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. [3] If the current in one of the coils is reversed, a uniform-gradient magnetic field is produced 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.
In physics the Lorentz force is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge q moving with a velocity v in an electric field E and a magnetic field B experiences a force of
Maxwell's equations are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric 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.
A magnetic field is a vector field that describes the magnetic influence on an electric charge of other moving charges or magnetized materials. A charge that is moving in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. The effects of magnetic fields are commonly seen in permanent magnets, which pull on magnetic materials such as iron, and attract or repel other magnets, creating a torque. In addition, a magnetic field that varies with location will exert a force on a range of non-magnetic materials by affecting the motion of their outer atomic electrons. Magnetic fields surround magnetized materials, and are created by electric currents such as those used in electromagnets, and by electric fields varying in time. Since both strength and direction of a magnetic field may vary with location, they are described as a map assigning a vector to each point of space or, more precisely—because of the way the magnetic field transforms under mirror reflection—as a field of pseudovectors.
Flux describes any effect that appears to pass or travel through a surface or substance. A 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 across an electrical conductor in a changing magnetic field.
In electromagnetism and electronics, inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The flow of electric current creates a magnetic field around the conductor. The field strength depends on the magnitude of the current, and follows any changes in 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, the purpose of which is to generate a controlled magnetic field through a coil wound into a tightly packed helix. The coil can be arranged to produce a uniform magnetic field in a volume of space when an electric current is passed through it. The term solenoid was coined in 1823 by André-Marie Ampère to designate a helical coil.
In classical electromagnetism, Ampère's circuital law relates the integrated magnetic field around a closed loop to the electric current passing through the loop. James Clerk Maxwell derived it using hydrodynamics in his 1861 published paper "On Physical Lines of Force" and it is now one of the Maxwell equations, which form the basis of classical electromagnetism.
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. 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.
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 basic law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (EMF)—a phenomenon known as electromagnetic induction. It is the fundamental operating principle of transformers, inductors, and many types of electrical motors, generators and solenoids.
Gaussian units constitute a metric system of physical units. This system is the most common of the several electromagnetic unit systems based on cgs (centimetre–gram–second) units. It is also called the Gaussian unit system, Gaussian-cgs units, or often just cgs units. The term "cgs units" is ambiguous and therefore to be avoided if possible: there are several variants of cgs with conflicting definitions of electromagnetic quantities and units.
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. Besides creating magnetic fields, Helmholtz coils are also used in scientific apparatus to cancel external magnetic fields, such as the Earth's magnetic field.
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:
Magnetic pressure is an energy density associated with a magnetic field. Any magnetic field has an associated magnetic pressure contained by the boundary conditions on the field. It is identical to any other physical pressure except that it is carried by the magnetic field rather than by the kinetic energy of gas molecules. A gradient in field strength causes a force due to the magnetic pressure gradient called the magnetic pressure force.
Magnets exert forces and torques on each other due to the rules of electromagnetism. The forces of attraction field of magnets are due to microscopic currents of electrically charged electrons orbiting nuclei and the intrinsic magnetism of fundamental particles that make up the material. Both of these are modeled quite well as tiny loops of current called magnetic dipoles that produce their own magnetic field and are affected by external magnetic fields. The most elementary force between magnets, therefore, is the magnetic dipole–dipole interaction. If all of the magnetic dipoles that make up two magnets are known then the net force on both magnets can be determined by summing up all these interactions between the dipoles of the first magnet and that of the second.
In the beginning of the 19th century, many experimental and theoretical works had been accomplished in understanding of electromagnetics. In the 1780s, Coulomb's law of electrostatics is established. In 1825, Ampère published his Ampère's law. Michael Faraday discovered the electromagnetic induction through his experiments and conceptually, he emphasized the lines of forces in this electromagnetic induction. In 1834, Lenz solved the problem of the direction of the induction, and 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 in urgent need at that time.
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 elctromagnetic 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.
