1. Spherical coordinates:
In class we defined the scale factors hi:
where xi are the Cartesian coordinates and for our case qk are the spherical
coordinates (n=3 in our case).
a) Find h1, h2, and h3. (2 points)
b) Find the expression for ∇φ in spherical coordinates using the general form
given below: (2 points)
c) Find the expression for ∇ × F using the general form given below: (2 points)
2. By integrating the relations for da and dV in spherical coordinates that we
discussed in class, find the surface area and volume of a sphere. (2 points)
3. Find the volume of a spherical shell of thickness dr and radius r (r is the radial
coordinate). (2 points)