Electromagnetic Theory (v2) #19 | Ampère's Circuit Law

Instructor: Dr. Süleyman Burak ÇELİK

``` Biot-Savart works for any current, but it forces you to integrate every element. Ampère's circuit law is the symmetric-geometry shortcut that plays the same role magnetostatics that Gauss's law played for electrostatics. We state the law — the closed line integral of H around any loop equals the enclosed current — and lay out the four-step recipe: identify the symmetry, pick an Amperian loop where H is constant along the path, evaluate the integral, and solve. We then apply it to an infinite straight wire and recover H = I/(2πρ)â_φ in three lines (the same result Biot-Savart took a full integration to produce). We close with the differential form ∇ × H = J — one of Maxwell's four equations — derived directly from Stokes' theorem. Topics: 0:00 Introduction 0:03 Why Ampère's Law? (Bridge from Biot-Savart) 0:29 The Setup: H-field circles around a wire (visualization) 0:50 Ampère's Circuit Law — Statement 1:30 Four-Step Recipe for Using the Law 2:15 Worked Example: Infinite Straight Wire 3:10 Differential Form: ∇ × H = J (Stokes + point form) 3:42 Summary Key equations: • ∮_C H · dl = I_enc (Ampère's circuit law — integral form) • H · 2πρ = I ⟹ H = I/(2πρ) â_φ (infinite wire — worked example) • ∇ × H = J (point form — one of Maxwell's equations) Reference: Sadiku, "Elements of Electromagnetics" 7th Ed, Section 7.3 ```