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3
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1
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Divergence Theorem, mathematical approach to Gauss's Law?
Let $D$ be a compact region in $\mathbb{R}^3$ with a smooth boundary $S$. Assume $0 \in \text{Int}(D)$. If an electric charge of magnitude $q$ is placed at $0$, the resulting force field is $q\vec{r}/...
user81012
16
votes
2
answers
2k
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Why isn't the path integral defined for non-homotopic paths?
Context
In the Aharonov Bohm effect, there is a solenoid which creates a magnetic field. Since the electron cannot be inside the solenoid, the configuration space is not simply connected.
Question
I'...
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9
votes
2
answers
1k
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Vector Potential for Magnetic field when the field is not in simply-connected region
According to Poincare's Lemma, if $U\subset \mathbb{R}^n$ is a star-shaped set and if $\omega$ is a $k$-form defined in $U$ that is closed, then $\omega$ is exact, meaning that there's some $(k-1)$-...
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