Coulomb's Law
The force on a charged point exerted by a second charge is proportional to the product of charges, and inversely proportional to the square of the distance between the charges, and acts either directly towards each other (opposite charges) or away from each other (same sign of charge).
F(vector) = k * q1 * q2 / r12^2 * direction(r12)
where
k = 1 / (4 * pi * epsilon) = 8.99E9 Newton Meter^2/Coulomb^2
where epsilon is the dielectric constant of the medium ( = 8.85E-12 for vacuum)
r12 is the scalar distance from point 1 to point 2
direction (r12) is a unit vector from point 1 to point 2
q1,q2 are charges on each point
Capacitance of two parallel plates
C = epsilon * Area / DistanceBetweenPlates
this neglects fringing effects, which for plates that are smaller than, say, 10 times the spacing, are pretty significant.
Capacitance of two concentric cylinders (e.g. coaxial cable)
C = 2 * pi * epsilon * length / ln( rOuter/rInner)
this assumes length >> r
Capacitance of two concentric spheres
C = 4 * pi * epsilon * rInner * rOuter/ (rOuter - rInner)
as rOuter goes to infinity, the fraction rOuter/(rOuter-rInner) goes to one, leading to the following handy equation:
Capacitance of isolated sphere
C = 4*pi*epsilon*radius = approx 111.2 pF/meter
this equation is derived from the equation for two concentric (nested) spheres, and letting the radius of the outer sphere go to infinity.
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