Laplace equation in spherical coordinates with some symmetry given a sphere with the radius r and the potential on its surface specified by vo k sin2 (1) where k is a constant and 0 is the polar angle. a) which symmetry does the potential obey? calculate the potential inside and outside the sphere the sphere b) calculate the surface charge density o(0) on hints use the ansatz for the symmetry which is derived in the lectures or from griffths chapter 3. use the boundary conditions to simplify the expression, i. e. get rid of some terms compare the coefficients to get the unknown coefficients using the ansatz and the boundary condition

To understand the electric potential and electric field of a point charge in three dimensions consider a positive point charge q, located at the origin of three-dimensional space. throughout this problem, use k in place of 14? ? 0. part adue to symmetry, the electric field of a point charge at the origin must point from the origin.answer in one word.part bfind e(r), the magnitude of the electric field at distance r from the point charge q.express your answer in terms of r, k, and q. part cfind v(r), the electric potential at distance rfrom the point charge q.express your answer in terms of r, k, and q part dwhich of the following is the correct relationship between the magnitude of a radial electric field and its associated electric potential ? more than one answer may be correct for the particular case of a point charge at the origin, but you should choose the correct general relationship. a)e(r)=dv(r)drb)e(r)=v(r)rc)e(r)=? dv(r)drd)e(r)=? v(r)r