An inverted hemispherical shell consists of two parts: the upper half of a sphere of radius R with its center at the origin of coordinates and a circle in the xy-plane with the same radius R and its center also at the origin. Both parts carry the same uniform surface charge density σ. There is no volume charge density. Find the potential difference between the hemispherical pole (on the z-axis at z=R) and the
origin by direct integration of Coulomb's law for the potential at the two points. Note that result is not zero!

Question

An inverted hemispherical shell consists of two parts: the upper half of a sphere of radius R with its center at the origin of coordinates and a circle in the xy-plane with the same radius R and its center also at the origin. Both parts carry the same uniform surface charge density σ. There is no volume charge density. Find the potential difference between the hemispherical pole (on the z-axis at z=R) and the
origin by direct integration of Coulomb's law for the potential at the two points. Note that result is not zero!

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