equation sheet

equation sheet - PHYSICS 198-142 Electromagnetism: F12 = k...

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PHYSICS 198-142 Electromagnetism : 12 2 2 1 12 ˆ r r q q k F = G , E q F G G = , r r q k r E e ˆ ) ( 2 = G , r r dq k r E e ˆ ) ( 2 = G , y k e ch line E e λ 2 ) arg ( = , 2 3 2 2 ) ( ) ( a x Qx k ring of axis E e + = , 0 2 ) ( ε σ = plane E , , , 12 2 1 r q q k U e = , . = Δ = Δ f i s d E q U V G G = = r dq k V r q k V e e , , 0 κε = , ) / ln( 2 ) ( , ) ( , / , ) ( 0 0 2 2 a b L cylinder C d A plate parallel C V Q C a x Q k ring V e κ πε = = = + = , = a b ab sphere C 0 4 ) ( , 2 2 1 CV U = , R I IV P 2 = = , IR V = , d nqv A I J = = , dt dQ I = , J E G G ρ = , A L R = , = = n i i eq C C 1 , = = n i i eq C C 1 1 1 , = = n i i eq R R 1 , = = n i i eq R R 1 1 1 , A d E d E G G . = Φ , = 0 . in q A d E G G , RC = τ , ) 1 ( ) ( 0 t e Q t Q = , t e Q t Q = 0 ) ( , 2 0 2 1 E u E = , B v q F G G G × = , B I F G A G G × = , × = b a B s d I F G G G B A NI G G × = , × = 2 0 ˆ 4 r r s d I B G G π μ , a I wire long B 2 ) ( 0 = ) sin (sin 4 ) ( 2 1 0 θ + = a I segment B , R I arc B 4 ) ( 0 = , 2 3 2 2 2 0 ) ( 2 ) ( R x IR loop of axis B + = , nI solenoid B 0 ) ( = , in I s d B = 0 . G G , = Φ A d B B G G . , Φ = = dt d s d E B G G . , v B A = , ) sin( t NBA ω = , dt dI L L = , I N L B Φ = , R L / = , ) 1 ( ) ( 0 t e I t I = , t e I t I = 0 ) ( , 2 2 1 LI U = , A A n solenoid L 2 0 ) ( = , 0 2 2 B u B = Optics : f v = , v c n = , 2 2 1 1 sin sin n n = , 2 2 1 1 n n = , f q p 1 1 1 = + , p q M = , m d = sin , m a = sin , d L m y m = , d L m y m ) 2 / 1 ( + = , m nt = 2 , ) 2 / 1 ( 2 + = m nt , Nm R avg = Δ = , D 22 . 1 min = , φ δ 2 / / = Physical constants
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