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Electricity · Magnetism
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Magnetostatics is the study of static magnetic fields. Electromagnetism is the Physics of the Electromagnetic field: a field which exerts a Force on particles that possess the property of In Physics, magnetism is one of the Phenomena by which Materials exert attractive or repulsive Forces on other Materials. In Classical electromagnetism, Ampère's circuital law, discovered by André-Marie Ampère, relates the integrated Magnetic field around a closed Electric current is the flow (movement of Electric charge. The SI unit of electric current is the Ampere. In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges Magnetic flux, represented by the Greek letter Φ ( Phi) is a measure of quantity of Magnetism, taking into account the strength and the extent of a Magnetic The Biot–Savart Law is an equation in electromagnetism that describes the Magnetic field B generated by an Electric current. In Physics, Astronomy, Chemistry, and Electrical engineering, the term magnetic moment of a system (such as a loop of Electric current In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges In electrostatics, the charges are stationary, whereas here, the currents are stationary or dc(direct current). Electrostatics is the branch of Science that deals with the Phenomena arising from what seems to be stationary Electric charges Since Classical Electric current is the flow (movement of Electric charge. The SI unit of electric current is the Ampere. 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.
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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 |
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| presumption |  |
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| Gauss's law for magnetism: |  |
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| presumption |  |
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| Ampère's law: |  |
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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. In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric In Mathematics, partial differential equations ( PDE) are a type of Differential equation, i The European Space Agency 's INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL) is detecting some of the most energetic radiation that comes from space In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric 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. In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric
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. The Biot–Savart Law is an equation in electromagnetism that describes the Magnetic field B generated by an Electric current. This vacuum means "absence of matter" or "an empty area or space" for the cleaning appliance see Vacuum cleaner. Temperature and layers The temperature of the Earth's atmosphere varies with altitude the mathematical relationship between temperature and altitude varies among five In Electromagnetism, permeability is the degree of Magnetization of a material that responds linearly to an applied Magnetic field. 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. In Numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite Integral, and by extension Since this equation is primarily used to solve linear problems, the complete answer will be a sum of the integral of each component section. The word linear comes from the Latin word linearis, which means created by lines.
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. In Physics, a magnetic monopole is a hypothetical particle that is a Magnet with only one pole (see Maxwell's equations for more on magnetic 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). The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J
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. Ferromagnetism is the basic mechanism by which certain materials (such as Iron) form Permanent magnets and/or exhibit strong interactions with Magnets it A ferrimagnetic Interaction is a specific type of Antiferromagnetic interaction in which the net spin of the System is not equal to zero due Paramagnetism is a form of magnetism which occurs only in the presence of an externally applied magnetic field 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. The magnetic core is a key component in electrical and electromechanical devices such as Electromagnets Transformers and Inductors A magnetic core is a A magnetic circuit is a closed path containing a Magnetic flux. When the air gaps are large in comparison to the magnetic circuit length, fringing becomes significant and usually requires a finite element calculation. A magnetic circuit is a closed path containing a Magnetic flux. The finite element method (FEM (sometimes referred to as finite element analysis) is a numerical technique for finding approximate solutions of Partial differential The finite element calculation uses a modified form of the magnetostatic equations above in order to calculate magnetic potential. The finite element method (FEM (sometimes referred to as finite element analysis) is a numerical technique for finding approximate solutions of Partial differential The magnetic potential provides a mathematical way to define a Magnetic field in Classical electromagnetism. The value of 
can be found from the magnetic potential. The magnetic potential provides a mathematical way to define a Magnetic field in Classical electromagnetism.
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