Question

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

score 43 · Answer 1 · 2026-03-26 19:11:48

43

Views

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

Published on 26 Mar 2026 - 19:11

score 50 · Answer 2 · 2026-03-26 17:31:24

50

Views

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

Published on 26 Mar 2026 - 17:31

score 102 · Answer 3 · 2026-03-26 17:34:59

102

Views

Visualizing the curl of curl

Published on 26 Mar 2026 - 17:34

score 17 · Answer 4 · 2026-05-05 14:03:32

17

Views

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

Published on 05 May 2026 - 14:03

score 82 · Answer 5 · 2026-03-26 17:29:33

82

Views

Conservative vector field given in polar coordinates

Published on 26 Mar 2026 - 17:29

score 76 · Answer 6 · 2026-04-11 11:00:54

76

Views

Divergence theorem with normal component of a curl to a surface

Published on 11 Apr 2026 - 11:00

score 31 · Answer 7 · 2026-03-26 17:32:17

31

Views

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

Published on 26 Mar 2026 - 17:32

score 46 · Answer 8 · 2026-03-26 17:34:48

46

Views

Curl without integrals

Published on 26 Mar 2026 - 17:34

score 184 · Answer 9 · 2026-03-26 17:33:08

184

Views

What is the adjoint of the curl operator?

Published on 26 Mar 2026 - 17:33

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 32 · Answer 11 · 2026-03-26 19:18:25

32

Views

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

Published on 26 Mar 2026 - 19:18

score 1k · Answer 12 · 2026-03-26 17:35:40

1k

Views

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

Published on 26 Mar 2026 - 17:35

score 30 · Answer 13 · 2026-03-26 19:14:14

30

Views

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

Published on 26 Mar 2026 - 19:14

score 86 · Answer 14 · 2026-03-26 19:19:01

86

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 26 Mar 2026 - 19:19

score 67 · Answer 15 · 2026-03-26 17:32:53

67

Views

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

Published on 26 Mar 2026 - 17:32

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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