MadSci Network: Physics |

Posted By:

Area of science:

ID:

The condition for the electric field vector to be written as the gradient of a scalar function is the curl of electric field is zero. Because if the curl of vector E is zero, the integration of vector E along different paths between two positions will be the same, therefor you can define a function of position A which is equal to the integral of vector E from a fixed position B to position A. The gradient of this function is vector E. According to Maxwell's equations, curl of E is equal to negative partial differentiation of magnetic flux density. Therefore in a region with static magnetic field, curl of E is zero, and vector E can be written as a gradient of a scalar function. After you write vector E as gradient of a scalar function, substitute it into the Gauss Law (divergence of E is equal to the charge density), then you get the Possion's equation.

Try the links in the MadSci Library for more information on Physics.

MadSci Network, webadmin@madsci.org

© 1995-2005. All rights reserved.