Electricity and Magnetism

Chapter 11

Potentials, Fields, and All That

The claim that it was possible to compute the electric field associated with a given potential

function was made at the end of Chapter 10.

Q: How does one go about doing this?

A: In short, the electric field is obtained by taking “minus the gradient of the potential,”

i.e.,

→

E = −

~

∇V .

To explicate this abbreviated answer, we present a brief synopsis of the analysis of the

relation between conservative forces and p otential energy functions found in volume i,

Chapter 26 [adapted to accommodate our present concerns].

~

∇ The potential difference between two points, both of which are situated in an

arbitrarily small ...