistance in an electrical circuit in that resistance is a measure of the opposition to the electric current. The definition of magnetic reluctance is analogous to Ohm's law in this respect. However, magnetic flux passing through a reluctance does not give rise to dissipation of heat as it does for current through a resistance. Thus, the analogy cannot be used for modelling energy flow in systems where energy crosses between the magnetic and electrical domains. An alternative analogy to the reluctance model which does correctly represent energy flows is the gyrator–capacitor model.

Magnetic reluctance is a scalar extensive quantity, akin to electrical resistance. The unit for magnetic reluctance is inverse henry, H⁻¹.

https://en.wikipedia.org/wiki/Magnetic_reluctance

Permeance, in general, is the degree to which a material admits a flow of matter or energy. Permeance is usually represented by a curly capital P: ${\mathcal {P}}$ .

Electromagnetism[edit]

In electromagnetism, permeance is the inverse of reluctance. In a magnetic circuit, permeance is a measure of the quantity of magnetic flux for a number of current-turns. A magnetic circuit almost acts as though the flux is conducted, therefore permeance is larger for large cross-sections of a material and smaller for smaller cross section lengths. This concept is analogous to electrical conductance in the electric circuit.

Magnetic permeance ${\mathcal {P}}$ is defined as the reciprocal of magnetic reluctance ${\mathcal {R}}$ (in analogy with the reciprocity between electric conductance and resistance):

{\mathcal {P}}={\frac {1}{{\mathcal {R}}}}

which can also be re-written:

{\mathcal {P}}={\frac {\Phi _{B}}{NI}}

using Hopkinson's law (magnetic circuit analogue of Ohm's law for electric circuits) and the definition of magnetomotive force (magnetic analogue of electromotive force):

{\mathcal {F}}=\Phi _{B}{\mathcal {R}}=NI

where:

Φ_B, magnetic flux,

I, current, in amperes,

N, winding number of, or count of turns in the electric coil.

Alternatively in terms of magnetic permeability (analogous to electric conductivity):

{\mathcal {P}}={\frac {\mu A}{\ell }}

where:

μ, permeability of material,

A, cross-sectional area,

\ell

, magnetic path length.

The SI unit of magnetic permeance is the henry (H), that is webers per ampere-turn.

Materials science[edit]

In materials science, permeance is the degree to which a material transmits another substance.

External articles and references[edit]

Electromagnetism[edit]

Properties of Magnetic Materials (units of magnetic permeance)

Material science[edit]

Bombaru, D., Jutras, R., and Patenaude, A., "Air Permeance of Building Materials". Summary report prepared by, AIR-INS Inc. for Canada Mortgage and Housing Corporation, Ottawa, 1988.

https://en.wikipedia.org/wiki/Permeance

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Magnetic alloys‎ (19 P)
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Pages in category "Electric and magnetic fields in matter"

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In physics and engineering, a phasor (a portmanteau of phase vector^[1]^[2]), is a complex number representing a sinusoidal function whose amplitude (A), angular frequency (ω), and initial phase (θ) are time-invariant. It is related to a more general concept called analytic representation,^[3] which decomposes a sinusoid into the product of a complex constant and a factor depending on time and frequency. The complex constant, which depends on amplitude and phase, is known as a phasor, or complex amplitude,^[4]^[5] and (in older texts) sinor^[6] or even complexor.^[6]

A common situation in electrical networks is the existence of multiple sinusoids all with the same frequency, but different amplitudes and phases. The only difference in their analytic representations is the complex amplitude (phasor). A linear combination of such functions can be factored into the product of a linear combination of phasors (known as phasor arithmetic) and the time/frequency dependent factor that they all have in common.

The origin of the term phasor rightfully suggests that a (diagrammatic) calculus somewhat similar to that possible for vectors is possible for phasors as well.^[6] An important additional feature of the phasor transform is that differentiation and integration of sinusoidal signals (having constant amplitude, period and phase) corresponds to simple algebraic operations on the phasors; the phasor transform thus allows the analysis (calculation) of the AC steady state of RLC circuits by solving simple algebraic equations (albeit with complex coefficients) in the phasor domain instead of solving differential equations (with real coefficients) in the time domain.^[7]^[8] The originator of the phasor transform was Charles Proteus Steinmetz working at General Electric in the late 19th century.^[9]^[10]

Glossing over some mathematical details, the phasor transform can also be seen as a particular case of the Laplace transform, which additionally can be used to (simultaneously) derive the transient response of an RLC circuit.^[8]^[10] However, the Laplace transform is mathematically more difficult to apply and the effort may be unjustified if only steady state analysis is required.^[10]

Fig 2. When function

\scriptstyle A\cdot e^{i(\omega t+\theta )}

is depicted in the complex plane, the vector formed by its imaginary and real parts rotates around the origin. Its magnitude is A, and it completes one cycle every 2

π

/ω seconds. θ is the angle it forms with the real axis at t = n•2

π

/ω, for integer values of n.

Notation[edit]

Phasor notation (also known as angle notation) is a mathematical notation used in electronics engineering and electrical engineering. $1\angle \theta$ can represent either the vector $(\cos \theta, \sin \theta)$ or the complex number $\cos \theta +j\sin \theta =e^{j\theta }$ , with $j^{2}=-1$ , both of which have magnitudes of 1. A vector whose polar coordinates are magnitude $A$ and angle $\theta$ is written $A\angle \theta .$ ^[11]

The angle may be stated in degrees with an implied conversion from degrees to radians. For example $1\angle 90$ would be assumed to be $1\angle 90^{\circ },$ which is the vector $(0,1)$ or the number $e^{j\pi /2}.$

Definition[edit]

Euler's formula indicates that sinusoids can be represented mathematically as the sum of two complex-valued functions:

A\cos(\omega t+\theta )=A\cdot {\frac {e^{i(\omega t+\theta )}+e^{-i(\omega t+\theta )}}{2}},

^[a]

or as the real part of one of the functions:

A\cos(\omega t+\theta )=\operatorname {Re} \{Ae^{i(\omega t+\theta )}\}=\operatorname {Re} \{Ae^{i\theta }\cdot e^{i\omega t}\}.

The function $Ae^{i(\omega t+\theta )}$ is called the analytic representation of $A\cos(\omega t+\theta )$ . Figure 2 depicts it as a rotating vector in a complex plane. It is sometimes convenient to refer to the entire function as a phasor,^[12] as we do in the next section. But the term phasor usually implies just the static complex number $Ae^{i\theta }$ .

https://en.wikipedia.org/wiki/Phasor

In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles. They are distinct from triangle identities, which are identities potentially involving angles but also involving side lengths or other lengths of a triangle.

These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.

Cosines and sines around the unit circle

https://en.wikipedia.org/wiki/List_of_trigonometric_identities#Angle_sum_and_difference_identities

The perturbed γ-γ angular correlation, PAC for short or PAC-Spectroscopy, is a method of nuclear solid-state physics with which magnetic and electric fields in crystal structures can be measured. In doing so, electrical field gradients and the Larmor frequency in magnetic fields as well as dynamic effects are determined. With this very sensitive method, which requires only about 10-1000 billion atoms of a radioactive isotope per measurement, material properties in the local structure, phase transitions, magnetism and diffusion can be investigated. The PAC method is related to nuclear magnetic resonance and the Mössbauer effect, but shows no signal attenuation at very high temperatures. Today only the time-differential perturbed angular correlation (TDPAC) is used.

Schema of PAC-Spectroscopy

https://en.wikipedia.org/wiki/Perturbed_angular_correlation

Zeroing the rifle[edit]

Let $\delta\theta$ be the bore angle required to compensate for the bullet drop caused by gravity. Standard practice is for the shooter to zero their rifle at a standard range, such as 100 or 200 meters. Once the rifle is zeroed, adjustments to $\delta\theta$ are made for other ranges relative to this zero setting. One can calculate $\delta\theta$ using standard Newtonian dynamics as follows (for more details on this topic, see Trajectory).

Two equations can be set up that describe the bullet's flight in a vacuum, (presented for computational simplicity compared to solving equations describing trajectories in an atmosphere).

x(t)=v_{{bullet}}\cos(\delta \theta )t\,

(Equation 1)

y(t)=v_{{bullet}}\sin(\delta \theta )t-{\frac {1}{2}}gt^{2}\,

(Equation 2)

Solving Equation 1 for t yields Equation 3.

t={\frac {x}{v_{{bullet}}\cos(\delta \theta )}}

(Equation 3)

Equation 3 can be substituted in Equation 2. The resulting equation can then be solved for x assuming that $y=0$ and $t\neq 0$ , which produces Equation 4.

y(t)=0=\left(v_{{bullet}}\sin(\delta \theta )-{\frac {1}{2}}gt\right)t

0=v_{{bullet}}\sin(\delta \theta )t-{\frac {1}{2}}gt^{2}

v_{{bullet}}\sin(\delta \theta )={\frac {1}{2}}gt={\frac {1}{2}}g{\frac {x}{v_{{bullet}}\cos(\delta \theta )}}

x={\frac {v_{{bullet}}^{2}2\sin(\delta \theta )\cos(\delta \theta )}{g}}\,

(Equation 4)

where $v_{{bullet}}$ is the speed of the bullet, x is the horizontal distance, y is the vertical distance, g is the Earth's gravitational acceleration, and t is time.

When the bullet hits the target (i.e. crosses the LOS), $x=R_{H}$ and $y=0$ . Equation 4 can be simplified assuming $x=R_{H}$ to obtain Equation 5.

R_{H}={\frac {v_{{bullet}}^{2}\;2\,\sin(\delta \theta )\,\cos(\delta \theta )}{g}}={\frac {v_{{bullet}}^{2}\sin(2\delta \theta )}{g}}\,

(Equation 5)

The zero range, $R_{H}$ , is important because corrections due to elevation differences will be expressed in terms of changes to the horizontal zero range.

For most rifles, $\delta\theta$ is quite small. For example, the standard 7.62 mm (0.308 in) NATO bullet is fired with a muzzle velocity of 853 m/s (2800 ft/s). For a rifle zeroed at 100 meters, this means that $\delta \theta =0.039^{\circ }$ .

While this definition of $\delta\theta$ is useful in theoretical discussions, in practice $\delta\theta$ must also account for the fact that the rifle sight is actually mounted above the barrel by several centimeters. This fact is important in practice, but is not required to understand the rifleman's rule.

https://en.wikipedia.org/wiki/Rifleman%27s_rule#Zeroing_the_rifle

Gamma correction or gamma is a nonlinear operation used to encode and decode luminance or tristimulus values in videoor still image systems.^[1] Gamma correction is, in the simplest cases, defined by the following power-law expression:

V_{\text{out}}=AV_{\text{in}}^{\gamma },

where the non-negative real input value $V_{{\text{in}}}$ is raised to the power $\gamma$ and multiplied by the constant A to get the output value $V_{{\text{out}}}$ . In the common case of A = 1, inputs and outputs are typically in the range 0–1.

A gamma value $\gamma <1$ is sometimes called an encoding gamma, and the process of encoding with this compressive power-law nonlinearity is called gamma compression; conversely a gamma value $\gamma >1$ is called a decoding gamma, and the application of the expansive power-law nonlinearity is called gamma expansion.

The effect of gamma correction on an image: The original image was taken to varying powers, showing that powers larger than 1 make the shadows darker, while powers smaller than 1 make dark regions lighter.

https://en.wikipedia.org/wiki/Gamma_correction

Nikiya Anton Bettey 2021

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Wednesday, September 22, 2021

09-22-2021-1654 - magnetic flux magnetic reluctance permeance Dielectric complex reluctance properties of magnetic materials Air Permeance of Building Materials ferrofluid

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