1. The problem statement, all variables and given/known data There are 2 coaxial cylindrical conductors. The inner cylinder has radius a, while the outer cylinder has radius b. There is no charge in the region a < r < b. If the inner cylinder is at potential Vo and the outer cylinder is grounded, we want to find the potential in the region between the cylinders. We assume L >> b > a and neglect end effects. a) Write Laplace's equation in cylindrical coordinates. b) Assuming V(r) is a function of the axial distance r alone, integrate the differential equation and use the boundary conditions to find V(r) , a ≤ r ≤ b. 2. Relevant equations ∇2V = 0 3. The attempt at a solution Laplace's equation in cylindrical coordinates would be (1/r)(d/dr)(r*dV/dr) =0 Since there is no phi or z dependence. Also I know it's a partial and not d but I can't type the symbol. To solve this (1/r)(d/dr)(r*dV/dr) =0 (d/dr)(r*dV/dr) =0 r*dV/dr = C dV/dr = C/r dV = C/r dr V = C*ln(r) + K , where C and K are constants. Using the boundary conditions: 0 = C*ln(b) + K Vo = C*ln(a) + K and using that to solve for constants: V = Vo/[ln(a/b)] * ln(r/b) Is that right?