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34 lines
1001 B
Plaintext
34 lines
1001 B
Plaintext
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Started with vector potential
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(pic) Demonstrated why 𝐉ᵦ = ∇×𝐌
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(pic) Find magnetic field of a uniformly magnetized sphere
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this development ended up converging with the sphere of constant surface charge
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(pic) Started with a reminder of displacement definition and origin.
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(pic) This leads to an analogy with 𝐉ₜₒₜ = 𝐉𝒻 + 𝐉ᵦ
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leads to very useful ∮𝐇⋅d𝐥 = 𝐈𝒻(s)
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Bit of an aside about how 𝐇 is easier to measure/control compared to 𝐁.
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(pic) An example of finding 𝐁 outside a thick rod.
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actually didn't develop this, but just warned about that M has a
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divergence at the edges, so 𝐇 is not so easy to find.
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Introduced linear materials
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𝐌 = χₘ 𝐇
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χₘ > 0 (paramagnetic)
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χₘ < 0 (diamagnetic)
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Example: an infinite solenoid carrying a surface current 𝐊 = K ϕ̂ filled
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with material of susceptibility χₘ. Find 𝐁.
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(pic) found 𝐇, then 𝐁, then bound and free 𝐊
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