Calculating electrostatic potential energy

[PeterRV]

Homework Statement

Consider potential field V(ρ, φ, z) = V_0/ρ in free space and cylindrical coordinates.
Calculate electrostatic potential energy stored in half cylindrical shell defined by a≤ρ≤b, 0≤φ≤π and 0≤z≤h.

Homework Equations

W_E=½∫∫∫ρ_vVdV

The Attempt at a Solution

I have no idea where to start, since I do not have the ρ_v ...

 

[rude man]

Homework Statement

Consider potential field V(ρ, φ, z) = V_0/ρ in free space and cylindrical coordinates.
Calculate electrostatic potential energy stored in half cylindrical shell defined by a≤ρ≤b, 0≤φ≤π and 0≤z≤h.

Homework Equations

W_E=½∫∫∫ρ_vVdV

The Attempt at a Solution

I have no idea where to start, since I do not have the ρ_v ...

I have not seen that formula for energy content of an electric field.
More common I believe is W = ∫∫∫(1/2)ε₀|E|²dv
dv =element of volume
where W = energy content
E = electric field vector field = E(ρ,φ,z).
So, what is the relation between E and V? Find E(ρ,φ,z), evaluate the integrand, and integrate.