Answer Happy

R A spherical cloud of charge with a radius of R and total charge +Q is shown above. Volume charge density of the sphere is described by p(r) = Po(1) for r ≤ R and p=0 for r>R where r is the distance from the center of the cloud. Express all answers in terms of Q, R, and fundamental constants. You may treat k as a fundamental constant as some textbooks use it as the Coulomb constant to simplify electrostatics equations k = 47€0 1. Write an equation describing the electric field E as a function of r for r > R. 2. Write an equation describing the electric potential V as a function of r for r > R. 3. A proton is placed at point P and released. Qualitatively describe the motion for a long time after its release. 4. An electron of charge magnitude e is now placed at point P, which is at a distance r from the center of the sphere, and released. Write an equation describing the kinetic energy of the electron as a function of r. 5. Derive an expression for Po. 6. Determine the magnitude E of the electric field as a function of r for r ≤ R.