World Library  
Flag as Inappropriate
Email this Article
 

Equipotential

An FEM computation of electrostatic equipotentials (black contours) between two electrically charged spheres

Equipotential or isopotential in mathematics and physics refers to a region in space where every point in it 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.

Note that 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, but it can also be a three-dimensional region 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.

Electrical conductors offer an intuitive example. If a and b are any two points within or at the surface of a given conductor, and given there is no flow of charge being exchanged between the two points, then the 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 is perpendicular to the equipotential surfaces of the gravity potential, and in electrostatics and in the case of steady currents the electric field (and hence the electric 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 (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 by the force of gravity if it is resting on a flat, horizontal surface, because it is an equipotential surface.

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.
  4. ^ "Electrostatics Explained." The University of Bolton. The University of Bolton, n.d. Web. 22 Aug 2011.

See also

External links

  • Electric Field Applet
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
 
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
 
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.
 



Copyright © World Library Foundation. All rights reserved. eBooks from World Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.