Problem 3 (20 points) - Find the equation sheet on Canvas. The last page summarizes each differential vector calculus operation in Cartesian, Cylindrical, and Spherical coordinates. Evaluate the following expressions. a)

(3 points) Take the gradient of the following scalar field: V(Robs) = V(Xobs, Yobs, Zobs) = Vo where V, and d are constants. b) (7 points) Take the divergence of the following vector field: Ē (Robs) = E(Pobs, Pobs, Zobs): = Zobs d Vs In(b)- In(a) Pobs (9) 1²/² -âp where Vs, a, b are constants. c) (7 points) Take the curl of the following vector field: Tobs cos Dobs A(Robs) = Ã(Tobs, Bobs, Pobs) = robs Sin Oobs âr +; d) (3 points) Take the Laplacian of the following scalar field: V(Robs) = V(Xobs, Yobs, Zobs) = Vo Zobs where Vo and d are constants. -âo