$$1\ Avagadro\ Constant = \frac{Number\ of\ Particles \ (N)\ 6.02214076 * 10^{23} }{1\ mol}$$ $$1\ Joule = \frac{1\ Kilo\ Gram * 1\ Meter^2}{1\ Second^2}$$ $$1\ Newton = \frac{1\ Kilogram * 1\ meter}{1\ Second^2}$$ $$1\ Newton\ Meter = \frac{1\ Kilogram * 1\ meter^2}{1\ Second^2}$$ $$\frac{1\ Kilogram}{1\ meter \cdot Second^2} = \frac{1\ Newton}{1\ meter^2}$$ $$1\ Watt = \frac{1\ Joule}{1\ Second} = \left(\ 1\ Volt * 1\ Ampere\ \right)$$ $$Planck\ Constant\ (h) = \frac{6.62607015*10^{-34}\ Joules}{1\ Second}$$ $$Reduced\ Planck\ Constant\ (\hbar) = \frac{Plank\ Constant\ (h)}{2*\pi} = \frac{1.054571817*10^{-34}\ Joules}{1\ Second}$$ $$1\ Hertz = \frac{60\ Revolutions}{1\ Minute} = \frac{2 *\ \pi\ Radians}{1\ Second}$$ $$Angular\ Veloctiy\ (\omega) = 2 * \pi * Frequency\ (f)\ Hertz$$ $$Frequency\ (f) = \frac{Angular\ Velocity\ (\omega)}{2 * \pi}$$ $$Speed\ of\ Light = \frac{299792458\ meters}{1\ Second}$$ $$1\ Electric\ Constant\ (\epsilon_0)\ (Vacuum\ Permittivity) = \frac{8.854187*10^{-12}\ Farads}{1\ Meter}$$
• Distributed Capacitance of the Vacuum
• Capability of Electric Field to Permeate a Vacuum
$$Force\ Between\ Two\ Separated\ Electric\ Charges\ with\ Spherical\ Symmetry\ in\ a\ Vacuum = F_C = \frac{1}{4*\pi * \epsilon_0}*\frac{q_1*q_2}{r^2}$$ $$Gravitational\ Constant = \frac{6.67408 * 10^{-11} Meters^3}{1\ Kilogram^3 * 1\ Second^2}$$ $$Force_{gravity} = \frac{Gravitatonal\ Constant\ (G)* Mass_1 * Mass_2}{Distance\ Between\ Mass_1\ and\ Mass_2\ (r)}$$ $$\frac{Force_{gravity}}{Force_{electric}} = \frac{Gravitational\ Constant\ (G) * Mass_1 * Mass_2}{Coulomb\ Constant * 1\ Elementary\ Charge\ (e^2)}$$ $$Acceleration\ Due\ To\ Gravity\ (a) = \frac{Gravitatonal\ Constant\ (G) * Mass}{(Radius\ of\ Earth\ (6.3781 * 10^6\ Meters))^2} = \frac{9.81\ Meters}{1\ Second^2}$$ $$Force = Mass * Acceleration$$ $$Energy_{photon} = \frac{Planks\ Constant\ (h) * Speed\ of\ Light\ (c)}{Wavelength\ \lambda_{photon} } = 4.66* 10^{-19}\ Joule$$ $$Energy_{photon} * Wavelength\ (\lambda)_{photon} = Plank\ Constant\ (h) * Speed\ of\ Light\ (C)$$ $$Energy_{photon} = Plank\ Constant\ (h) * Frequency_{Proton}\ (f)$$ $$Energy_{photon} = \frac{6.62607015*10^{-34}\ Joules}{1\ Second} * \frac{4.60 * 10^{14}Frequency_{Proton}\ (f)\ Hertz}{1\ Second}$$ $$Characterization\ of\ Electromagnetic\ Force , Finate\ Structure\ Constant\ (\alpha) = \frac{2*\pi *\ Coulomb\ Constant (k) * (1\ Elementary\ Charge)^2}{E_{photon}*Wavelength\ (\lambda)_{photon}} = \frac{2* \pi * Coulomb\ Constant (k) * (1\ Elementary\ Charge)^2}{h *c } = \frac{1}{137}$$ $$Fine\ Structure\ Coupling\ Strength\ (1\ Elementary\ Charge^2) = 4 * \pi * Electric\ Constant\ (\epsilon_0) * Reduced\ Planck\ Constant\ (\hbar) * Elementary\ Charge\ (c) * Gap\ Between\ Spectral\ Lines\ of\ Hydrogen\ (\alpha)$$ $$1\ Elementary\ Charge = \sqrt{\left(4*\pi *Fine-Structure\ Constant\ (a)\right)} * \sqrt{Reduced\ Planck's\ Constant\ (\hbar ) * Speed\ of\ Light\ (C)}$$ $$1\ Elementary\ Charge\ (e) = \frac{1\ Farad}{1\ Avagadro\ Constant}$$ $$1\ Elementary\ Charge\ (e) = 1.602176634*10^{-19} Coulomb$$ $$1\ Coulomb = 1.036 * 10^{-5}\ mols \cdot Na\ elementary\ charge$$ $$1\ Ohm\ (\Omega) = \frac{1\ Joule \cdot Second}{1\ Coulomb^2}$$ $$1\ Ampere\ (A)(Amp) = \frac{1\ Coulomb}{1\ Second}$$ $$\ Siemen\ (S) = [\Omega^{-1}] = \frac{1\ Ampere\ (A)}{1\ Volt}$$ $$1\ Siemen\ (S) = \frac{1\ Coulomb^2}{1\ Joule \cdot Second}$$ $$Conductance\ (G) = \frac{1}{Resistance} = \frac{Current\ (I)}{Voltage\ (V)} = Siemens$$ $$\left[2\ Plates\ Charge\ Separation\ ,\ (+Q,-Q)\ ,\ Coulomb\ , \frac{1\ Ampere}{1\ Second}\right]$$ $$\left[Capacitance\ ,\ (C)\ ,\ Farad\ , \frac{1\ Ampere}{1\ Second}\right]$$ $$\left[Potential\ Difference\ ,\ (\Delta V)\ ,\ Volt\ ,\ \frac{1\ Joule}{1\ Coulomb}\right]$$ $$Charge\ (Q) = Capacitance\ (C) * Potential\ Difference\ (\Delta V)$$ $$Capacitance = \frac{Charge\ (Q)}{Potential\ Difference\ (\Delta V)}$$ $$Potential\ Difference\ (\Delta V) = \frac{Charge\ (Q)}{Capacitance\ (C)}$$