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A Helmholtz coil Helmholtz coil schematic drawing. 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 ...
The Helmholtz equation has a variety of applications in physics and other sciences, including the wave equation, the diffusion equation, and the Schrödinger equation for a free particle. In optics, the Helmholtz equation is the wave equation for the electric field. [1] The equation is named after Hermann von Helmholtz, who studied it in 1860. [2]
Two coils in an anti-Helmholtz configuration are used to generate a weak quadrupolar magnetic field; here, we will consider the coils as being separated along the -axis. In the proximity of the field zero, located halfway between the two coils along the z {\displaystyle z} -direction, the field gradient is uniform and the field itself varies ...
The Sommerfeld radiation condition is used to solve uniquely the Helmholtz equation. For example, consider the problem of radiation due to a point source in three dimensions, so the function in the Helmholtz equation is () = (), where is the Dirac delta function. This problem has an infinite number of solutions, for example, any function of the ...
English: Cross section of B (magnetic field strength) magnitude in a Helmholtz coil (actually consisting of two coils: one at the top, one at the bottom in the plot). The eight contours are for field magnitudes of 0.5 {\displaystyle B_0}, 0.8 {\displaystyle B_0}, 0.9 {\displaystyle B_0}, 0.95 {\displaystyle B_0}, 0.99 {\displaystyle B_0}, 1.01 {\displaystyle B_0}, 1.05 {\displaystyle B_0}, and ...
Helmholtz coil An arrangement of coils useful for producing a uniform magnetic field within a certain volume. henry The SI unit of inductance. Hertz The SI unit of frequency, equivalent to one cycle per second. heterodyne The process of mixing signals of a number of frequencies to produce new frequencies. heterostructure
When charged particles move in electric and magnetic fields the following two laws apply: Lorentz force law: = (+),; Newton's second law of motion: = =; where F is the force applied to the ion, m is the mass of the particle, a is the acceleration, Q is the electric charge, E is the electric field, and v × B is the cross product of the ion's velocity and the magnetic flux density.
The fast multipole method (FMM) is a numerical technique that was developed to speed up the calculation of long-ranged forces in the n-body problem.It does this by expanding the system Green's function using a multipole expansion, which allows one to group sources that lie close together and treat them as if they are a single source.