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Physics
Classical Physics
Electromagnetism
Corollary of the Uniqueness Theorem in Electrostatics
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[QUOTE="PhDeezNutz, post: 6141520, member: 577620"] 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. [/QUOTE]
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Forums
Physics
Classical Physics
Electromagnetism
Corollary of the Uniqueness Theorem in Electrostatics
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