Why Earth is called a geoid and why do these surfaces get closer together the closer you get to the charges?
The Earth is not called a geoid; rather, it is described as being approximately geoid-shaped. A geoid is a three-dimensional shape that represents the Earth's gravitational field. It's essentially the shape that the surface of the oceans would take under the influence of Earth's gravity and rotation, disregarding other influences such as winds and tides. The Earth is not a perfect sphere due to its rotation, equatorial bulge, and both irregular and continue redistribution of mass, resulting in the so called geoid shape. The second part of your question I am not really understand you what do you mean with the charges, maybe you refer non-tidal and tidal loading?
Earth surface is called ellipsoid. The geoide is an gravitational equipotential surface matches with MSL. The elevation of any point on the earth surface from MSL is called orthometric height and from ellipsoid is called ellipsoidal height. The difference between these is known as geoid undulation.
Earth is slightly flattened at the poles. The Earth is slightly flattened at the poles. That is why it is referred to as a “Geoid”. The geoid is an imaginary sea level surface that undulates over all of the earth; it isn't just for the oceanic areas, it also extends through the land masses. Although a geoid may seem to be a smooth, regular shape, it isn't. The Earth's mass is unevenly distributed, meaning that certain areas of the planet experience more gravitational "pull" than others. The geoid surface is irregular, unlike the reference ellipsoid but is considerably smoother than Earth's physical surface. The relationship between the electric field and potential due to charge is given as E = dV/R. Thus if dV is constant and R is inversely proportional to E. Therefore, all equipotential surfaces are closer at a higher value of E. For any charge E is higher near load thus equipotential surfaces are closer to the charge. The equipotential surfaces are close together as the distance between the surface and source charge increases because of a strong electric field near the source charge. Because the potential diminishes with increasing distance from the charge, the equipotential surface becomes wider apart. The potential is greatest near the charge and drops as we travel away from it.Equipotential surfaces have equal potentials everywhere on them. For stronger fields, equipotential surfaces are closer to each other! These equipotential surfaces are always perpendicular to the electric field direction, at every point.
I do not agree with the comments of Mr Naresh. The geoidal surface is equipotential surface. The gravity at the surface varies and depends on the density of the material below that point. The geoidal surface is undulating because of the change of density of the material. I could not understand your comparision of electrical potential with gravitational potential. There is only gravitational attractive force between any two masses.
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