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Started with vector potential
(pic) Demonstrated why 𝐉ᵦ = ∇×𝐌
(pic) Find magnetic field of a uniformly magnetized sphere
this development ended up converging with the sphere of constant surface charge
(pic) Started with a reminder of displacement definition and origin.
(pic) This leads to an analogy with 𝐉ₜₒₜ = 𝐉𝒻 + 𝐉ᵦ
leads to very useful ∮𝐇⋅d𝐥 = 𝐈𝒻(s)
Bit of an aside about how 𝐇 is easier to measure/control compared to 𝐁.
(pic) An example of finding 𝐁 outside a thick rod.
actually didn't develop this, but just warned about that M has a
divergence at the edges, so 𝐇 is not so easy to find.
Introduced linear materials
𝐌 = χₘ 𝐇
χₘ > 0 (paramagnetic)
χₘ < 0 (diamagnetic)
Example: an infinite solenoid carrying a surface current 𝐊 = K ϕ̂ filled
with material of susceptibility χₘ. Find 𝐁.
(pic) found 𝐇, then 𝐁, then bound and free 𝐊