In the early years of the 20th century, a leading model of the structure of the atom was that of the English physicist J. J. Thomson (the discoverer of the electron). In Thomson's model, an atom consisted of a sphere of positively charged material in which were embedded negatively charged electrons, like chocolate chips in a ball of cookie dough. Consider such an atom consisting of one electron with mass m and charge −e, which may be regarded as a point charge, and a uniformly charged sphere of charge +e and radius R.
A) Is equilibrium position of the electron at the center of the nucleus?
B)In Thomson's model, it was assumed that the positive material provided little or no resistance to the motion of the electron. If the electron is displaced from equilibrium by a distance r less than R, find the net force on the electron.
Express your answer in terms of the variables r⃗ , R, e, and constants π and ϵ0.
C) Calculate the frequency of oscillation. Express your answer in terms of the variables m, R, e, and constants π and ϵ0.