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etotheipi

When you ground something in electrostatics, the potential of that body becomes the potential of the Earth once equilibrium has been reached. In this context, it is usually taken that the Earth is at 0V. There are two possibilities for this. Either the constant of integration is chosen such that the Earth is the zero reference point for potential. Or, the potential of the Earth is negligible enough w.r.t. a zero reference at infinity that we take the potentials of the Earth and infinity to be equal: this would imply that the Earth is neutral.

These two options are actually quite different. If we are doing an electrostatics problem with some charged spheres (for instance), we might need to ground one of the spheres: that fixes the potential of that sphere equal to that of the Earth. To calculate the potential of the other spheres in the problem, it is then usually required to do an integral

In that case, what is the nature of the "Earth" in the context of electrostatics? I'm aware of the modelling assumptions that it is a conductor with an infinitely large charge donating/accepting capacity, however do we also take it to

These two options are actually quite different. If we are doing an electrostatics problem with some charged spheres (for instance), we might need to ground one of the spheres: that fixes the potential of that sphere equal to that of the Earth. To calculate the potential of the other spheres in the problem, it is then usually required to do an integral

*from infinity*to the sphere in question. If the Earth were the true (constant of integration) 0 reference, we would instead compute the integral from the*Earth*to the other sphere instead, however I have never seen this done. In fact, it wouldn't even be feasible since we'd need much more information about the technicalities of the grounding and the surface charge of the Earth.In that case, what is the nature of the "Earth" in the context of electrostatics? I'm aware of the modelling assumptions that it is a conductor with an infinitely large charge donating/accepting capacity, however do we also take it to

*always have zero net charge*? And do we take the Earth to always be at 0V w.r.t. infinity? Thank you.
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