Consider elliptical cylindrical coordinates (μ,φ,z) which are related to the Cartesian coordi- nates by x = acoshμ cosφ, y = asinhμ sinφ, z = z, where a is a constant. Write down Laplace’s equation...

Consider elliptical cylindrical coordinates (μ,φ,z) which are related to the Cartesian coordi- nates by

x = acoshμ cosφ, y = asinhμ sinφ, z = z,

where a is a constant. Write down Laplace’s equation ∇2V = 0 in elliptical cylindrical coordinates.

b) Show that Laplace’s equation in elliptical cylindrical coordinates is separable. How many in- dependent separation constants are there? (You don’t have to solve the ODEs, but you have to derive them.)