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In electrostatics, a conductor is a three-dimensional equipotential region. In the case of a hollow conductor (Faraday cage [4]), the equipotential region includes the space inside. A ball will not be accelerated left or right by the force of gravity if it is resting on a flat, horizontal surface, because
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]
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 method consists of filling the flow area with stream and equipotential lines, which are everywhere perpendicular to each other, making a curvilinear grid.Typically there are two surfaces (boundaries) which are at constant values of potential or hydraulic head (upstream and downstream ends), and the other surfaces are no-flow boundaries (i.e., impermeable; for example the bottom of the dam ...
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 ...
where in fact is the volume flux per unit length across a surface enclosing the source or sink. The velocity field in polar coordinates are The velocity field in polar coordinates are u r = Q 2 π r , u θ = 0 {\displaystyle u_{r}={\frac {Q}{2\pi r}},\quad u_{\theta }=0}
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