# Talk:QB/a19ElectricPotentialField Capacitance

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

${\vec {E}}=-{\tfrac {\partial V}{\partial x}}{\hat {i}}-{\tfrac {\partial V}{\partial y}}{\hat {j}}-{\tfrac {\partial V}{\partial z}}{\hat {k}}=-{\vec {\nabla }}V$ $q\Delta V$ = change in potential energy (or simply $U=qV$ )

$Power={\tfrac {\Delta U}{\Delta t}}={\tfrac {\Delta q}{\Delta t}}V=IV=e{\tfrac {\Delta N}{\Delta t}}$ Electron (proton) mass = 9.11×10−31kg (1.67× 10−27kg). Elementary charge = e = 1.602×10−19C.

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

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

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

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

$Q=CV$ defines capacitance.

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

${\text{Series}}:\;{\tfrac {1}{C_{S}}}=\sum {\tfrac {1}{C_{i}}}.$ ${\text{ Parallel:}}\;C_{P}=\sum C_{i}.$ $u={\tfrac {1}{2}}QV={\tfrac {1}{2}}CV^{2}={\tfrac {1}{2C}}Q^{2}$ = stored energy

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