calculus problem

4. Suppose that the electric potential V in a medium is given by: k 2 View) = \"'3" Z4 where k is a constant with V measured in volts and w, y, z in meters. P2 of 4 (a) Poisson's equation states that the Laplacian of the electric potential V is equal to the negative of the volume charge density ,0 divided by the dielectric constant of the medium e, i. e. V2V= 9 E Evaluate the Laplacian of the electric potential V in cylindrical coordinates to nd the volume charge density p(r, 6, z) in this medium in terms of e. [9 marks] (b) Find the maximum rate of decrease of the electric potential V at the point (1, 8, 2) and the unit vector giving the direction in which it occurs. [7 marks]