" I've found out so much about electricity that I've reached the point where I understand nothing and can explain nothing"
[Describing his experiments with the Leyden jar.]
Pieter van Musschenbroek

• Suppose we are given the electric potential, V, as a function of position.  Is it possible to determine the E field from this V ?

Starting from the definition of the potential difference in terms of the E field,

then if the path A to B is along the x axis we obtain,

• This expression can be written in the alternative form,

If the path A to B is in an arbitrary direction we obtain the most general expression of "E from V",

" I am an expert of electricity. My father occupied the chair of applied electricity at the state prison."
W. C. Fields

 

Dr. C. L. Davis
Physics Department
University of Louisville
email: c.l.davis@louisville.edu