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By Bossavit A.

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Thus, there can exist a permanent charge imbalance at some places in the conductor. But Lorentz force acts on this charge packet. Why doesn’t it move? 1. Don’t worry about differentiability issues: Assume all fields are smooth. 2. Imitate the classical computation about the convective derivative in fluid dynamics (which is very close to our treatment of charge conservation, p. 4) . 3. For x → a × x, divergence: 0, curl: 2a. For x → x, curl-free, the divergence is the constant scalar field x → 3.

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