Can a 'Good Surface' Be Found for Any Continuous Vector Field?

[HungryChemist]

I am terribly sorry for not being able to write this simple equation in Latex form. (I will be really glad if someone can tell me where I can learn how to use Latex to write math symbol)

Let F' be a vector field given by F' = r r' (r' = radial unit vector) and also let p be a point on the space R distance away. Then one can imagine a sphere of radius of R (centered at origin). Now, every patch of this surface has normal vector n' that is in the same direction as F' at that point.

I hope I am being clear, the more specific example of above kind would be an electric field due to a single positive charge and gaussian surface(shperical) such that E dot dA will simply come out as magnitue of E times magnitude of dA. If the gaussian surface wasn't sphere former is not true. So let me call such surface a 'good surface'.

Now my question is...

Shouldn't there be such 'good surface' for any vector field that is continuous everywhere? If so how can one show it? Also how can one devise a methord of finding such surface that encloses point in question? In other words, given vector field and a point in that vector space, find the good ' surface'

Please, help me out carrying this utterly confused process...

 

[yourdadonapogostick]

tex tags. [ tex ]mathstuff[ /tex ] without the spaces.

 

[rachmaninoff]

You want to find surfaces on which the vector field is everywhere perpendicular? Look up "conservative vector fields," and "equipotentials". The principle is that vector fields with the property you want uniquely define a scalar potential function, and its equipotential surfaces are everywhere normal to the vector field.

As for using TeX on the Physics Forum, the introduction is located here .