These 2 sources are the mandatory and rapid exponential decay of net electrical charge within a conducting material. Mathematically, the combination of the continuity equation, Ohm's law ($\vec{\jmath}=\sigma \vec{E}$), and Gauss's law demonstrates that if the charge density ($\rho$) is non-zero, it must decrease exponentially over time, described by the relationship $\frac{\partial \rho}{\partial t}=-\frac{\sigma}{\varepsilon_0} \rho$. This mathematical necessity proves that the only stationary solution for charge inside a conductor with non-zero conductivity ($\sigma$) is zero charge density ($\rho=0$), with the decay rate determined by the constant $\sigma / \varepsilon_0$. Conceptually, this highly efficient self-correction means that any net electrical charge introduced inside the material must instantaneously dissipate and move to the surface. This unavoidable flow of charge is driven by the internal electric field and is governed by the charge relaxation time, which is extremely short in metals due to their typically enormous conductivity, making the dissipation effectively immediate.
block-beta
columns 5
CC["Criss-Cross"]:5
%% Condensed Notes
CN["Condensed Notes"]:5
RF["Relevant File"]:5
NV["Narrated Video"]:4 VO["Voice-over"]
PA("Plotting & Analysis")AA("Animation & Analysis")KT("Summary & Interpretation") ID("Illustration & Demo") PO("Polyptych")
%% Proof and Derivation
PD["Proof and Derivation"]:5
AF("Derivation Sheet"):5
NV2["Narrated Video"]:4 VO2["Voice-over"]
PA2("Plotting & Analysis")AA2("Animation & Analysis")KT2("Summary & Interpretation") ID2("Illustration & Demo") PO2("Polyptych")
classDef color_1 fill:#8e562f,stroke:#8e562f,color:#fff
class CC color_1
classDef color_2 fill:#14626e,stroke:#14626e,color:#fff
class CN color_2
class RF color_2
classDef color_3 fill:#1e81b0,stroke:#1e81b0,color:#fff
class NV color_3
class PA color_3
class AA color_3
class KT color_3
class ID color_3
classDef color_4 fill:#47a291,stroke:#47a291,color:#fff
class VO color_4
class PO color_4
%% Proof and Derivation
classDef color_5 fill:#307834,stroke:#307834,color:#307834
class PD color_5
class AF color_5
classDef color_6 fill:#38b01e,stroke:#38b01e,color:#38b01e
class NV2 color_6
class PA2 color_6
class AA2 color_6
class KT2 color_6
class ID2 color_6
classDef color_7 fill:#47a291,stroke:#47a291,color:#47a291
class VO2 color_7
class PO2 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]
© 2025 Sayako Dean
</aside>