Equipotential

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Computed electrostatic equipotentials (black contours) between two electrically charged spheres

In

region in space where every point is at the same potential.[1][2][3] This usually refers to a scalar potential (in that case it is a level set of the potential), although it can also be applied to vector potentials. 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'.

An equipotential region of a scalar potential in three-dimensional space is often an equipotential surface (or potential

mathematical solid in space. The gradient
of the scalar potential (and hence also its opposite, as in the case of a vector field with an associated potential field) is everywhere perpendicular to the equipotential surface, and zero inside a three-dimensional equipotential region.

potential difference is zero between the two points. Thus, an equipotential would contain both points a and b as they have the same potential
. Extending this definition, an isopotential is the locus of all points that are of the same potential.

gravity potential, and in electrostatics and steady electric currents, the electric field (and hence the current, if any) is perpendicular to the equipotential surfaces of the electric potential (voltage
).

In gravity, a hollow sphere has a three-dimensional equipotential region inside, with no gravity from the sphere (see shell theorem). 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 it is an equipotential surface. For the
mean sea level is called the geoid
.

See also

References

  1. ^ Weisstein, Eric W. "Equipotential Curve." Wolfram MathWorld. Wolfram Research, Inc., n.d. Web. 22 Aug 2011.
  2. ^ "Equipotential Lines." HyperPhysics. Georgia State University, n.d. Web. 22 Aug 2011.
  3. ^ Schmidt, Arthur G. "Equipotential Lines." Northwestern University. Northwestern University, n.d. Web. 22 Aug 2011. Archived 2010-06-11 at the Wayback Machine
  4. ^ ""Electrostatics Explained." The University of Bolton. The University of Bolton, n.d. Web. 22 Aug 2011". Archived from the original on 17 March 2011. Retrieved 11 April 2010.

External links

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