Search results
Results from the WOW.Com Content Network
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]
The Helmholtz decomposition in three dimensions was first described in 1849 [9] by George Gabriel Stokes for a theory of diffraction. Hermann von Helmholtz published his paper on some hydrodynamic basic equations in 1858, [10] [11] which was part of his research on the Helmholtz's theorems describing the motion of fluid in the vicinity of vortex lines. [11]
A pair of Helmholtz coils produces a uniform and measurable magnetic field at right angles to the electron beam. This magnetic field deflects the electron beam in a circular path. By measuring the accelerating potential (volts), the current (amps) to the Helmholtz coils, and the radius of the electron beam, e/m can be calculated. [8]
Two coils in an anti-Helmholtz configuration are used to generate a weak quadrupolar magnetic field; by convention, the coils are separated along the -axis.In the proximity of the field zero, located halfway between the two coils along the -direction, the field gradient is uniform and the field itself varies linearly with displacement from the field zero.
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
To simplify the notation, let = ˙ and define a collection of n 2 functions Φ j i by =. Theorem. (Douglas 1941) There exists a Lagrangian L : [0, T] × TM → R such that the equations (E) are its Euler–Lagrange equations if and only if there exists a non-singular symmetric matrix g with entries g ij depending on both u and v satisfying the following three Helmholtz conditions:
The Sommerfeld radiation condition is used to solve uniquely the Helmholtz equation. For example, consider the problem of radiation due to a point source x 0 {\displaystyle x_{0}} in three dimensions, so the function f {\displaystyle f} in the Helmholtz equation is f ( x ) = δ ( x − x 0 ) , {\displaystyle f(x)=\delta (x-x_{0}),} where δ ...