v = v i e i v 1 ] T v = = v 1 v n v n ] a r +q = a a r 3q =

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Beata Lewandowska
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1 v U = e i,..., e n ) v = n v i e i i= e i i v T v = = v v n v v v v n 3q q q q r q = r 3q = E = E q E 3q E q = k q rq 3 k 3q r 3q 3 r q = k q rq 3 = kq 4 3 ) 4 q d b d c d d X d ± = d

2 r = x y T d ± r ± = r x d r ± = r d ± = x ± d = y y E = E E = k q r 3 r k q r 3 r = kq r 3 x d y ) x d r 3 y r ± = b y = x = x ± d ) y E y = ) = kq ) x d E x = ) = kq x d d ) d 3/ 4 y ) ) c r 3 r 3 d/ r 3 ± = x ) ± d y ) 3 = ) 3 3 ± d ) x x y ) 5... x y r 3 3 xd r 5 d E r d) = kq r 3 3 xd r 5 d µ = qd T µ E x = ) = k ) d 3/ 4 y E r d) = k µ µr 3k r3 r 5 r 3q q q q A A b x y )

3 c A V = kq ) b q q 3q W = kq 3kq ) = kq 6 ) c r = x y T r x q = y r 3q = x y r x q = y ) V x, y) = kq x y ) 3 x ) y x ) y ) x Ex, y) = V x, y) = kq 3x) x x y ) ) 3 x) y ) 3 x) y ) ) 3 y ) 3y y x y ) ) 3 x) y ) 3 x) y ) ) 3 x = y = q d b d V = kq ) r r r ) = x r ± r± 3 x ± d ) r ) y r ± = r± 3 y

4 b r r d/ r ± r xd r 3 V r d) = kq xd r 3 = k µr r 3 r = x y T µ = µ x µ x T r = x y r d x V E = k µx r 3 µ y r 3 3 µxxµyy r 5 3 µxxµyy r 5 V x, y) = k µ xx µ y y x y ) 3/ V x = k µ x r 3 3k µ xx µ y y r 5 x x = k r3 y µ x µ y 3k µ xx µ y y r 5 x y = k µ µr 3k r3 r 5 r Q µ b c A α A A A 3q q µ 9 q A b c m = l = Q x = α F = k Q x F n F g = mg

5 F n sin α = k Q x F n cos α = mg F n sin α kq = tn α = F n cos α mgx = x l 4 x Q = mgx3 k l 4 x / Q e q q 3q q b r q = r q = µ = q 3 3 r 3q = r q = 3 6 r q = r 3q = q q d q b q b b 3 3

6 c ϱ σ < b < c c λ σ S r E ds E ds = E ds S E ds = E S ds = 4πr E = q ϵ E = 4πϵ q r b Q = 4 3 πb3 3 )ϱ Q = 4πc σ r r S E ds = E I = r b b r < c r > c r = c S E ds = 4πr E = 4πr3 3 )ϱ E II = ϱ r 3 3 ) 3ϵ 3ϵ r 4πr E = Q ϵ = 4πb3 3 )ϱ E III = ϱ b 3 3 ) 3ϵ 3ϵ r 4πr E = Q Q = 4 ϵ ϵ 3 πb3 3 )ϱ 4πc σ E IV = ϵ r 3 b3 3 )ϱ c σ r V r) = r E dr = c V II r) = c V III r) = Q Q b 4πϵ r dr c r V IV r) = Q Q r 4πϵ r dr c Q r 4πϵ r dr b E dr Q Q 4πϵ r dr = Q Q 4πϵ r Q 4πϵ r dr = Q 4πϵ r Q ) c ϱ b 3 3 ) 3ϵ r dr = Q 4πϵ r Q ) ϱ r c 3ϵ b 3 r ) b

7 V I r) = Q 4πϵ r Q ) ϱ c 3ϵ b 3 ) b c l Q = λl Q = πlσ r S S S r < S E ds = E ds S S E ds = E r > S ds = πrle = Q ϵ E I = λ πrϵ E II = λ πσ πrϵ R > r < r λ πσ V II = E dr = ln πϵ R V I = λ πrϵ ln R r ) σ ϵ ln V x, y) = y x A = y x y = A x E = x A E dr E dr = dx dx dr = = dy x dx x R r R ) ) dx = x dx E dr E E q m

8 v b v k d r = T v = v T F = qe = qe T m x x X x = v x = ẍ vt) = rt) = = qe qe m t v qe m t v t xy) = qe mv b qed y W = qed = m v k v ) v k = v qe m d Y E φ I ˆα = digα, α, α ) ) b c E U E cos φ E = E sin φ U

9 α µ = ˆαE = α α U E cos φ E sin φ U = b τ = µ E = e x e y e z α E cos φ α E sin φ E cos φ E sin φ α E cos φ α E sin φ U = E α α ) sin φ cos φ e z I I d φ dt = E α α ) sin φ cos φ sin φ cos φ = sinφ) φ = φ d φ dt E α α ) φ = I ω = E α α c I de p = µ de = α cos φ α sin φ)e de E p = α cos φ α sin φ)e α µ µ r µ µ = r µ α = r µ α = µ µ E p µ, µ ) = µ k µ rµ 3 3 µ ) r µ µ µ µ µ rµ 5 r µ µ = k µ rµ 3 3 µ ) r µ µ )µ r µ µ ) µ rµ 5 = 3k µ 8 3 µ µ

10 α E µ µ E p µ, α) E p µ, α) = αe µ µ E µ µ = k µ rµ 3 α 3 µ ) r µ α rµ 5 r µ α k µ α rµ 3 α E µ µ = E µ µ E µ µ = 4k 6 µ µ ) E p = 3k 8 3 µ µ k 6 αµ µ ) 3 µ ) r µ α rµ 5 r µ α = k α 3 µ µ ) d ϱ Q V b d V Q c d L V Q Q ϱ ϱ d S b ϵ c b d L b ϵ S d U ϵ A B b c R

11 U C b ϵ c b d c e d R I b A I b c < b < c b I d ϱ v X Y b b I

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v = v i e i v 1 ] T v =

v = v i e i v 1 ] T v = v U = e i,..., e n ) v = n v i e i i= e i i v T v = = v v n v n U v v v +q 3q +q +q b c d XY X +q Y 3q r +q = r 3q = r +q = r +q = r 3q = r +q = E = E +q + E 3q + E +q = k q r+q 3 + k 3q r 3q 3 b V = kq