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An equipotential of a scalar potential function in n-dimensional space is typically an (n − 1)-dimensional space. The del operator illustrates the relationship between a vector field and its associated scalar potential field. An equipotential region might be referred as being 'of equipotential' or simply be called 'an equipotential'.
The electric field is perpendicular, locally, to the equipotential surface of the conductor, and zero inside; its flux πa 2 ·E, by Gauss's law equals πa 2 ·σ/ε 0. Thus, σ = ε 0 E. In problems involving conductors set at known potentials, the potential away from them is obtained by solving Laplace's equation, either analytically or ...
Being an equipotential surface, the geoid is, by definition, a surface upon which the force of gravity is perpendicular everywhere, apart from temporary tidal fluctuations. This means that when traveling by ship, one does not notice the undulation of the geoid ; neglecting tides, the local vertical (plumb line) is always perpendicular to the ...
The geoid, or mathematical mean sea surface, is defined not only on the seas, but also under land; it is the equilibrium water surface that would result, would sea water be allowed to move freely (e.g., through tunnels) under the land. Technically, an equipotential surface of the true geopotential, chosen to coincide (on average) with mean sea ...
The surfaces of constant geopotential or isosurfaces of the geopotential are called equigeopotential surfaces (sometimes abbreviated as geop), [1] also known as geopotential level surfaces, equipotential surfaces, or simply level surfaces. [2] Global mean sea surface is close to one equigeopotential called the geoid. [3]
A cylindrical Gaussian surface is commonly used to calculate the electric charge of an infinitely long, straight, 'ideal' wire. A Gaussian surface is a closed surface in three-dimensional space through which the flux of a vector field is calculated; usually the gravitational field, electric field, or magnetic field. [1]
where (,) is the velocity field and (,) is the vorticity field. Like any vector field having zero curl, the velocity field can be expressed as the gradient of certain scalar, say φ ( x , t ) {\displaystyle \varphi (\mathbf {x} ,t)} which is called the velocity potential , since the curl of the gradient is always zero.
Taylor's derivation is based on two assumptions: (1) that the surface of the cone is an equipotential surface and (2) that the cone exists in a steady state equilibrium. To meet both of these criteria the electric field must have azimuthal symmetry and have R {\displaystyle {\sqrt {R}}\,} dependence to counter the surface tension to produce the ...