Electromagnetic Theory (v2) #24 | Problem Solving #01: Coordinate Conversion

Instructor: Dr. Süleyman Burak ÇELİK

First problem-solving episode of the EMT (v2) series. One point, three coordinate systems: take P = (−2, 6, 3) in Cartesian and convert it to cylindrical (ρ, φ, z) and spherical (r, θ, φ). Walk-through in three clean steps — cylindrical: ρ = 2√10, φ = 108.43° (quadrant II via atan2); spherical: r = 7, θ = 64.62° from +z, same φ. Sanity check: ρ = r sinθ ✓. Answer: (ρ, φ, z) = (2√10, 108.43°, 3), (r, θ, φ) = (7, 64.62°, 108.43°). Reference: Sadiku 7th Ed, Chapter 2 (worked-example).