# Talk:QB/a19ElectricPotentialField Capacitance

${\displaystyle \Delta V_{AB}=V_{A}-V_{B}=-\int _{A}^{B}{\vec {E}}\cdot d{\vec {\ell }}}$ = electric potential

${\displaystyle {\vec {E}}=-{\tfrac {\partial V}{\partial x}}{\hat {i}}-{\tfrac {\partial V}{\partial y}}{\hat {j}}-{\tfrac {\partial V}{\partial z}}{\hat {k}}=-{\vec {\nabla }}V}$

${\displaystyle q\Delta V}$ = change in potential energy (or simply ${\displaystyle U=qV}$)

${\displaystyle Power={\tfrac {\Delta U}{\Delta t}}={\tfrac {\Delta q}{\Delta t}}V=IV=e{\tfrac {\Delta N}{\Delta t}}}$

Electron (proton) mass = 9.11×10−31kg (1.67× 10−27kg). Elementary charge = e = 1.602×10−19C.

${\displaystyle K={\tfrac {1}{2}}mv^{2}}$=kinetic energy. 1 eV = 1.602×10−19J

${\displaystyle V(r)=k{\tfrac {q}{r}}}$ near isolated point charge

Many charges: ${\displaystyle V_{P}=k\sum _{1}^{N}{\frac {q_{i}}{r_{i}}}\to k\int {\frac {dq}{r}}}$.

The alpha-particle is made up of two protons and two neutrons.

${\displaystyle Q=CV}$ defines capacitance.

${\displaystyle C=\varepsilon _{0}{\tfrac {A}{d}}}$ where A is area and d<<A1/2 is gap length of parallel plate capacitor

${\displaystyle {\text{Series}}:\;{\tfrac {1}{C_{S}}}=\sum {\tfrac {1}{C_{i}}}.}$   ${\displaystyle {\text{ Parallel:}}\;C_{P}=\sum C_{i}.}$

${\displaystyle u={\tfrac {1}{2}}QV={\tfrac {1}{2}}CV^{2}={\tfrac {1}{2C}}Q^{2}}$ = stored energy

${\displaystyle u_{E}={\tfrac {1}{2}}\varepsilon _{0}E^{2}}$ = energy density