Electric Field of a Point Charge from the Potential

• This problem is used in the following sequences

  1. << Electric Field of a Line Source From Potential | Gradient Sequence |

• Static Fields 2021

  The electrostatic potential due to a point charge at the origin is given by: \begin{equation*} V=\frac{1}{4\pi\epsilon_0} \frac{q}{r} \end{equation*}

  1. (2pts) Find the electric field due to a point charge at the origin as a gradient in rectangular coordinates.
  2. (2pts) Find the electric field due to a point charge at the origin as a gradient in spherical coordinates.
  3. (2pts) Find the electric field due to a point charge at the origin as a gradient in cylindrical coordinates.