How to write a Vector Field in Cylindrical Co-ordinates?
Oct 31, 2016 · The vector arrows circulate a central axis, you can think of them as tangents to circles. The field does not depend on the height z. The lengths of the arrows is a function of …
Why Vector Spaces Explain The World: A Historical Perspective
Mar 13, 2025 · Vector spaces are often described as a set of arrows, i.e. a line segment with a direction that can be added, stretched, or compressed. That's where the term linear to …
Just what does it mean when a vector field has 0 divergence?
May 8, 2011 · Homework Statement Yeah I've been pondering over that, my book doesn't really do the justice of nailing it down for me. Does having 0 divergence means having "absolute …
Difference between a vector space and a field? - Physics Forums
Dec 19, 2007 · I'm just wondering what are the differences between vector spaces and fields. From what I understand by the definitions, both of these are collections of objects where …
Introduction to Electric Vector Potential and Its Applications
Oct 9, 2020 · For our vector potential we are however free to choose (by gage invariance or direct verification). Then which are of course 3 scalar equations, one of which is and by similarity to …
How to observe if a vector field has curl or not? - Physics Forums
Nov 26, 2021 · These are the vector fields. I really have no idea how to see if there is a curl or not. I have been looking at the rotation of the vector fields. The fields d and e seem to have …
Is There a Difference Between a Vector Field and a Vector Function ...
Jul 31, 2007 · My related questions 1 Is there any difference between 'vector field' and 'vector function'? 'vector function' is also called 'vector-valued function' (Thomas calculus). According …
If curl A = 0, how is it the gradient of something? - Physics Forums
Sep 16, 2012 · The discussion focuses on the relationship between the curl of a vector field and its representation as the gradient of a scalar field. It clarifies that if the curl of a vector field A is …
What Defines a Uniform Vector Field? • Physics Forums
Mar 22, 2011 · A uniform vector field is defined as one where the vector assigned to every point is the same, meaning it has constant magnitude and direction throughout the field. This implies …
What's the physical meaning of Curl of Curl of a Vector Field?
Apr 4, 2024 · The curl of the curl of a vector field, expressed as ∇ × (∇ × A), relates to how much the curl itself rotates counterclockwise. This operation can be simplified using the identity ∇ × …