Electromagnetic Theory (v2) #21 | Magnetic Flux Density B & Maxwell (Static)

Instructor: Dr. Süleyman Burak ÇELİK

``` Magnetostatics gets its last missing piece. We've been working with H — the field a current produces — but the physical field that acts on charges is B, the magnetic flux density. In this video we close the loop: B = μH connects the two, μ₀ = 4π × 10⁻⁷ H/m fixes the SI scale, and μ = μ₀μᵣ handles materials. We define the magnetic flux Φ as the surface integral of B · dS, measured in Webers, and explain why we bother — flux through loops is what drives induction later. Then the big contrast with Gauss's law: ∇ · B = 0, because there are no magnetic monopoles. Cut a bar magnet in half, you get two magnets, not isolated poles. Field lines are always closed loops. We finish by writing all four of Maxwell's equations in their static form and note that in statics, E and B decouple completely — time variation is what couples them into waves later. Topics: 0:00 Introduction 0:03 Recap: we have H, now we want B 0:31 The Definition B = μH + the SI constant μ₀ 1:36 Magnetic Flux Φ = ∫ B · dS 2:18 No Magnetic Monopoles → ∇ · B = 0 (visualization + derivation) 3:33 Maxwell's Equations — Static Form (all four side by side) 4:41 Statics closed — what's next Key equations: • B = μH (magnetic flux density) • μ₀ = 4π × 10⁻⁷ H/m (free-space permeability) • Φ = ∫_S B · dS [Wb = T·m²] (magnetic flux) • ∇ · B = 0 (no magnetic monopoles) • ∮_S B · dS = 0 (integral form via divergence theorem) • Maxwell static set: ∇·D = ρᵥ, ∇·B = 0, ∇×E = 0, ∇×H = J Reference: Sadiku, "Elements of Electromagnetics" 7th Ed, Sections 7.5-7.6 ```