Information about Magnetostatics
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Magnetostatics is the study of static magnetic fields. In electrostatics, the charges are stationary, whereas here, the currents are stationary. As it turns out magnetostatics is a good approximation even when the currents are not static as long as the currents do not alternate rapidly.
Applications
Magnetostatics as a special case of Maxwell's equations
Starting from Maxwell's equations, the following simplifications can be made:- ignore any electrostatic charge
- ignore the electric field
- presume the magnetic field is constant with respect to time
| Name | Partial differential form | Integral form |
|---|---|---|
| presumption |  | |
| Gauss's law for magnetism: |  |  |
| presumption |  | |
| Ampère's law: |  |  |
The quality of this approximation may be guessed by comparing the above equations with the full version of Maxwell's equations and considering the importance of the terms that have been removed. Of particular significance is the comparison of the
term against the 
term. If the term is substantially larger, then the smaller term may be ignored without significant loss of accuracy.
Re-introducing Faraday's law
A common technique is to solve a series of magnetostatic problems at incremental time steps and then use these solutions to approximate the term
. Plugging this result into Faraday's Law finds a value for 
(which had previously been ignored). This method is not a true solution of Maxwell's equations but can provide a good approximation for slowly changing fields.
Solving magnetostatic problems
If all currents in a system are known (i.e. if a complete description of is available) then
the magnetic field can be determined from the currents by the Biot-Savart equation:
This technique works well for problems where the medium is a vacuum or air or some similar material with a relative permeability of 1. This includes Air core inductors and Air core transformers. One advantage of this technique is that a complex coil geometry can be integrated in sections, or for a very difficult geometry numerical integration may be used. Since this equation is primarily used to solve linear problems, the complete answer will be a sum of the integral of each component section.
One pitfall in the use of the Biot-Savart equation is that it does not implicitly enforce Gauss's law for magnetism so it is possible to come up with an answer that includes magnetic monopoles. This will occur if some section of the current path has not been included in the integral (implying that electrons are being continuously created in one place and destroyed in another).
Using Biot-Savart in the presence of Ferromagnetic, Ferrimagnetic or Paramagnetic materials is difficult because the external current induces a surface current in the magnetic material which in turn must be included in the integral. The value of the surface current depends on the magnetic field which was what you were trying to calculate in the first place. For these problems, using Ampère's law (usually in integral form) is a better choice. For problems where the dominant magnetic material is a highly permeable magnetic core with relatively small air gaps, a magnetic circuit approach is useful. When the air gaps are large in comparison to the magnetic circuit length, fringing becomes significant and usually requires a finite element calculation. The finite element calculation uses a modified form of the magnetostatic equations above in order to calculate magnetic potential. The value of
can be found from the magnetic potential.
Electromagnetism is the physics of the electromagnetic field: a field which exerts a force on particles that possess the property of electric charge, and is in turn affected by the presence and motion of those particles.
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Electricity (from New Latin ēlectricus, "amberlike") is a general term for a variety of phenomena resulting from the presence and flow of electric charge. This includes many well-known physical phenomena such as lightning, electromagnetic fields and electric currents,
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magnetism is one of the phenomena by which materials exert attractive or repulsive forces on other materials. Some well known materials that exhibit easily detectable magnetic properties (called magnets) are nickel, iron and their alloys; however, all materials are influenced to
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Electrostatics (also known as static electricity) is the branch of physics that deals with the phenomena arising from what seem to be stationary electric charges. This includes phenomena as simple as the attraction of plastic wrap to your hand after you remove it from a
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Flavour in particle physics
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Coulomb's law, developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated as follows:
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- The magnitude of the electrostatic force between two points electric charges is directly proportional to the product of the magnitudes of each
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electric field. This electric field exerts a force on other electrically charged objects. The concept of electric field was introduced by Michael Faraday.
The electric field is a vector field with SI units of newtons per coulomb (N C−1
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The electric field is a vector field with SI units of newtons per coulomb (N C−1
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In physics and mathematical analysis, Gauss's law is the electrostatic application of the generalized Gauss's theorem giving the equivalence relation between any flux, e.g.
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Electric potential is the potential energy per unit of charge associated with a static (time-invariant) electric field, also called the electrostatic potential, typically measured in volts. It is a scalar quantity.
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In physics, the electric dipole moment (or electric dipole for short) is a measure of the polarity of a system of electric charges.
In the simple case of two point charges, one with charge and one with charge , the electric dipole moment is:
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In the simple case of two point charges, one with charge and one with charge , the electric dipole moment is:
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magnetic field is a field that permeates space and which exerts a magnetic force on moving electric charges and magnetic dipoles. Magnetic fields surround electric currents, magnetic dipoles, and changing electric fields.
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Magnetic flux, represented by the Greek letter Φ (phi), is a measure of quantity of magnetism, taking account of the strength and the extent of a magnetic field.
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The Biot-Savart Law is an equation in electromagnetism that describes the magnetic field vector B in terms of the magnitude and direction of the source electric current, the distance from the source electric current, and the magnetic permeability weighting factor.
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In physics, the magnetic moment or magnetic dipole moment is a measure of the strength of a magnetic source. In the simplest case of a current loop, the magnetic moment is defined as:
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Classical electromagnetism (or classical electrodynamics) is a theory of electromagnetism that was developed over the course of the 19th century, most prominently by James Clerk Maxwell.
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Electric current is the flow (movement) of electric charge. The SI unit of electric current is the ampere (A), which is equal to a flow of one coulomb of charge per second.
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Definition
The amount of electric current (measured in amperes) through some surface, e.g...... Click the link for more information.
Lorentz force is the force exerted on a charged particle in an electromagnetic field. The particle will experience a force due to electric field of qE, and due to the magnetic field qv × B.
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Electromotive force (emf, ) is a term used to characterize electrical devices, such as voltaic cells, thermoelectric devices, electrical generators and transformers, and even resistors.
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For magnetic induction, see .
Electromagnetic induction is the production of voltage across a conductor situated in a changing magnetic field or a conductor moving through a stationary magnetic field...... Click the link for more information.
Faraday's law of induction (more generally, the law of electromagnetic induction) states that the induced emf (electromotive force) in a closed loop equals the negative of the time rate of change of magnetic flux through the loop.
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Displacement current is a quantity related to changing electric field. It occurs in dielectric materials and also in free space.
In the particular case of when it occurs in free space, it is not believed to involve the motion of electric charge as is the case with
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In the particular case of when it occurs in free space, it is not believed to involve the motion of electric charge as is the case with
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For thermodynamic relations, see .
In electromagnetism, Maxwell's equations are a set of four equations that were first presented as a distinct group in 1884 by Oliver Heaviside in conjunction with Willard Gibbs...... Click the link for more information.
The electromagnetic field is a physical field produced by electrically charged objects. It affects the behaviour of charged objects in the vicinity of the field.
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Electromagnetic (EM) radiation is a self-propagating wave in space with electric and magnetic components. These components oscillate at right angles to each other and to the direction of propagation, and are in phase with each other.
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Electrical resistance is a measure of the degree to which an object opposes an electric current through it. The SI unit of electrical resistance is the ohm. Its reciprocal quantity is electrical conductance measured in siemens.
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Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential. The most common form of charge storage device is a two-plate capacitor.
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inductance, or more accurately self-inductance of the circuit. The term was coined by Oliver Heaviside in February 1886. It is customary to use the symbol for inductance, possibly in honour of the physicist Heinrich Lenz.
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Electrical impedance, or simply impedance, describes a measure of opposition to a sinusoidal alternating current (AC). Electrical impedance extends the concept of resistance to AC circuits, describing not only the relative magnitudes of the voltage and current, but also the
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A resonator is a device or system that exhibits resonance or resonant behavior. Many objects that use resonant effects are referred to simply as resonators. Examples of resonators are discussed in this article.
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theory of relativity, or simply relativity, refers specifically to two theories: Albert Einstein's special relativity and general relativity.
The term "relativity" was coined by Max Planck in 1908 to emphasize how special relativity (and later, general relativity)
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The term "relativity" was coined by Max Planck in 1908 to emphasize how special relativity (and later, general relativity)
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