Δ V A B = V A − V B = − ∫ A B E → ⋅ d ℓ → {\displaystyle \Delta V_{AB}=V_{A}-V_{B}=-\int _{A}^{B}{\vec {E}}\cdot d{\vec {\ell }}} = electric potential
E → = − ∂ V ∂ x i ^ − ∂ V ∂ y j ^ − ∂ V ∂ z k ^ = − ∇ → V {\displaystyle {\vec {E}}=-{\tfrac {\partial V}{\partial x}}{\hat {i}}-{\tfrac {\partial V}{\partial y}}{\hat {j}}-{\tfrac {\partial V}{\partial z}}{\hat {k}}=-{\vec {\nabla }}V}
q Δ V {\displaystyle q\Delta V} = change in potential energy (or simply U = q V {\displaystyle U=qV} )
P o w e r = Δ U Δ t = Δ q Δ t V = I V = e Δ N Δ t {\displaystyle Power={\tfrac {\Delta U}{\Delta t}}={\tfrac {\Delta q}{\Delta t}}V=IV=e{\tfrac {\Delta N}{\Delta t}}}
Electron (proton) mass = 9.11×10−31kg (1.67× 10−27kg). Elementary charge = e = 1.602×10−19C.
K = 1 2 m v 2 {\displaystyle K={\tfrac {1}{2}}mv^{2}} =kinetic energy. 1 eV = 1.602×10−19J
V ( r ) = k q r {\displaystyle V(r)=k{\tfrac {q}{r}}} near isolated point charge
Many charges: V P = k ∑ 1 N q i r i → k ∫ d q r {\displaystyle V_{P}=k\sum _{1}^{N}{\frac {q_{i}}{r_{i}}}\to k\int {\frac {dq}{r}}} .
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= electric potential
= change in potential energy (or simply 
)
=kinetic energy. 1 eV = 1.602×10−19J
near isolated point charge
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