The investigation into the flux dynamics of weighted radial vector fields demonstrates that a surface integral involving a $1/r^5$ weighting can be converted into a volume integral where the scalar field $\phi(\vec{x})$ is defined as $-1/r^5$, provided the origin is excluded. This specific weighting is significant because, unlike the standard $1/r^3$ case associated with Gauss's Law, it leads to a divergent integral at the origin, requiring an "exclusion zone" around the singularity for the mathematical identities to hold true. By utilising 3D and high-contrast 2D visualisations, the project effectively bridges abstract vector calculus with physical intuitions regarding potential wells and flux conservation.
A derivative illustration based on our specific text and creative direction
A derivative illustration based on our specific text and creative direction
block-beta
columns 6
CC["Criss-Cross"]:6
%% Condensed Notes
CN["Condensed Notes"]:6
RF["Relevant File"]:6
NV["Narrated Video"]:6
PA("Plotting & Analysis")AA("Animation & Analysis")KT("Summary & Interpretation") ID("Illustration & Demo") VA1("Visual Aid")MG1("Multigraph")
%% Proof and Derivation
PD["Proof and Derivation"]:6
AF("Derivation Sheet"):6
NV2["Narrated Video"]:6
PA2("Plotting & Analysis")AA2("Animation & Analysis")KT2("Summary & Interpretation") ID2("Illustration & Demo")VA2("Visual Aid") MG2("Multigraph")
classDef color_1 fill:#8e562f,stroke:#8e562f,color:#fff
class CC color_1
%% %% Condensed Notes
classDef color_2 fill:#14626e,stroke:#14626e,color:#14626e
class CN color_2
class RF color_2
classDef color_3 fill:#1e81b0,stroke:#1e81b0,color:#1e81b0
class NV color_3
class PA color_3
class AA color_3
class KT color_3
class ID color_3
class VA1 color_3
classDef color_4 fill:#47a291,stroke:#47a291,color:#47a291
class VO color_4
class MG1 color_4
%% Proof and Derivation
classDef color_5 fill:#307834,stroke:#307834,color:#fff
class PD color_5
class AF color_5
classDef color_6 fill:#38b01e,stroke:#38b01e,color:#fff
class NV2 color_6
class PA2 color_6
class AA2 color_6
class KT2 color_6
class ID2 color_6
class VA2 color_6
classDef color_7 fill:#47a291,stroke:#47a291,color:#fff
class VO2 color_7
class MG2 color_7
‣
<aside> <img src="/icons/report_pink.svg" alt="/icons/report_pink.svg" width="40px" />
Copyright Notice
All content and images on this page are the property of Sayako Dean, unless otherwise stated. They are protected by United States and international copyright laws. Any unauthorized use, reproduction, or distribution is strictly prohibited. For permission requests, please contact [email protected]
©️2026 Sayako Dean
</aside>