Using basic relationship between field and potential with conductors at electrostatic equilibrium

Any excess is located on the surface and electric field is zero at any of the interior point of a conductor in ee

Field is other than 0 in conductor

Force on charge carriers would move, creating current but there can't be current in interior points so it must field must be 0 at all interior points

Finding potential inside conductor

By connecting two points with a line and integrating Es, potential difference, deltaV= V2- V1 can be found along line as the electric field is 0 in the interior points so efield is 0 and the value of the integral is o=> so potential difference is zero so the two points are at the same potential in the electrostatic equilibrium conductor

If potential difference is zero, then the two points are at the same potential in the electrostatic equilibrium conductor and

Entire conductor is the same potential and even with the contact of different conductors, the exchange charge is exchanged till it is reached

If electric potential is always perpendicular to an equipotential surface, then

Eexterior of a charged conductor is also always perpendicular to surface where the excess charge is on the surface of the charged conductor

At sharpest points, why is the electric field the largest

Higher surface density which makes sense based on the earlier equation with the surface of sphere= R with the electric field being then written as E= Vo/R and as Vo is the same potential with the sectioning of spheres of a conductor, the field strength needs to be the largest at the smallest radii

Summarization of components of conductors at the electrostatic equilibrium

1) All excess charge is on surface 2) Surface is equipotential 3) Electric field inside is always 0 4) Interior has always the same potential throughout the whole conductor 5) Exterior electrical field is perpendicular ton surface 6) Surface charge density and electric field strength are largest at sharpest points at smallest radii

Electric field and potential between two conductors

Surfaces of sphere and flat plane are equipotential, so electric field is perpendicular to both and closer to the surface it is nearly perpendicular so an equipotential surface close to an electrode is roughly matches that of an electrode