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3D motion of fluid near vortex lines
In fluid mechanics, Helmholtz's theorems, named after Hermann von Helmholtz, describe the three-dimensional motion of fluid in the vicinity of vortex
Helmholtz's_theorems
Certain vector fields are the sum of an irrotational and a solenoidal vector field
In physics and mathematics, the Helmholtz decomposition theorem or the fundamental theorem of vector calculus states that certain differentiable vector
Helmholtz_decomposition
Topics referred to by the same term
several theorems known as the Helmholtz theorem: Helmholtz decomposition, also known as the fundamental theorem of vector calculus Helmholtz reciprocity
Helmholtz_theorem
Thermodynamics-like result in classical mechanics
The Helmholtz theorem of classical mechanics reads as follows: Let H ( x , p ; V ) = K ( p ) + φ ( x ; V ) {\displaystyle H(x,p;V)=K(p)+\varphi (x;V)}
Helmholtz theorem (classical mechanics)
Helmholtz_theorem_(classical_mechanics)
Theorem in electrical circuit analysis
to the individual forces. Using this theorem, as well as Ohm's law, Helmholtz proved the following three theorems about the relation between the internal
Thévenin's_theorem
Theorem in vector calculus
classical mechanics and fluid dynamics it is called Helmholtz's theorem. Theorem 2-1 (Helmholtz's theorem in fluid dynamics). Let U ⊆ R 3 {\displaystyle U\subseteq
Stokes'_theorem
This is a list of notable theorems. Lists of theorems and similar statements include: List of algebras List of algorithms List of axioms List of conjectures
List_of_theorems
German physicist and physiologist (1821–1894)
several contributions, including Helmholtz's theorems for vortex dynamics in inviscid fluids. 1889 copy of Helmholtz's "Über die Erhaltung der Kraft",
Hermann_von_Helmholtz
Type of fluid flow
boundary velocities: this is known as the Helmholtz minimum dissipation theorem. The Lorentz reciprocal theorem states a relationship between two Stokes
Stokes_flow
In fluid mechanics, Helmholtz minimum dissipation theorem (named after Hermann von Helmholtz who published it in 1868) states that the steady Stokes flow
Helmholtz minimum dissipation theorem
Helmholtz_minimum_dissipation_theorem
Helmholtz resonance Helmholtz theorem (classical mechanics) Generalized Helmholtz theorem Helmholtz's theorems Helmholtz–Kohlrausch effect Helmholtz-Smoluchowski
List of things named after Hermann von Helmholtz
List_of_things_named_after_Hermann_von_Helmholtz
Theorem in mathematics
_{a}^{b}g(x)\,dx.} There are various slightly different theorems called the second mean value theorem for definite integrals. A commonly found version is
Mean_value_theorem
Equations of motion for viscous fluids
of the body force. This result follows from the Helmholtz theorem (also known as the fundamental theorem of vector calculus). The first equation is a pressureless
Navier–Stokes_equations
Relationship between derivatives and integrals
The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at every
Fundamental theorem of calculus
Fundamental_theorem_of_calculus
Statement relating differentiable symmetries to conserved quantities
corresponding conservation law. This is the first of two theorems (see Noether's second theorem) published by the mathematician Emmy Noether in 1918. The
Noether's_theorem
Equations of electromagnetism
solutions to Maxwell's equations in the potential formulation (see the Helmholtz theorem). To obtain the fields, these expressions are substituted into the
Jefimenko's_equations
Flow of electric charge
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Electric_current
Phenomena related to electric charge
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Electricity
Theorem in calculus relating line and double integrals
Integral Theorems of Vector Analysis". Vector Calculus (6th ed.). New York: W. H. Freeman and Company. ISBN 978-1-4292-1508-4. Green's Theorem on MathWorld
Green's_theorem
Fluid flow revolving around an axis of rotation
limiting case of a vortex tube with zero diameter. According to Helmholtz's theorems, a vortex line cannot start or end in the fluid – except momentarily
Vortex
Conditions for switching order of integration in calculus
function over its domain. The Fubini and Tonelli theorems are usually combined and form the Fubini–Tonelli theorem, which gives the conditions under which it
Fubini's_theorem
Quantity in electromagnetism
ϕ {\displaystyle \phi } is guaranteed from these two laws using Helmholtz's theorem. For example, since the magnetic field is divergence-free (Gauss's
Magnetic_vector_potential
Assemblage of connected electrical elements
product of the resistance and the current flowing through it. Norton's theorem: Any network of voltage or current sources and resistors is electrically
Electrical_network
Foundational law of electromagnetism relating electric field and charge distributions
as Gauss's flux theorem or sometimes Gauss's theorem, is one of Maxwell's equations. It is an application of the divergence theorem, and it relates the
Gauss's_law
SI derived unit of power
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Watt
Rate at which electrical energy is transferred by an electric circuit
representation is often called the power triangle. Using the Pythagorean theorem, the relationship among real, reactive and apparent power is: (apparent
Electric_power
Measure of electric field through surface
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Electric_flux
Theorem in calculus
In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem relating the flux of a vector field through
Divergence_theorem
Imbalance of electric charges within or on the surface of a material
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Static_electricity
Electric current that periodically reverses direction
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Alternating_current
Magnet in the shape of a horseshoe
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Horseshoe_magnet
Object that has a magnetic field
expression of the force between two magnetic dipoles. Dipole magnet Earnshaw's theorem Electret Electromagnetic field Electromagnetism Halbach array Magnetic
Magnet
Undergraduate textbook by David J. Griffiths
Appendix A: Vector Calculus in Curvilinear Coordinates Appendix B: The Helmholtz Theorem Appendix C: Units Index Paul D. Scholten, a professor at Miami University
Introduction to Electrodynamics
Introduction_to_Electrodynamics
Surface integral of the magnetic field
the definition of the magnetic vector potential A and the fundamental theorem of the curl the magnetic flux may also be defined as: Φ B = ∮ ∂ S A ⋅ d
Magnetic_flux
Resistance to magnetic flux
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Magnetic_reluctance
Equation (H2) is a system of ordinary differential equations: the usual theorems on the existence and uniqueness of solutions to ordinary differential equations
Inverse problem for Lagrangian mechanics
Inverse_problem_for_Lagrangian_mechanics
Branch of theoretical physics
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Classical_electromagnetism
Unidirectional flow of electric charge
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Direct_current
Electromagnetic opposition to change
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Lenz's_law
Specialty of electronic engineering
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Radio-frequency_engineering
Study of still or slow electric charges
or λ d ℓ {\displaystyle \lambda \,\mathrm {d} \ell } . The divergence theorem allows Gauss's law to be written in differential form: ∇ ⋅ E = ρ ε 0 .
Electrostatics
Difference in electric potential between two points in space
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Voltage
Types of electrical circuits
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Series_and_parallel_circuits
Hohenberg–Kohn theorem Quantum mechanics Pierre Hohenberg and Walter Kohn Helmholtz's theorems Helmholtz theorem Helmholtz free energy Helmholtz decomposition
List of scientific laws named after people
List_of_scientific_laws_named_after_people
Italian chemist and physicist (1745–1827)
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Alessandro_Volta
English chemist and physicist (1791–1867)
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Michael_Faraday
Force acting on charged particles in electric and magnetic fields
Larmor formula Cyclotron radiation Magnetoresistance Scalar potential Helmholtz decomposition Field line Coulomb's law Electromagnetic buoyancy In SI
Lorentz_force
Incorrect but seminal physical theory
should be capable of supporting such stable vortices. According to Helmholtz's theorems, these vortices would correspond to different kinds of knot. Thomson
Vortex_theory_of_the_atom
Production of voltage by a varying magnetic field
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Electromagnetic_induction
Approximation of a function by a polynomial
the complex plane. However, its usefulness is dwarfed by other general theorems in complex analysis. Namely, stronger versions of related results can be
Taylor's_theorem
English early pioneer of electrical research
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
George_Singer
Theorem regarding circulation in a barotropic ideal fluid
\mathrm {d} S} Bernoulli's principle Euler equations (fluid dynamics) Helmholtz's theorems Thermomagnetic convection Kundu, P and Cohen, I: Fluid Mechanics
Kelvin's_circulation_theorem
Basic law of electromagnetism
time t. It can also be written in an integral form by the Kelvin–Stokes theorem: ∮ ∂ Σ E ⋅ d l = − ∬ Σ ∂ B ∂ t ⋅ d A {\displaystyle \oint _{\partial \Sigma
Faraday's_law_of_induction
Electric and magnetic fields produced by moving charged objects
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Electromagnetic_field
Electromagnetic effect in physics
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Hall_effect
Law of electrical current and voltage
Maximum power transfer theorem Norton's theorem Electric power Sheet resistance Superposition theorem Thermal noise Thévenin's theorem Uses LED-Resistor circuit
Ohm's_law
Fundamental interaction between charged particles
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Electromagnetism
Material that does not conduct an electric current
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Insulator_(electricity)
Technique in chemistry and manufacturing
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Electrolysis
Electromagnetic property of matter
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Electric_charge
Electrically insulating substance able to be polarised by an applied electric field
write this relationship as a function of frequency. Due to the convolution theorem, the integral becomes a simple product, P ( ω ) = ε 0 χ e ( ω ) E ( ω )
Dielectric
Expulsion of a magnetic field from a superconductor
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Meissner_effect
Physical quantity, density of magnetic moment per volume
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Magnetization
German physicist (1857–1894)
and Berlin, where he studied under Gustav Kirchhoff and Hermann von Helmholtz. In 1880, Hertz obtained his Ph.D. from the University of Berlin, and
Heinrich_Hertz
Theorem in physics showing the conservation of energy for the electromagnetic field
list (link) Kinsler, P.; Favaro, A.; McCall M.W. (2009). "Four Poynting theorems" (PDF). European Journal of Physics. 30 (5): 983. arXiv:0908.1721. Bibcode:2009EJPh
Poynting's_theorem
Thermodynamic potential
In thermodynamics, the Helmholtz free energy (or Helmholtz energy) is a thermodynamic potential that measures the useful work obtainable from a closed
Helmholtz_free_energy
Statement on equilibrium in electromagnetism
Earnshaw's theorem states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic
Earnshaw's_theorem
On converting relations to functions of several real variables
Function Theorem. Modern Birkhauser Classics. Birkhauser. ISBN 0-8176-4285-4. de Oliveira, Oswaldo (2013). "The Implicit and Inverse Function Theorems: Easy
Implicit_function_theorem
Opposition of a circuit to a current when a voltage is applied
analysis, such as voltage division, current division, Thévenin's theorem and Norton's theorem, can also be extended to AC circuits by replacing resistance
Electrical_impedance
Material property
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Permeance
Magnetic analog of electric potential valid outside materials
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Magnetic_scalar_potential
4D analogue of electric current density
current (CVC) hypothesis for electroweak interactions. Four-vector Noether's theorem Covariant formulation of classical electromagnetism Ricci calculus Rindler
Four-current
Type of pump
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Electromagnetic_pump
Process of energy release of a contracting star or planet
The Kelvin–Helmholtz mechanism is an astronomical process that occurs when the surface of a star or a planet cools. The cooling causes the internal pressure
Kelvin–Helmholtz_mechanism
Line integral of the electric field
E {\textstyle V_{\mathbf {E} }} well-defined everywhere. The gradient theorem then allows us to write: E = − ∇ V E {\displaystyle \mathbf {E} =-\mathbf
Electric_potential
Object or material which allows the flow of electric charge with little energy loss
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Electrical_conductor
the magnetic field would go with it. The theorem describing this effect is called the frozen-in-field theorem. Even in a fluid with a finite conductivity
Earth's_magnetic_field
Electrical conductivity with exactly zero resistance
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Superconductivity
Law of classical electromagnetism
the origin). Loops such as the one described appear in devices like the Helmholtz coil, the solenoid, and the Magsail spacecraft propulsion system. Calculation
Biot–Savart_law
Amount of charge flowing through a unit cross-sectional area per unit time
the decrease in the total charge inside the volume. From the divergence theorem: ∮ S j ⋅ d A = ∫ V ∇ ⋅ j d V {\displaystyle \oint _{S}{\mathbf {j} \cdot
Current_density
Evaluates a line integral through a gradient field using the original scalar field
tool used in the analysis of many physical systems. Many of the critical theorems of vector calculus generalize elegantly to statements about the integration
Gradient_theorem
Model in aerodynamics
Publications, Inc., New York ISBN 0-486-60541-8 Helmholtz's theorems Kutta condition Kutta–Joukowski theorem Prandtl's lifting-line model Trailing vortices
Horseshoe_vortex
Fundamental physical law of electromagnetism
Gauss's law does not give any information regarding the curl of E (see Helmholtz decomposition and Faraday's law). However, Coulomb's law can be proven
Coulomb's_law
Relativistic vector field
notation) can be decomposed[clarification needed] via the Hodge decomposition theorem as the sum of an exact, a coexact, and a harmonic form, A = d α + δ β +
Electromagnetic four-potential
Electromagnetic_four-potential
Measure of the electric polarizability of a dielectric material
this relationship as a function of frequency. Because of the convolution theorem, the integral becomes a simple product, P ( ω ) = ε 0 χ ( ω ) E (
Permittivity
French physicist (1819–1896)
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Hippolyte_Fizeau
Motor which works on direct current
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
DC_motor
Measure of directional electromagnetic energy flux
Kinsler, Paul; Favaro, Alberto; McCall, Martin W. (2009). "Four Poynting Theorems". European Journal of Physics. 30 (5): 983. arXiv:0908.1721. Bibcode:2009EJPh
Poynting_vector
Opposition to the passage of an electric current
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Electrical resistance and conductance
Electrical_resistance_and_conductance
3D generalization of the Leibniz integral rule
calculus, the Reynolds transport theorem (also known as the Leibniz–Reynolds transport theorem), or simply the Reynolds theorem, named after Osborne Reynolds
Reynolds_transport_theorem
Foundational law of classical magnetism
charge or mass can build up in a volume of space. Due to the Helmholtz decomposition theorem, Gauss's law for magnetism is equivalent to the following statement:
Gauss's_law_for_magnetism
first discovered by E. M. Lifshitz in 1946. It follows from Helmholtz's Theorem (see Helmholtz decomposition.) The general metric perturbation has ten degrees
Scalar–vector–tensor decomposition
Scalar–vector–tensor_decomposition
Russian physicist (1804–1865)
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Emil_Lenz
Concept in classical electromagnetism
form". The forms are exactly equivalent, and related by the Kelvin–Stokes theorem (see the "proof" section below). Forms using SI units, and those using
Ampère's_circuital_law
Liquid that is attracted by poles of a magnet
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Ferrofluid
Charge transfer due to contact or sliding
approaches to triboelectrification. Alessandro Volta and Hermann von Helmholtz suggested that the role of sliding was to produce more contacts per second
Triboelectric_effect
French physicist (1736–1806)
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Charles-Augustin_de_Coulomb
Concept in physics
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations
Magnetomotive_force
Force in which the work done in moving an object depends only on its displacement
D. (The equivalence of 1 and 3 is also known as (one aspect of) Helmholtz's theorem.) The term conservative force comes from the fact that when a conservative
Conservative_force
Electrical action produced by a non-electrical source
"Abhandlungen zur Thermodynamik, von H. Helmholtz. Hrsg. von Max Planck". (Tr. "Papers to thermodynamics, on H. Helmholtz. Hrsg. by Max Planck".) Leipzig, W
Electromotive_force
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HELMHOLTZS THEOREMS
HELMHOLTZS THEOREMS
HELMHOLTZS THEOREMS
HELMHOLTZS THEOREMS
HELMHOLTZS THEOREMS
HELMHOLTZS THEOREMS
HELMHOLTZS THEOREMS
HELMHOLTZS THEOREMS
HELMHOLTZS THEOREMS
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