Question

$\vec \nabla \times \vec F=0 $ $\implies$ $\exists$ a scalar potential $\phi$ such that $\nabla \phi=\vec F$. Prove it.

score 42 · Answer 1 · 2023-06-14 14:43:04

42

Views

$\vec \nabla \times \vec F=0 $ $\implies$ $\exists$ a scalar potential $\phi$ such that $\nabla \phi=\vec F$. Prove it.

Published on 14 Jun 2023 - 14:43

score 49 · Answer 2 · 2023-06-28 08:58:10

49

Views

Holomorphic in $\mathbb{C}$ vs divergence-and-curl-free in $\mathbb{R}^2$

Published on 28 Jun 2023 - 8:58

score 101 · Answer 3 · 2023-06-29 13:38:38

101

Views

Visualizing the curl of curl

Published on 29 Jun 2023 - 13:38

score 11 · Answer 4 · 2026-03-10 08:29:20

11

Views

In studying waveguide mode vectors I have difficulty in interpreting the expression

Published on 10 Mar 2026 - 8:29

score 81 · Answer 5 · 2023-08-19 14:12:29

81

Views

Conservative vector field given in polar coordinates

Published on 19 Aug 2023 - 14:12

score 75 · Answer 6 · 2026-02-23 10:07:21

75

Views

Divergence theorem with normal component of a curl to a surface

Published on 23 Feb 2026 - 10:07

score 30 · Answer 7 · 2023-08-22 15:00:13

30

Views

Can you characterize a vector field $v$ with uniform curl as $v(x) = a + b \times x$?

Published on 22 Aug 2023 - 15:00

score 45 · Answer 8 · 2023-09-07 22:43:08

45

Views

Curl without integrals

Published on 07 Sep 2023 - 22:43

score 183 · Answer 9 · 2023-09-14 23:30:11

183

Views

What is the adjoint of the curl operator?

Published on 14 Sep 2023 - 23:30

score 64 · Answer 10 · 2026-03-25 23:09:37

64

Views

Green's theorem example application for engineers and physicists.

Published on 25 Mar 2026 - 23:09

score 31 · Answer 11 · 2023-10-11 21:58:10

31

Views

Curl of normal unit vector of a smooth and closed surface?

Published on 11 Oct 2023 - 21:58

score 1k · Answer 12 · 2023-10-16 22:37:45

1k

Views

Why does it seem the inner curls within a surface always cancels in order for greens theorem to be true

Published on 16 Oct 2023 - 22:37

score 29 · Answer 13 · 2023-10-20 12:24:12

29

Views

How do I find orthogonal vectors using the del operator in an arbitrary coordinate system?

Published on 20 Oct 2023 - 12:24

score 85 · Answer 14 · 2023-11-22 17:41:23

85

Views

How to prove that $\vec{\nabla}\times\vec{\nabla}\times(e^{i\vec{k}\cdot\vec{x}}\vec{\omega})=k^2(e^{i\vec{k}\cdot\vec{x}}\vec{\omega})$

Published on 22 Nov 2023 - 17:41

score 66 · Answer 15 · 2023-11-27 12:19:49

66

Views

How to solve this kind of surface integral with Hamilton Operator?

Published on 27 Nov 2023 - 12:19

List Question

$\vec \nabla \times \vec F=0 $ $\implies$ $\exists$ a scalar potential $\phi$ such that $\nabla \phi=\vec F$. Prove it.

Holomorphic in $\mathbb{C}$ vs divergence-and-curl-free in $\mathbb{R}^2$

Visualizing the curl of curl

In studying waveguide mode vectors I have difficulty in interpreting the expression

Conservative vector field given in polar coordinates

Divergence theorem with normal component of a curl to a surface

Can you characterize a vector field $v$ with uniform curl as $v(x) = a + b \times x$?

Curl without integrals

What is the adjoint of the curl operator?

Green's theorem example application for engineers and physicists.

Curl of normal unit vector of a smooth and closed surface?

Why does it seem the inner curls within a surface always cancels in order for greens theorem to be true

How do I find orthogonal vectors using the del operator in an arbitrary coordinate system?

How to prove that $\vec{\nabla}\times\vec{\nabla}\times(e^{i\vec{k}\cdot\vec{x}}\vec{\omega})=k^2(e^{i\vec{k}\cdot\vec{x}}\vec{\omega})$

How to solve this kind of surface integral with Hamilton Operator?

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