- #1

coquelicot

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Assume furthermore that a conductor A, with a definite shape and volume, is placed in field ##E_{ext}##, and is connected to an infinitely far ground ##G## with a very thin electrical wire. The potential of G is supposed to be ##0.##

By electrostatic induction, free charges in A move to G, and conductor A, after equilibrium, experiences a distribution of charge ##\sigma## on its surface.

Assume furthermore that the charge ##\sigma## does not influence ##\rho##, so that ##E_{ext}## and ##V_{ext}## are given and fixed in this problem.

**Question:**how to characterize the total charge ##Q = \int_{S(A)} \sigma dS## of A, as a function of ##E_{ext}## or ##V_{ext}##, using, e.g. surface integrals on A etc. ?