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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]
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]
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 ...
The coil cancels the Earth's magnetic field within a central 6-foot (1.8 m) spherical volume. Fluctuations in the ambient field are removed by a servo control, producing stability to half a nanotesla. An artificial magnetic vector can be produced and rotated at a variable rate. 9.42-foot (2.87 m) Helmholtz coils are used for perm/deperm ...
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 -direction, the field gradient is uniform and the field itself varies linearly with positi
Maxwell's geometry of the coils. 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 .