CP CALC A region in space contains a total positive charge Q that is distributed sph...

CP CALC A region in space contains a total positive charge Q that is distributed spherically such that the volume charge density ρ(r) is given by

Here a is a positive constant having units of C/m³. (a) Determine a in terms of Q and R. (b) Using Gauss’s law, derive an expression for the magnitude of the electric field as a function of r. Do this separately for all three regions. Express your answers in terms of Q. (c) What fraction of the total charge is contained within the region R/2 ≤ r ≤ R? (d) What is the magnitude of at r = R/2? (e) If an electron with charge q’ = -e is released from rest at any point in any of the three regions, the resulting motion will be oscillatory but not simple harmonic. Why?