We examine the electrostatic vector field functions in this post. This is roughly patterned after chapter 1 of Shey's classic book Div, Grad, Curl and All that...
Now a tangential vector field:
Now let's look at the charge between two particles in free space in MKS units. This law of Physics was discovered by the French physicist Charles-Augustin de Coulomb (June 1736 - 23 August 1806). He was best known for developing Coulomb's law, the definition of the electrostatic force of attraction and repulsion, but also did important work on friction. The SI unit of electric charge, the coulomb, was named after him.
Try the above electrostatics App in the Wolfram Cloud here.
Exercise 1-1 (a)
Exercise 1-1 (b)
You get the idea. More worked out electrostatic vector fields can be found in the Wolfram notebook here.