A Maxwell coil is a device for producing a large volume of almost constant (or constant-gradient) magnetic field. It is named in honour of the Scottish physicist James Clerk Maxwell.
A Maxwell coil is an improvement of a Helmholtz coil: in operation it provides an even more uniform magnetic field (than a Helmholtz coil), but at the expense of more material and complexity.
A constant-field Maxwell coil set consists of three coils oriented on the surface of a virtual sphere. [1] According to Maxwell's original 1873 design: [2] each of the outer coils should be of radius , and distance from the plane of the central coil of radius .
Maxwell specified the number of windings as 64 for the central coil and 49 for the outer coils. Though Maxwell did not specifically state that current for the coils came from the same source, his work was specifically describing the construction of a sensitive galvanometer designed to detect a single current source. It follows that the ampere-turns for each of the smaller coils must be exactly of the turns of the larger.
A gradient-field Maxwell coil is essentially the same geometry of the 3-coil configuration above, with the central coil removed to leave only the smaller two coils and the current in one of these reversed. [3] This produces a uniform-gradient magnetic field near the centre of the two coils. Maxwell describes the use of the 2-coil configuration for the generation of a uniform force on a small test coil. [4] A Maxwell coil of this type is similar to a Helmholtz coil with the coil distance increased from coil radius to and the coils fed with opposite currents.
Magnetism is the class of physical attributes that occur through a magnetic field, which allows objects to attract or repel each other. Because both electric currents and magnetic moments of elementary particles give rise to a magnetic field, magnetism is one of two aspects of electromagnetism.
Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, electric and magnetic circuits. The equations provide a mathematical model for electric, optical, and radio technologies, such as power generation, electric motors, wireless communication, lenses, radar, etc. They describe how electric and magnetic fields are generated by charges, currents, and changes of the fields. The equations are named after the physicist and mathematician James Clerk Maxwell, who, in 1861 and 1862, published an early form of the equations that included the Lorentz force law. Maxwell first used the equations to propose that light is an electromagnetic phenomenon. The modern form of the equations in their most common formulation is credited to Oliver Heaviside.
A magnetic field is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. A permanent magnet's magnetic field pulls on ferromagnetic materials such as iron, and attracts or repels other magnets. In addition, a nonuniform magnetic field exerts minuscule forces on "nonmagnetic" materials by three other magnetic effects: paramagnetism, diamagnetism, and antiferromagnetism, although these forces are usually so small they can only be detected by laboratory equipment. Magnetic fields surround magnetized materials, electric currents, and electric fields varying in time. Since both strength and direction of a magnetic field may vary with location, it is described mathematically by a function assigning a vector to each point of space, called a vector field.
Flux describes any effect that appears to pass or travel through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications to physics. For transport phenomena, flux is a vector quantity, describing the magnitude and direction of the flow of a substance or property. In vector calculus flux is a scalar quantity, defined as the surface integral of the perpendicular component of a vector field over a surface.
Electromagnetic or magnetic induction is the production of an electromotive force (emf) across an electrical conductor in a changing magnetic field.
In physics, specifically electromagnetism, the Biot–Savart law is an equation describing the magnetic field generated by a constant electric current. It relates the magnetic field to the magnitude, direction, length, and proximity of the electric current.
Capacitance is the capability of a material object or device to store electric charge. It is measured by the charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are two closely related notions of capacitance: self capacitance and mutual capacitance. An object that can be electrically charged exhibits self capacitance, for which the electric potential is measured between the object and ground. Mutual capacitance is measured between two components, and is particularly important in the operation of the capacitor, an elementary linear electronic component designed to add capacitance to an electric circuit.
Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The electric current produces a magnetic field around the conductor. The magnetic field strength depends on the magnitude of the electric current, and follows any changes in the magnitude of the current. From Faraday's law of induction, any change in magnetic field through a circuit induces an electromotive force (EMF) (voltage) in the conductors, a process known as electromagnetic induction. This induced voltage created by the changing current has the effect of opposing the change in current. This is stated by Lenz's law, and the voltage is called back EMF.
A solenoid is a type of electromagnet formed by a helical coil of wire whose length is substantially greater than its diameter, which generates a controlled magnetic field. The coil can produce a uniform magnetic field in a volume of space when an electric current is passed through it.
Classical electromagnetism or classical electrodynamics is a branch of theoretical physics that studies the interactions between electric charges and currents using an extension of the classical Newtonian model. It is, therefore, a classical field theory. The theory provides a description of electromagnetic phenomena whenever the relevant length scales and field strengths are large enough that quantum mechanical effects are negligible. For small distances and low field strengths, such interactions are better described by quantum electrodynamics which is a quantum field theory.
A Treatise on Electricity and Magnetism is a two-volume treatise on electromagnetism written by James Clerk Maxwell in 1873. Maxwell was revising the Treatise for a second edition when he died in 1879. The revision was completed by William Davidson Niven for publication in 1881. A third edition was prepared by J. J. Thomson for publication in 1892.
"A Dynamical Theory of the Electromagnetic Field" is a paper by James Clerk Maxwell on electromagnetism, published in 1865. In the paper, Maxwell derives an electromagnetic wave equation with a velocity for light in close agreement with measurements made by experiment, and deduces that light is an electromagnetic wave.
Faraday's law of induction is a law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (emf). This phenomenon, known as electromagnetic induction, is the fundamental operating principle of transformers, inductors, and many types of electric motors, generators and solenoids.
A Helmholtz coil is a device for producing a region of nearly uniform magnetic field, named after the German physicist Hermann von Helmholtz. It consists of two electromagnets on the same axis, carrying an equal electric current in the same direction. Besides creating magnetic fields, Helmholtz coils are also used in scientific apparatus to cancel external magnetic fields, such as the Earth's magnetic field.
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.
The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum. It is a three-dimensional form of the wave equation. The homogeneous form of the equation, written in terms of either the electric field E or the magnetic field B, takes the form:
Heaviside–Lorentz units constitute a system of units and quantities that extends the CGS with a particular set of equations that defines electromagnetic quantities, named for Oliver Heaviside and Hendrik Antoon Lorentz. They share with the CGS-Gaussian system that the electric constant ε0 and magnetic constant µ0 do not appear in the defining equations for electromagnetism, having been incorporated implicitly into the electromagnetic quantities. Heaviside–Lorentz units may be thought of as normalizing ε0 = 1 and µ0 = 1, while at the same time revising Maxwell's equations to use the speed of light c instead.
By the first half of the 19th century, the understanding of electromagnetics had improved through many experiments and theoretical work. In the 1780s, Charles-Augustin de Coulomb established his law of electrostatics. In 1825, André-Marie Ampère published his force law. In 1831, Michael Faraday discovered electromagnetic induction through his experiments, and proposed lines of forces to describe it. In 1834, Emil Lenz solved the problem of the direction of the induction, and Franz Ernst Neumann wrote down the equation to calculate the induced force by change of magnetic flux. However, these experimental results and rules were not well organized and sometimes confusing to scientists. A comprehensive summary of the electrodynamic principles was needed.
Electromagnetism is one of the fundamental forces of nature. Early on, electricity and magnetism were studied separately and regarded as separate phenomena. Hans Christian Ørsted discovered that the two were related – electric currents give rise to magnetism. Michael Faraday discovered the converse, that magnetism could induce electric currents, and James Clerk Maxwell put the whole thing together in a unified theory of electromagnetism. Maxwell's equations further indicated that electromagnetic waves existed, and the experiments of Heinrich Hertz confirmed this, making radio possible. Maxwell also postulated, correctly, that light was a form of electromagnetic wave, thus making all of optics a branch of electromagnetism. Radio waves differ from light only in that the wavelength of the former is much longer than the latter. Albert Einstein showed that the magnetic field arises through the relativistic motion of the electric field and thus magnetism is merely a side effect of electricity. The modern theoretical treatment of electromagnetism is as a quantum field in quantum electrodynamics.
The Maxwell-Lodge effect is a phenomenon of electromagnetic induction in which an electric charge, near a solenoid in which current changes slowly, feels an electromotive force (e.m.f.) even if the magnetic field is practically static inside and null outside. It can be considered a classical analogue of the quantum mechanical Aharonov–Bohm effect, where instead the field is exactly static inside and null outside.
