All Questions
Tagged with gauss-law mathematical-physics
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Gauss divergence theorem (GDT) in physics
Some of the statements for $GDT$ which I find in modern textbooks (both electromagnetism and multivariable calculus textbooks) are:
(1) Calculus: Several variables Adams
Let $D$ be a regular, ...
- 11
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Will the flux through an arbitrary closed surface be finite or infinite when a plane charge intersects the Gaussian surface?
Let's consider a closed Gaussian surface (in red).
The white line and the white shaded part lies inside the Gaussian surface and the black line and the portion above it lies outside the Gaussian ...
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Formal Connection Between Symmetry and Gauss's Law
In the standard undergraduate treatment of E&M, Gauss's Law is loosely stated as "the electric flux through a closed surface is proportional to the enclosed charge". Equivalently, in differential ...
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Is the gravitational field $\mathbf{g}(x)=-G\int_{\Bbb R^3}\rho(y)\frac{x-y}{|x-y|^3}\,\mathrm{d}y$ continuously differentiable?
I apologize for mathematician-style question, but I was wondering if for continuous mass density $\rho:\Bbb R^3\to\Bbb R$ with compact support, the gravitational field $$\mathbf{g}(x)=-G\int_{\Bbb R^3}...
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Calculating the potential on a surface from the potential on another surface
The question is short: If a charge (or mass) distribution $\rho$ is enclosed by surface $S_1$, I can calculate the electrostatic (or gravitational) potential on that surface by integrating $\rho(r') \ ...
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Divergence of Electric Field: Moving Del Operator Inside Integral
I'm reading Griffiths E&M book (4th edition), and on page 71 he starts with the expression for the electric field of a volume charge distribution:
$$
\vec{E}(\vec{r}) = \frac{1}{4\pi \epsilon_0}\...
- 758
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Is there a "more rigorous" derivation of the electrostatic boundary conditions?
When I first saw a derivation of the electrostatic boundary conditions it wasn't quite rigorous. It was essentially the argument used by Griffiths in his book:
Suppose we draw a wafer-thin Gaussian ...
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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}/...
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