Differential Analysis - Cylindrical Coordinate System - Field Theory.
Differential Length(dl): In General the differential length is given as dl = dρ a ρ + ρdφ a φ + dz a z Differential Length for a surface is given as: - dl = dρ a ρ + ρdφ a φ ---(For ρ-φ Plane or Z constant Plane) - dl = ρdΦ a φ + dz a z ---(For φ-z Plane or ρ Constant Plane) - dl = dρ a ρ + dz a z ---(For ρ-z Plane or φ Constant Plane) Differential length for a line parallel to ρ, φ and z axis are respectively given as: - dl = dρ a ρ ---(For a line parallel to ρ axis) - dl = ρdφ a φ ---(For a line parallel to φ axis) ∫ dl = ∫ o 2π ρdφ = ρ( 2π - 1) = 2πρ This resembles the circumference of a circle. Hence if φ varies with ρ and z constant, then the length is the circumference of the circle. dl = dza z ---(For a line parallel to z axis) Differential Surface (ds): - ds = ρdρ dφ a z This surface describes a circular disc. Always remember- To define a circular disk we need two parameter one distance measure and one angular mea...