Lets consider two imaginary systems, each of them is composed of an electron and a proton, which are separated and therefore form a dipole. Two protons and two electrons are located on the axis, as shown in the figure. The distance between 1 and 1, as well as the distance between 2 and 2 , is = 1. The proton charge is 1.602 1019, and the electron charge is 1.602 1019.

a) The coulomb interaction is calculated using the formula = 1 40 12 where is the distance between 1 and 2 charges. Write an expression for the interaction energy () of the four point-charges (i.e. neglect the following interactions: 1 1, 2 2). b) Write an expression, (), for the interaction energy of the two dipoles (the dipoles are: 1 1, 2 2). The dipoles are fixed in the orientation above.

c) Plot the two functions on the same graph using a computer program (MatLab/Origin), where 2 10. d) According to the plots, in what range (approximately) the expression for the dipole- dipole interactions obey the Coulomb Law.