Answer Happy

please solve those questions a to c step by step and if you are handwriting then please write the letters clearly. Thank you so much.
1. Electric field of a charged ball [4 points (hand-in)] Consider a spherically symmetric charge density pr") that is confined to a ball of radius R, p() = Qnr"O(R -r), n > -3 in spherical coordinates (r, 0,4). The total charge of the distribution is Q. a) Obtain the constant an as a function of n and Q. b) Considering the symmetries of the system, explain in which direction the electric field must point, on which variables it can depend. Make an Ansatz for Ē(7"). Use this Ansatz and Gauß theorem to derive the electric field from the Maxwell equations. P() c) Now, compute the electric potential (F) = d'. IF - FT Verify that Ē(7)= -7°() holds. 1 atro San Mateo 4по Hint: c) Due to rotational symmetry, it is sufficient to compute p(7") for 1 = (0,0,r)T. Use this to express 7 - 7'| in terms of r, r' and 0'. Then, substitute u = - cos O'.