# Corollary of the Uniqueness Theorem in Electrostatics

• PhDeezNutz

#### PhDeezNutz

Following my instructor's notes the statement of the Uniqueness Theorem(s) are as follows

"If ##\rho_{inside}## and ##\phi_{boundary}## (OR ##\frac{d \phi_{boundary}}{dn}## ) are known then ##\phi_{inside}## is uniquely determined"

A few paragraphs later the notes state

"For the field inside S (a surface), knowing ##\phi_{boundary}##(OR ##\frac{d \phi_{boundary}}{dn}##) everywhere on S is as good as knowing all the outside charges; it carries all the same information about their effects"

I don't see how this follows from the statement of the Uniqueness Theorem. If anything it **seems to me** that the instructor is saying the converse of the Uniqueness Theorem while flipping definitions of "inside" and "outside".

"If ##\phi_{boundary}## (OR ##\frac{d \phi_{boundary}}{dn}## ) are known on surface S then ##\rho_{outside}## is uniquely determined"

Can anyone help me

1) decipher what my instructor is trying to say

2) Offer help in the way of a formal proof or a convincing physical argument

Any help would be appreciated. Thanks in advanced.