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The simplest definition for a potential gradient F in one dimension is the following: [1] = = where ϕ(x) is some type of scalar potential and x is displacement (not distance) in the x direction, the subscripts label two different positions x 1, x 2, and potentials at those points, ϕ 1 = ϕ(x 1), ϕ 2 = ϕ(x 2).
A plot of geopotential height for a single pressure level in the atmosphere shows the troughs and ridges (highs and lows) which are typically seen on upper air charts. The geopotential thickness between pressure levels – difference of the 850 hPa and 1000 hPa geopotential heights for example – is proportional to mean virtual temperature in ...
For convenience it is often defined as the negative of the potential energy per unit mass, so that the gravity vector is obtained as the gradient of the geopotential, without the negation. In addition to the actual potential (the geopotential), a theoretical normal potential and their difference, the disturbing potential, can also be defined.
Because the atmospheric electric field is negatively directed (meaning toward the ground) in fair weather, the convention is to refer to the potential gradient, which has the opposite sign (meaning the electrical potential increases with distance from the ground) and is about 100 V/m at the surface, at a distance from thunderstorms. [6]
The potential has units of energy per mass, e.g., J/kg in the MKS system. By convention, it is always negative where it is defined, and as x tends to infinity, it approaches zero. The gravitational field, and thus the acceleration of a small body in the space around the massive object, is the negative gradient of the gravitational potential ...
Ground potential rise is a concern in the design of electrical substations because the high potential may be a hazard to people or equipment. The change of voltage over distance (potential gradient) may be so high that a person could be injured due to the voltage developed between two feet, or between the ground on which the person is standing ...
It has a potential energy = where U is the gravitational potential energy and h is the height above the surface. This means that gravitational potential energy on a contour map is proportional to altitude. On a contour map, the two-dimensional negative gradient of the altitude is a two-dimensional vector field, whose vectors are always ...
On Earth the effect on gravity of elevation is 0.3086 mGal m −1 decrease when going up, minus the gravity of the Bouguer plate, giving the Bouguer gradient of 0.1967 mGal m −1. More generally, for a mass distribution with the density depending on one Cartesian coordinate z only, gravity for any z is 2π G times the difference in mass per ...