For a finite charge distribution in free space with the "ground" nearby; do we take the potential to be 0 at infinity and also at the position of the ground?

Most textbooks I've seen don't really explain as such, and I'm not completely sure. Is it true that the work done by our charge distribution to bring a unit positive charge from infinity, to any point on the ground and along the ground, is zero? That means while moving quasi statically along the ground, the force on the test charge due to our given charge distribution is always balanced by the electrostatic force due to the charges on the ground.


In treating the physical ground (as in, the literal ground on which we walk, a.k.a. "true ground") as zero potential is an approximation where the literal ground is treated as a conductor that extends to infinity (as it practically does). Since infinitely far away is conventional ground any conductor that extends there must also be at zero potential.

The reality is, of course, more complicated, with the literal ground being a rather poor conductor. It is, nevertheless, a large pool of charges from which electrons can be taken or shunted to without worry of significantly effecting it.

Because of these factors, and the use of the literal ground as a place to dump excess charges (e.g. lightning rods), the terms "ground" and "earth" have become synonymous with "place we specify as having zero electric potential", especially with respect to circuits.


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