Given the potential field V = (A 4 + B 4 ) sin 4: (a) Show that 2 V = 0. (b) Select A

Given the potential field V = (Aρ⁴ + Bρ⁻⁴) sin 4ϕ:

(a) Show that ∇²V = 0.

(b) Select A and B so that V = 100 V and |E| = 500 V/m at P(ρ = 1, ϕ = 22.5◦, z = 2).