OpenStax University Physics/E&M/Electric Charges and Fields

${\displaystyle {\mathcal {E}}\&{\mathcal {M}}}$ (Vol. 2):    5:Electric Charges and Fields    6:Gauss's Law    7:Electric Potential    8:Capacitance    9:Current and Resistance    10:Direct-Current Circuits    11:Magnetic Forces and Fields    12:Sources of Magnetic Fields    13:Electromagnetic Induction    14:Inductance    15:Alternating-Current Circuits    16:Electromagnetic Waves

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Elementary charge = e = 1.602×10⁻¹⁹C (electrons have charge q=−e and protons have charge q=+e.)

▭ By superposition, ${\displaystyle {\vec {F}}={\tfrac {1}{4\pi \varepsilon _{0}}}Q\sum _{i=1}^{N}{\tfrac {q_{i}}{r_{Qi}^{2}}}{\hat {r}}_{Qi}}$ where ${\displaystyle {\vec {r}}_{Qi}={\vec {r}}_{Q}-{\vec {r}}_{i}}$
▭ Electric field ${\displaystyle {\vec {F}}=Q{\vec {E}}}$ where ${\displaystyle {\vec {E}}({\vec {r}}_{P})={\tfrac {1}{4\pi \varepsilon _{0}}}\sum _{i=1}^{N}{\tfrac {q_{i}}{r_{Pi}^{2}}}{\hat {r}}_{Pi}}$ is the field at ${\displaystyle {\vec {r}}_{P}}$ due to charges at ${\displaystyle {\vec {r}}_{i}}$
▭ The field above an infinite wire ${\displaystyle {\vec {E}}(z)={\tfrac {1}{4\pi \varepsilon _{0}}}{\tfrac {2\lambda }{z}}{\hat {k}}}$ and above an infinite plane ${\displaystyle {\vec {E}}={\tfrac {\sigma }{2\varepsilon _{0}}}{\hat {k}}}$
▭ An electric dipole ${\displaystyle {\vec {p}}=q{\vec {d}}}$ in a uniform electric field experiences the torque ${\displaystyle \tau ={\vec {p}}\times {\vec {E}}}$