Final answer:
The divergence of an electric field E created by a point charge q, denoted by E = kq r/|r|^3, is 0 everywhere except at the location of the charge, where it is not defined.
Step-by-step explanation:
To compute the divergence of the electric field E at a point r due to a charge q at the origin, we will use Coulomb's Law. According to Coulomb's Law, the electric field due to a point charge Q is given by E = k|Q|/r², where k is Coulomb's constant, Q is the point charge, and r is the distance from the point charge to the point of interest.
The student's given field vector R(r) = q r/|r|³ is possibly meant to represent the electric field, typically denoted as E. In standard vector notation, we'd express the electric field caused by a charge q at the origin as E = kq r/|r|³. To find the divergence of this electric field, we use the divergence operator in spherical coordinates, as the electric field has spherical symmetry due to the point charge. We find that div E = 0 for all points r except at the origin, where the divergence is not defined because a point charge creates an electric field that diverges from a single point.