The CSDA range for protons in aluminum (in units of mass thickness g/cm2) are 2.953×10−4, 4.020×10−3, and 0.1692 for protons with energies of 0.1 MeV, 1 Mev, and 10 MeV, respectively [Janni 1982]. Use the empirical Eq. (7.47) to estimate these ranges and compute the percent difference. 21. Shultis, J. Kenneth; Faw, Richard E.. Fundamentals of Nuclear Science and Engineering (p. 220). CRC Press. Kindle Edition.

Consider a uniformly charged ring in the xy plane, centered at the origin. the ring has radius a and positive charge qdistributed evenly along its circumference. a)what is the direction of the electric field at any point on the z axis? . b)what is the magnitude of the electric field along the positive z axis? use k in your answer, where k=14πϵ0. d)the ball will oscillate along the z axis between z=d and z=−d in simple harmonic motion. what will be the angular frequency ω of these oscillations? use the approximation d≪a to simplify your calculation; that is, assume that d2+a2≈a2. express your answer in terms of given charges, dimensions, and constants