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An equipotential region might be referred as being 'of equipotential' or simply be called 'an equipotential'. An equipotential region of a scalar potential in three-dimensional space is often an equipotential surface (or potential isosurface), but it can also be a three-dimensional mathematical solid in space.
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 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]
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 equipotential surface for the potential value is the implicit surface (,,) = which is a sphere with center at point . The potential of 4 {\displaystyle 4} point charges is represented by
Lines of constant ψ are known as streamlines and lines of constant φ are known as equipotential lines (see equipotential surface). Streamlines and equipotential lines are orthogonal to each other, since [11]
The shift in the stream function, , is equal to the total volumetric flux, per unit thickness, through the surface that extends from point ′ to point . Consequently Δ ψ = 0 {\displaystyle \Delta \psi =0} if and only if A {\displaystyle A} and A ′ {\displaystyle A'} lie on the same streamline.
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 ...