ULTIMATE Cheat Sheet

# ULTIMATE Cheat Sheet - Find magnitude and direction Charge...

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Unformatted text preview: Find magnitude and direction Charge expressed in sum of protons and electrons q = e ! N p " N e ( ) Coulomb ʼ s Law F = k q 1 q 2 r 2 k = 8.99 ! 10 9 N ! m 2 C 2 k = 1 4 " # \$ = 8.85 ! 10 % 12 C 2 N ! m 2 Equilibrium Position (charge at origin and elsewhere is positive) F 1 ! 3 = F 2 ! 3 k q 1 q 3 x 3 " x 1 ( ) 2 = k q 3 q 2 x 2 " x 3 ( ) 2 x 3 = q 1 x 2 + q 2 x 1 q 1 + q 2 Charged balls hang from ceiling with insulated ropes ¡nd mass T sin ! " F e = 0; T cos ! " F g = F g = mg ; F e = k q 2 d 2 sin ! = d / 2 l F e = k q 2 d 2 = k q 2 4 l 2 sin 2 ! T sin ! T cos ! = F e F g m = kq 2 4 gl 2 sin 2 ! tan ! Force between electrons of electrostatic force and gravitational force F e F g = kq 2 e Gm 2 e Bead on a wire slanted, ¡nd mass of second bead F e = k q 1 q 2 d 2 ; F g = m 2 g sin ! k q 1 q 2 d 2 = m 2 g sin ! m 2 = k q 1 q 2 d 2 g sin ! F x = k q 1 q 4 d 2 + k q 2 q 4 2 d ( ) 2 cos 45 ° = kq 4 d 2 q 1 + q 2 2 cos 45 ° ! " # \$ % & F y = k q 2 q 4 2 d ( ) 2 sin 45 ° ' k q 3 q 4 d 2 = kq 4 d 2 q 2 2 sin 45 ° + q 3 ! " # \$ % & F = F 2 x + F 2 y ;tan ( = F y F x F = kq 4 d 2 q 1 + q 2 2 cos 45 ° ! " # \$ % & 2 + q 2 2 sin 45 ° + q 3 ! " # \$ % & 2 ( = tan ' 1 q 2 2 sin 45 ° + q 3 ! " # \$ % & q 1 + q 2 2 cos 45 ° ! " # \$ % & Four charged objects ¡nd force on fourth charge Chapter 21: Electrostatics Electric Field from a point charge E x = F 1, x + F 2, x + ... + F n , x q E y = F 1, y + F 2, y + ... + F n , y q Electric ¡eld do particles at center from 4 point charges ! E center , x = k q 2 r 2 ( ! ˆ x ) + k q 3 r 2 ( ˆ x ) = k r 2 q 3 ! q 2 ( ) ! E center , y = k q 1 r 2 ( ! ˆ y ) + k q 4 r 2 ( ˆ y ) = k r 2 q 4 ! q 1 ( ) E center = ! E 2 center , x + ! E 2 center , y " k r 2 q 3 ! q 2 ( ) 2 + q 4 ! q 1 ( ) 2 = 2 k a 2 q 3 ! q 2 ( ) 2 + q 4 ! q 1 ( ) 2 # = tan ! 1 q 4 ! q 1 q 3 ! q 2 \$ % & ' ( ) Electric ¡eld everywhere on x-axis (dipole) E = q 4 !" 1 x # 1 2 d \$ % & ' ( ) 2 # 1 x + 1 2 d \$ % & ' ( ) 2 * + , , , ,- . / / / / Vector electric dipole moment ! p = q ! d Electric ¡eld far away from electric dipole E = p 2 !" x 3 d ¡ (10 ¢ 10 m )cos52.5 ° ¡ 0.6 £ 10 ¢ 10 m p ¡ 2 ed ¡ 2 £ 10 ¢ 29 Cm Electric dipole moment of water Electric ¡eld from three point charges E 1 = K Q 1 b 2 ! x E 3 = K Q 3 a 2 ! y E 2 = KQ 2 cos ! a 2 + b 2 " # \$ % & ' ! x + KQ 2 sin ! a 2 + b 2 " # \$ % & ' ! y E = E 2 x + E 2 y ! = pE sin " Torque on electric dipole Electric ¢ux ¢ = EA cos £ ! = ! e " d ! A " ## Guass ʼ s Law ! = ! e " D ! A = " ## Q \$ cyclindrical symmetry E = ¡ 2 ¢£ r = 2 k ¡ r planar symmetry E = ! 2 " planar symmetry, conductor E = ! " Charge distributed uniformly throughout sphere, inside E inside = ¤ r 1 3 ¥ E inside = Qr 1 4 ¦¥ R 3 = kQr 1 R 3 E outside = kQ r 2 2 outside Electric ¡eld from a ring of charge E z ( z ) = KDQ r 2 !...
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ULTIMATE Cheat Sheet - Find magnitude and direction Charge...

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