π²³ ∞ ° → ~ µ ρ σ τ ω ∑ … √ ∫ ≤ ≥ ± ∃ · θ φ ψ Ω α β γ δ ∂ ∆ ∇ ε λ Λ Γ ô 1. The problem statement, all variables and given/known data Consider the cylindrical in free space as shown below. The resistor has diameter 2a, length l, is filled with a inhomogeneous material with a z dependent electrical conductivity σ(z) and is capped by 2 thin disks of materials with infinite conductivity. A static voltage φ0 is applied to the 2 disks with a battery. Show that the potential inside the battery is given by φ (z)= ∫ (C1/σ(z)) dz+ C2 C1,C2 are constants 2. Relevant equations 3. The attempt at a solution I am trying to use poisson's equation in cylindrical coordinates. But I am not sure, how to get the right hand side The potential varies only along Z and is constant along r and φ Therefore, poissons eqn will reduce to d2(φ)/dz2 = -ρ/ε I need σ(z) on the right hand side, but I have ρ/ε. How do I arrive at σ(z)?