Basic Formulas for Chapter 4 Test 1 EE 140 Prof Mostafavi 0 8 854 10 12 0 4 10 7 e 1 60 10 19 F m C H m c 3 10 8 m s Electric field intensity F E lim q 0 q V m SI unit for E is V m F qE N Postulates of Electrostatics in Free Space Differential Form Integral From E v 0 E ds E 0 E d 0 s Q 0 C Electric field intensity of an isolated point charges at the origin E a R E R a R q 4 0 R 2 V m Electric field intensity of an isolated point charge at an arbitrary location P q R R EP 3 4 0 R R V m Force experienced by q2 due to electric field intensity E12 of q1 F12 q2 E12 a 12 q1q2 4 0 R122 N Electric field of a system of discrete point charges 1 E 4 0 n k 1 qk R Rk 3 R Rk V m Electrical field intensity of a volume distribution of charge 1 E 4 0 a V R v dv R2 V m Electrical field intensity of a surface distribution of charge 1 E 4 0 s ds R R2 a S V m Electrical field intensity of a line charge 1 E 4 0 a L R d R2 V m Electrical field intensity due to an infinite long straight line charge of a uniform density E a r 2 0 r V m Gauss s law Applying Gauss s law to an infinite planar charge distribution Q E ds S E a z E z a z s 2 0 0 E a z E z a z s 2 0 z 0 Electrostatic Potential Electrostatic field intensity from electric potential E V z 0 Electrostatic potential difference between P2 and P1 equals the work done in moving a unit charge from P1 to P2 P2 E d V2 V1 V P1 Electrostatic potential of a point charge referred to infinity V q 4 0 R V V 1 4 0 n k 1 q k R Rk V Finding electrostatic potential for electric dipole p a R qd cos V V 2 4 0 R 4 0 R 2 Electric potential due to continuous charge distributions volume surface line V 1 4 0 v R dv V V V 1 d V 4 0 L R Inside a Conductor Under Static Conditions 1 4 0 s R ds S V V Boundary Conditions at a Conductor Free Space Interface E t 0 v 0 E 0 En Equivalent polarization surface charge density ps P a n C m 2 Equivalent polarization volume charge density P pv D v C m 3 Definition of electric displacement D D 0 E P C m 2 Generalized Gauss s law D ds Q S C s 0 Definition of a linear dielectric medium and a homogeneous dielectric medium D 0 1 e E 0 r E E C m 2 Boundary conditions for electrostatic fields Tangential components Normal componenents a n 2 D1 D2 s E1t E 2t D1n D2 n s Electric field transition between two dilelectic media 2 1 2 E 2 E1 sin 1 cos 1 2 tan 2 2 tan 1 1 1 2 Definition of capacitance Q CV C Q V12 F Capacitance of a parallel plate capacitor C Q S V12 d Capacitance of a cylindrical capacitor C Q 2 L Vab b ln a Electric energy stored in a system of discrete point charges 1 N We Q k V k 2 k 1 J Electric energy stored in a continuous distribution of charge We 1 vVdv V 2 J Electric energy in terms of E and D E and We 1 D Edv V 2 J We 1 E 2 dv V 2 J Electric energy stored in a capacitor 1 We CV 2 2 J Poisson s equation in operator form 2V 2V 2V 2V v 2 2 v 2 x y z V m 2 Laplace equation in operator form 2V 0 Method of images Point charge and its image Qi Q Line charge and its image i di a2 d Capacitance per unit length of parallel wires C C 0 ln D 2a 0 ln D a D 2a 2 1 0 cosh D 2a 1 F m F m Basic Formulas for Chapter 4 Test 2 EE140 Prof Mostafavi Current Density and Ohm s Law Convection Current J Nqu A m2 I J s I J ds A S J v u Conduction current J N i qi ui i ue e E J e e E A m2 Point Form of Ohm s Law Definition of Conductivity subscripts e electrons h holes J E e e h h A m2 Resistance of a straight homogeneous material of uniform cross section R S Equation of Continuity and Kirchhoff s Current Law Equation of Continuity J v t A m3 For steady current J 0 Steady Electric Current is Solenoidal J ds S I 0 j 0 A j Kirchhoff s Current Law Volume Density of Charge Decays exponentially with Time in a conducting material with conductivity and permittivity v 0 e t C m 3 Joule s Law P E Jdv V Power Dissipation W P I 2 R W Governing Equations For Steady Current Density Governing Equations for Steady Current Density J 0 J ds S J 0 Differential Form 1 J d 0 C 0 Integral Form Boundary Condition of Current Density Normal Component Tangential Component J1t 1 J 2t 2 A m2 J 1n J 2 n Resistance Calculation Capacitance Resistance D d s E Q ds C s S V E d E d L L E d E V d R L L I J ds E ds Relation connecting C and R or G between two conductors RC C G S S