# Electricity, Magnetism and Circuits

## List of Symbols and notations

 A, B ... points in space, curves, surfaces and solids A , B ... phasor A, B ... a, b ... units $A$, $B$... $a$, $b$... variables or vectors modules $\vec{A}$, $\vec{B}$... $\vec{a}$, $\vec{b}$... vectors $\hat{A}$, $\hat{B}$... $\hat{a}$, $\hat{b}$... unit vectors $\vec{a}\cdot\vec{b}$ dot product between vectors $\vec{a}\times\vec{b}$ vector product of vectors $\bar{f}$ Average value of the function $f$ $f_{\mathrm{ef}}$ rms value of the periodic function $f$ $f_{\mathrm{max}}$ maximum value of the sine function $f$ $\dfrac{\mathrm{d}\,f}{\mathrm{d}\,x}$, $\dfrac{\mathrm{d}^2\,f}{\mathrm{d}\,x^2}$... derivatives of function $f$ with respect to $x$ $\dot{f}$, $\ddot{f}$... derivatives of function $f$ with respect to time $\tilde{f}$ or $\mathscr{L}\{f\}$ Laplace transform of function $f$ $a$ acceleration $A$ area of a surface A ampere (SI unit of current) $\vec{a}$ acceleration vector $\vec{B}$ magnetic field $C$ electrical capacity C coulomb (SI unit of charge) $c$ speed of light c centi prefix (10 -2 ) $d$ distance d deci prefix (10 -1 ) $\vec{E}$ electric field $e$ elementary charge e Euler number (base of the natural logarithm) $E_\mathrm{max}$ dielectric strength eV electron-volt (energy unit) $\vec{F}$ force F farad (SI unit of capacity) $f$ frequency G gauss (magnetic field unit); Giga prefix (10 9 ) $\vec{g}$ gravity field g gram (SI unit of mass) $H$ transfer function; frequency response function H henry (SI unit of inductance) $h$ Planck's constant $I$ electric current i imaginary number $\sqrt{-1}$ $\hat{\imath}, \hat{\jmath}, \hat{k}$ unit vectors along the Cartesian axes $x$, $y$ and $z$ J joule (SI unit of work and energy) $K$ dielectric constant K kelvin (SI unit of temperature) $k$ Coulomb's constant k prefix kilo (10 3 ) $k_\mathrm{m}$ magnetic constant kg kilogram (SI unit of mass) $L$ inductance; length $M$ mutual inductance M Mega prefix (10 6 ) $m$ mass m meter (SI unit of length) N newton (SI unit of force) $\hat{n}$ Unit vector normal to a surface n prefix nano (10 -9 ) $\vec{p}$ momentum $P$ power P prefix pico (10 -12 ) $Q$, $q$ electric charge $R$ electrical resistance; radius of a sphere. $R$, $\theta$, $z$ cylindrical coordinates $\hat{R}$, $\hat{e}_\theta$, $\hat{k}$ unit vectors of cylindrical coordinates $\vec{r}$ position vector $r$, $\theta$, $\phi$ spherical coordinates $\hat{r}$, $\hat{e}_\theta$, $\hat{e}_\phi$ unit vectors of spherical coordinates $s$ position in the path; the frequency domain in the Laplace transform. s second (SI unit of time) $T$ period of a sine wave; temperature T tesla (SI unit of magnetic field); prefix tera (10 12 ) $t$ time $t_C$, $t_L$ time constants $U_\mathrm{e}$ electric potential energy $U_\mathrm{g}$ gravitational potential energy $u$ unit step function $V$ potential V volt (SI unit of electric potential) $\vec{v}$ velocity vector $W$ work W watt (SI unit of power) $X$ reactance $x$, $y$, $z$ Cartesian coordinates $Z$ impedance $\alpha$ temperature Coefficient $\Delta\,a$ increment of the variable $a$ $\Delta\,V$ voltage $\delta$ Dirac delta function $\varepsilon$ electromotive force (emf) $\varepsilon'$ back emf $\varPhi$ electric flux $\varPsi$ magnetic flux $\varphi$ initial phase $\lambda$ linear charge density; wave-length $\mu$ magnetic permeability μ prefix micro (10 -6 ) $\pi$ relationship between the length of a circle to its diameter $\rho$ charge density; resistivity $\sigma$ surface charge density $\vec{\omega}$ angular velocity $\varOmega$ angular frequency Ω ohm (SI unit of resistance) ° degree (angle unit) W degree Celsius (temperature unit)