Electromagnetic Theory (v2) #20 | Applications of Ampère's Law

Instructor: Dr. Süleyman Burak ÇELİK

``` Ampère's circuit law is the fastest route to H when the geometry is symmetric. In this video we apply the four-step recipe to three classic geometries you will meet again and again: the infinite sheet of current, the coaxial cable, and the long solenoid. For the sheet, a rectangular Amperian loop gives H = K/2 on each side. For the coaxial cable, a single circular loop handles all three regions — inside the inner conductor (H = Iρ / 2πa²), between the conductors (H = I/2πρ), and outside the shield where the enclosed currents cancel exactly (H = 0, which is why coax cables don't leak magnetic field). For the solenoid, a rectangular loop straddling the edge gives H = nI — the magnetic analogue of a parallel-plate capacitor. We close with a summary table of the four classic Ampère's-law results. Topics: 0:00 Introduction 0:03 Recap: Ampère's Law in 4 Steps 0:36 Application 1: Infinite Sheet of Current (H = K/2) 1:40 Application 2: Coaxial Cable — Cross Section & 3 Regions 2:15 Coaxial — H(ρ) in each region (worked derivation) 3:37 Application 3: Long Solenoid (H = nI) 4:43 Four Classic Results — Summary Table Key equations: • ∮_C H · dl = I_enc (Ampère's law — integral form) • H = K / 2 (infinite sheet of current) • H = I ρ / (2π a²) (coax, 0 ≤ ρ ≤ a — inside inner conductor) • H = I / (2π ρ) (coax, a ≤ ρ ≤ b — between conductors) • H = 0 (coax, ρ ≥ b — outside shield) • H = n I (long solenoid) Reference: Sadiku, "Elements of Electromagnetics" 7th Ed, Section 7.4 ```