HSC Physics Coulomb's Law

A tutorial sheet of harder problems on Coulomb’s law is given below.

  1. Point charges +4Q and -Q are placed a distance d apart in a vacuum. Where is the resultant electric field zero?
  2. Draw the electric field lines around the charges in question 1.
  3. Two point charges +4Q and +Q are placed a distance d apart in a vacuum. Where is the resultant electric field zero?
  4. Draw the electric field lines around the charges in question 3.
  5. Three equal point charges +Q are placed at the vertices of an equilateral triangle of side d. Is the resultant electric field ever zero?
  6. Draw the electric field lines around the charges in question 5.
  7. Four equal point charges +Q are placed at the corners of a square of side d. Is the resultant electric field ever zero?
  8. Draw the electric field lines around the charges in question 7.
  9. Four equal point charges +Q are placed at the corners of a regular tetrahedron of side d. Calculate the magnitude of the resultant force acting on one of the charges. [F√6, where F is the force between two of the charges]
  10. Eight equal point charges +Q are placed at the corners of a cube of side d. Is the resultant electric field zero at the centre of the cube?
  11. *In question 10 what is the magnitude of the resulant electric field at a small distance from the centre of the cube?