q1 q2 r3 r 4 0 U q 1 q 4 0 r 1 L 2 2 i 1 r q1 q2 r2 Equations 1 F electric 4 0 q1 q2 r 9 109 r2 F 1 E field 4 0 q0 E p torque on dipole d neg to pos p q E d l f V Vf Vi i dq V r r Vpt chg 4 0 1 qsource r r2 E finite line E infinite line Vinf line E ring of charge Vring of chg 2 1 x2 L 4 x 2 0 x i 2 0 ln r0 V r0 0 Vf r r z r2 z2 3 2 1 2 0 2 0 Q 1 2 4 0 z2 r2 z E disk 2 z 4 0 1 E infinite parallel sheets Gauss s Law r2 z2 4 4 0 electric electric Sphere of charge E inside E outside E d A ke E d A Qenclosed Qenclosed 0 0 A A V r 4 0 a3 Q r Q 4 0 r2 Conductors charge moves to the surface always E inside 0 n E conductor surface 0 E cylindrical conductor Uelectrostatic U f Ui E grad V Ampere s Law B d l o Iencl Loop 0 I 2 x d l r r2 length B 0 I L 2 x L2 4x2 B inf line B 0 I 4 L B I B line 0 I r2 B ring of current 3 2 r2 z2 2 0 I 2 x F q v vel Binf line Magnetic dipole moment Solenoid B Linduct 0 n2 Vvolume I Aarea 0 n I Linduct 0 N I Llength 0 N 2 Aarea Llength B torus 0 N I 2 r Linduct 0 n2 Vvolume if rcoil rtorus Incr Temp conductors conduct worse b c electrons moving but semiconductors better b c more electrons free at incr temp Faraday E d l Moving wire in out of magnetic field d dt loop area d B dt d A V 2 Pext Wext B2 L2 vvel 2 R F v dt tend t0 voltage R RLC XL L XC Z 1 C R2 XL XC 2 1 resonance L C Vrms Imax 2 Irms Irms Z arctan XL XC R Pavg Vrms Irms cos cos Power factor Lenz s Law an induced current always opposes the change in magnetic flux Capacitors 0 A d C sphere C par plts 2 0 L C q ln b a 4 0 1 1 a b V ue engry dnsty C cylind 0 E 2 2 Q t chg RC C 1 e t R C Q t disch RC Q0 e t R C U C V 2 2 Inductors U L I2 2 ub enrgy dnsty Inverse adding in parallel B2 2 0 L B I Resistors and Inductors not capacitors 1 0 8 85 10 12 9 109 4 0 dq dt R Presistor I2 R V I R 0 4 10 7 0 I1 I2 F 2 x repulsive if antiparallel L 2 0 r on surface q F d l f i 0 f i E d l 1 2 2 E infinite disk 4 0 F pt chg in uniform fld q E
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