1.5 Notation used in these notes

A consistent notation makes long derivations much easier to follow. The same conventions are kept throughout (Table 1.5.1).

• Vectors carry an arrow, $A$, $E$, and their magnitudes are written $A=|A|$, $E=|E|$.
• Unit vectors are written $a$ with the coordinate as subscript: $a_x,a_y,a_z$ (Cartesian), $a_{\rho },a_{\varphi },a_z$ (cylindrical), $a_r,a_{\theta },a_{\varphi }$ (spherical). The symbol $a_n$ denotes a unit normal to a surface.
• The point at which a field is evaluated is the field point P, with position vector $r$ and unprimed coordinates $(x,y,z)$. A point of the source is the source point Q, with position vector $r{}^{\prime }$ and primed coordinates $(x^{\prime },y^{\prime },z^{\prime })$. Integrals over a source are always taken over the primed variables.
• The displacement vector from the source point to the field point is $R=r-r{}^{\prime }$, with magnitude $R=|r-r{}^{\prime }|$.

Table 1.5.1. Principal symbols.

Symbol	Meaning	Unit
$q$, $Q$	point charge, total charge	C
${\rho }_L$, ${\rho }_S$, ${\rho }_v$	line, surface, volume charge density	C/m, C/m², C/m³
$r$, $r{}^{\prime }$	position vectors of the field point P and source point Q	m
$R=r-r{}^{\prime }$	displacement vector from Q to P	m
$F$	force	N
$E$	electric field intensity	V/m
$D$	electric flux density	C/m²
$P$	polarisation vector	C/m²
$V$	electrostatic potential	V
$W$	energy	J
$C$	capacitance	F
${\epsilon }_0$	permittivity of free space	F/m
$\epsilon$, ${\epsilon }_r$	permittivity, relative permittivity	F/m, none
$d{l}^{\prime }$, $d{S}^{\prime }$, $d{V}^{\prime }$	differential length, area, volume at the source	m, m², m³
$\nabla$	nabla operator (gradient, divergence, curl)	1/m