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 describe addition and …
Just what does it mean when a vector field has 0 divergence?
May 8, 2011 · A vector field with zero divergence indicates that the quantity flowing into a region equals the quantity flowing out, signifying conservation within that region. Specifically, for the electric field …
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 their radial …
How to observe if a vector field has curl or not? - Physics Forums
Nov 26, 2021 · Explore examples of vector fields with non-zero curl and analyze their properties Investigate the implications of singularities in vector field analysis Students and professionals in …
Difference between a vector space and a field? - Physics Forums
Dec 19, 2007 · The discussion clarifies the fundamental differences between vector spaces and fields, emphasizing that while both are algebraic structures, they serve distinct purposes. A vector space is …
Is There a Difference Between a Vector Field and a Vector Function ...
Jul 31, 2007 · The conversation also distinguishes between scalar functions and scalar fields, emphasizing that while a scalar function assigns numbers to points in space, a scalar field is a …
What Defines a Uniform Vector Field? - Physics Forums
Mar 22, 2011 · A uniform vector field is defined as a vector field where the vector assigned to every point is the same, represented mathematically as \ (\vec A = \hat {x} k_x + \hat {y} k_y + \hat {z} k_z\) with …
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 the …
Divergence of radial unit vector field - Physics Forums
Jul 15, 2015 · The divergence of the actual radial vector field, ∇ · r = 3, remains constant regardless of position, highlighting the relationship between flow magnitude and divergence. Understanding these …
Finding the Flux of a Vector Field - Physics Forums
Sep 4, 2018 · The discussion focuses on calculating the flux of a vector field defined as v → = a/ (x^2 + y^2)z through specified rectangles in the xy-plane and yz-plane. The correct approach involves using …