(ne03) The Electric Field 電場


PreAmble

Key Points (note similar to gravity)

Point Charges and Symmetry

Base Case + Three General Cases
$$ \mathbf E_{point} $$$$ \mathbf E_{line,\infty} $$ $$ \mathbf E_{plane,\infty} $$$$ \mathbf E_{sphere} $$
$$ q \, [C] $$ $$ \lambda \, [C m^{-1}] $$$$ \eta \, [C m^{-2} ] $$ $$ Q \, [C] $$
$$ = {1 \over {4 \pi \epsilon_o}} \, \color{fuchsia} {q \over r^2} \, { \mathbf r \over r } $$ $$ = {1 \over {4 \pi \epsilon_o}} \, \color{fuchsia}{2 \lambda \over r} \, { \mathbf r \over r } $$ $$ = {1 \over {4 \pi \epsilon_o}} \, \color{fuchsia}{2 \pi\eta } \, { \mathbf z \over z } $$ $$ = \mathbf E_{point} $$

Dipoles

$$ \mathbf p = |q| \mathbf s $$
$$ \mathbf E_{dipole,axis} $$ $$ \mathbf E_{dipole,plane} $$
$$ = {1 \over {4 \pi \epsilon_o}} \, \color{fuchsia} {2 \mathbf p \over r^3} $$ $$ = {1 \over {4 \pi \epsilon_o}} \, \color{fuchsia} { \mathbf p \over r^3} $$

(Observable) Acceleration: Linear & Angular

$$ \mathbf a = { q \over m_e} \mathbf E + { m_g \over m_e} \mathbf G $$ $$ \mathbf \alpha = {{\mathbf \tau} \over {I}} = {{\mathbf p \times \mathbf E} \over I} $$

Powerpoints: Knight Chapter 26 The Electric Field.


Charges and Fields
Monopoles and Dipoles

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