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(CIP) ().:. 2004.11 ISBN 7-04 - 015565-6... - -.O4-44 CIP (2004)092157 010-64054588 4 800-810 - 0598 100011 http:www.hep.edu.cn 010-58581000 http:www.hep.com.cn 8501168 1 32 1 8.625 220 000 12.00,. :15565-00
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1 12 21 31 37 44 54 65 73 87 95 106 112 127 133 148 162 190 201 1. 201 2. 204 3. 206 4. 207
5. 211 6. 216 7. 219 8. 221 9. 223 10. 225 11. 230 12. 233 13. 239 14. 243 15. 246 16. 254 17. 255 18. 260 19. 263 20. 266
1-1 : (1 ),? (2 ),? (3 ),? ( 4) x x,? (5 ),? :,. r( t), r ( t) v ( t), v ( t) a( t)., r( t)v ( t) a( t) t,. ;,., (1 ) a0, v = 0.,. :,,. (2 ) v = v,,. :, 1
. (3 ). ;.,. (4 ) x ( ),,,., v < 0 a > 0, x, x. :,. (5 ) ( 2),.,,.,,,,,. 1-2 : (1 )??? (2 )???? : ( 1) r, s. 1-2, P 1 P 2 r = r 2 - r 1, P 1 P 2, P 1 P 2, t, ; t s, P 1 P 2 = r,.,., r, lim r = d r, d r = d s., t0 2
1-2,. (2 ) v = r, v = s. t t v t r, r, v = r t, ; v,, v v. v = 0, v0.,. v v. v t0 d r, v t0, r t0,.v v, v = v., v = v = v = s,.v = lim t v = lim t0 d r d t v = lim t0 t0 = d s d t, s, t t0 v t0 3
. 1-3 : (1 ) :,,? (2 ) :,,,? (3 ) :,,,? :,,,.,,. (1 ),,,. :,,.,,. (2 ),,,,.,,.,,,. (3 ),,.,,.,. :, a n = v2 R 4
. 1-4 x = x( t), y = y( t),, v = d r d t r = x 2 + y 2, a = d2 r d t 2 ;,, v = d x d t 2 + d y d t 2 a =?? d 2 x d t 2 2 + d2 y d t 2 :,.,. 2. 1-4 Ox y, r = x ( t) i + y( t) j, r = x 2 + y 2 t r. v = d r d t, v, 5
v = v = d r d t = d x d t 2 + d y d t r v r = d r d t = d d t x 2 + y 2, d r d r. v, d r,, r.,,,,, d r = d x 2 + y 2 = 0, d r 0., d x d t 2 d r d t, v = + d y d t 2., O xy v = v x ( t ) i + v y ( t ) j, a = d v d t = d2 r v.a d t 2 d2 d 2 a = d v d t = d v x d t 2 + d v y d t 2 = d 2 x d t 2 r. d t 2 2 2, + d2 y d t 2 a d v, v, r., r =, d r d t = 0, r = 0. a = 0, d t 2., r r. v a 6 2.
, v = v r ( t) e r + v ( t) e a = a r ( t) e r + a ( t) e. v r = d r d t, a r = d2 r d t 2., v a. 1-5 : (1 )?? (2 ),?? :,,.,,,. (1 ),. g,. g,., v d v, a ;, v, d v g.,. (2 ),,,,,.,,, a t. = d v, d t 1-6 : (1 ),, 7
. (2 ),,.,. :,. v v,., a = a n + a t = v2 e n + d v d t e t. a t, a n. (1 )., v,,. (2 )., v,., a n = v2. 1-7, r = r ( t), v = v ( t), (1 ) d r d t = 0, d r 0,? d t (2 ) d v d t = 0, d v 0,? d t : ( 1), d r d t = 0, r ; d r 0, d t r.. (2 ) d v d t 8 = 0 v ;
d v 0, v. d t. 1-8?? :, v,,,., v,,.,,.,,,, ;,,. 1-9 ABCDEFG,,. A B C D E F G 1-9 9
1-10,?,,? :.,.,,.,,.,,.,.,,. 1-11, v, v,? 1-11 : : v = v + v, v = v - v = v + ( - v ), v = v 2 + v 2, 10
= arctan v = v. 1-11. v v 1-12 v 0,? :, g. v y = 0, v = v x = v 0. an = v2 = v2 0 = g, = v2 0 g. 11
2-1 : (1 )? (2 ),? (3 ),? (4 ),? :, ;,,.,.., (1 ).,,..,. (2 ).,,,,. (3 ).,,,.,,,. (4 )... ( ),., 12
.,,. 2-2?. :,,.,. :,,,.,. 2-3,,, ( 1) : : ; (2 ) :,,.? :.,,.,.,.,,,.,,.,,,. 2-4, 13
,??? 2-4 :, 2-4., F T + mg = ma n e n, F T + mg = ma n, F T = ma n - mg.., F T - mg = ma n, F T = ma n + mg.. 2-5, 2-5,,?,? (1 ) ; (2 ). : ( 2).. (1 ), F 1 - mg = 0, F 1 = mg. (2 ), F 2 cos - mg = 0, F 2 sin = ma n = mr 2, 14
F 2 = ( mg) 2 + ( ma n ) 2 = mg 1 + 2 2 r g mg, F 2 > F 1. 2-5 2-6 2-6,,, F T cos - G = 0, F T, F T - Gcos = 0.,,? 2-6 :,., F. 15
, F. :, F = F T sin = ma n. F = F T sin = Gtan.. a, F T a, F T - Gcos 0. 2-7??. :.,,,.,,,..,. : m ( ) h,,, mgh.,.,,,,,.,. : h,,. E 0 = 0,, v, 1 2 m v2, m v, E = 1 2 m v2 - mgh = E 0 = 0. 16
2-8,?,? : m 1 v 1 m 2 v 2, m 1 > m 2. (1 ), 1 2 m 1 v 2 1 = 1 2 m 2 v 2 2, v 2 = m 1 m 2 v 1 > v 1, p 1 = m 1 v 1 p 2 = m 2 v 2, m 1 m 2 p 2 = m 2 v 1 = m 1 v 1 m2 m1. (2 ), m1 v1 = m2 v2, < p 1. v 2 = m 1 m 2 v 1 > v 1, E k1 = 1 2 m 1 v 2 1, E k2 = 1 2 m 2 v 2 2, E k2 = 1 2 m 2 m 1 m 2 v 1 2 = 1 2 m 1 v 2 1 m 1 m 2 > E k1.. 2-9,,,,? :,,. v,.. v, t, F., Ft = m v = m v, F = m v t., v, 17
t, F., F= - F,,. 2-10,,.,,??,?? :,,.,,, ( ).,. 2-10,,.,,,,,. 2-11,,? :.,,,., 0 = m v + m v, v = - m m v v = - m m v. 18
,, ; m m, v, v 0,.. 2-12.??? : :. A = 2 Fd r 1 = 2 1 Gcos 1 d s + 2 1 F r cos 2 d s + 2 1 F N cos 3 d s,, G d r 1 < 2,. F r,. F N. d r 2 =, 3 =, 2 2-13,? : A = E k,.:, (1 ) F = 0,,.. ;,. (2 ) F d r,.:, ;, 19
.,,,. 2-14,,,?? :, A, B. h, A v 0, l. A, h = 1 2 gt2, mgh + 1 2 m v2 0 = 1 2 mv2, t v A. t = 2 h g v = 2 gh + v 2 0 B, l = 1 2 at 2 = 1 2 gsin t 2, mgh = 1 2 m v 2, tvb. t= h = lsin. 2 l gsin = v= 2 gh < v. 2 h gsin 2 > t, A, B. 2-14 20
3-1,?. :,,,.,.,,.,,, ; ( ),,,,.,,,,,,.,,. 3-2,,? :,.,,., 21
,,.A, F A P 0 : E p P 0 A Fd r A P, E p A, E = P 0 A p = P 0 P Fd r = P A Fd r. Fd r + P 0 P Fd r = P A P, A E p A = P A Fd r = E p A - E p. Fd r + E p,, A E p,,.,,., F E p ( r ), F = - E p ( r ) e r r, F, E p ( r ), F = 0,., E p ( r),,, F = 0.,,,.,,,,,.. E p ( y) = mgy, y, y y, y A 22
E p A = E p A - E p = mgy - mgy= mg( y - y ) > 0, E p A > 0, y = y - y < 0, E p A < 0. y, y A,.,, y= 0,,,. E p ( x ) = 1 2 k x2, x, x = 0. F = 0 x,,. x,. ( ) x, () x A, E p A = E p A - E p = 1 2 k x2 A - 1 2 kx 2 = 1 2 k( x2 A - x 2 ). x < x A, E p A > 0,,., x A,,. m m 0, r, E p ( r) = - G m m 0 r. r, E p, m 0.,. m 0 ( m ) (m ) m 0 r, m r A E p A,, E p A = E p A - E p = - G m 0 m + r A 23
G m 0 m r.r A,. < r, E p A < 0,,., m, r= R,, h m hr, E p A = - G m m R + h + G m m, R E p A m G m R 2 h = mgh.,. 3-3 : (1 )??? (2 )??? (3 ).? (4 ),? :...,, g,.., m h E p = mgh. h, (,, ), r, E p = - G m m = - mg r R 2 R + h, g = G m. R 2 24
, ( )., ( ), ( ). 3-4,,? :. p = m v, v ; Ek = 1 2 m v2,.,,,,. h,. mgh = 1 2 m v2,,. 3-4 3-5? :.,.., 25
,.,.,. 3-6,,.,? :.,.,,.,,,,,.,,,. 3-7,?? : :.,,,,,. :,.,,,,.,. 3-8 :,,? :... 26
. :,,.. ( ).,,,,.,. 3-9 m m, m m,,? (1 ) m m, m; (2 ) m m, m; (3 ) ; (4 ). 3-9 : :., (1 ) m m,, ; m m m,,, ; m, m,,. (2 ), m m, 27
.m,,,. (3 ) ( 2),. (4 ) ( 1 ) ( 2 ),. 3-10??. : : ; :..,.,, ;,. :,, ; O,,. 3-10 28
3-11, F = d ( mv )?? d t : ( ). :, ; ;.,,,., F = d ( mv ), d t m v,., p = m v = m i v i, d d t m i v i = F.,,.,, ( ). F = d p Fd t = d p d t, ( m + d m), m t v, d m u. d d t ( m v ) = F + d m d t u. :.., d ( m v ) = F, d d t d t m i v i = F,., m v = m i v i,, ; m v, 29
.,. 3-12? :,.,, ;,,,. 30
4-1? :,, ( ).,,,,.,,,,. 4-2,?. :,.,, 4-2. 4-3,.? 4-2 :,,, L = J=, J 31
,.,,.,.,. ( ),,,,.,,. 4-4,,? :,, F i = ma c = 0,.., M = M i = r i F i. M = J,.,,,,,,,. 4-5, ( 1)? (2 )? : M = r i F i sin i = J= J d d t,.,,,, (1 ), F i., 32
,. (2 ), M.,. 4-6,?? :,,.,, M i.,.z, M z = M iz, M iz = F i r i sin, F i i, r i ( z )F i, r i F i., z F i, F i z ( ) d i = r i sin. 4-7 :,,. :, i F i = ma c.,,.? 4-8, 33
:. :..,,. 4-9,.,.: (1 ),?? (2 ), (3 ),? :,. J = r2 d m,,. M = JL = J, : (1 ) M,, ; (2 ),, ; (3 ),,,. 4-10,,.. :,,,. A = E k, 34
,. 4-11,,?? :.,.,,.,,,..,,,,.,. 4-12,,,,?,? (.) m1 :. m2, R., ( ). M = d L d t = m 2 gr - m 1 gr. ( 1) v1 v2, ( )., L = m 1 v 1 R - m 2 v 2 R. ( 2), m1 = m2.(1 ), M = 0., L = L 0 = L 1 = =. 35
(2 ), v 1 = v 2.,., m 1 m 2.( 1), m 1 < m 2, d L d t, M 0. > 0,, m 1 ; m 1 > m 2, d L d t < 0, m 2.. :, 36
5-1? :,,., ( ),,,,.,. 5-2,,, :,.? :,.,,.,. 5-3 :,. 2 g 16 g, 37
25 J,,? :,,. 2 g 16 g, 25 J. m = E c 2 = 25 ( 310 8 ) 2 kg2. 810-1 6 kg0. :,,,.,.,..,. 5-4? (1 ),. (2 ),,,. : ( 1),., x = 0, t = 0, : x= 0, t= 0.. (2 ) K, t = 0, x0, K, 38 x = x - vt 1 - v c 2 0, t= t - 1 - v c 2 x v c 2 0,
K.,. 5-5 A B, A,? B,? :, A, A, ; B,., B, B, ; A,. 5-6?? : -,.,,..,,. : ( 1) ; (2 ) ; ( 3 ),. ;, ; v c,,. 5-7?? 39
5-7 : 5-7, K, K K v x.kx x = x B - x A,, x B x A,x. K v x,, K x A x B., x A x B,,, x = x B - x A K., x= x - vt 1 - v c 2. K x A x B, t = 0. x= x = x1-1 - x v c v c 2 2, < x., K x x,. 40
KK, v c,, vc,, ;, K K, ;,,,. 5-8, p = m v F = d p d t,?, F = ma?? :, K p = m v,,, K v, m = 1 - m 0 v c 2,, K p = m v =,, p = m 0 v., K,, F = d p d t, F = d p d t = d d t m 0 1 - v 1 - v c m 0 v v c 2.. vc, : 2. 41
F = d p d t = m 0 a.,,.,,,,., F = ma. 5-9?? : E = mc 2,. E, m, E = mc 2., m, c 2 m,,e.,,, m,,..,,.. 5-10??? : E 2 = m 2 c 4 = c 2 p 2 + m 2 0 c 4,, E, E = mc 2.. m 0 c 2, m 0. m 0 c 2 m 0. 42
,., E k = E - E 0 = mc 2 - m 0 c 2. 43
6-1,. :., ;, ;,,.,,, ;,,,,,,,.. 6-2??? :,,,,.., ( pv T ).,,,.,,,,. 44, ( )
,,. (, ).. 6-3,, ;,.,? : p = 2 3 n w,, T, w, p V, n,,., V, n, p T, w,,.. 6-4, : n,., T, V, : p i = m i Mi R T V = n i k T,, m i M i i ; p i i ; n i. i,. 45
p = p i n i = 1 n = n i kt = nk T, i = 1 n n = n i. i = 1. 6-5,.,?? :, p = nk T,, p = 0, n n = - T T, T n.,t > 0,, n < 0..,,.? 6-6 :., H 2 He, N 2 O 2.,,.,, H 2 46.,
,.,. v 2 = 3 k T m,, H2, N2 O2.,..,,,,.,,..? 6-7 : (1 ) vv + v (2 )? (3 ) v,? : ( 1), vv +v N N = 4 m 2k T 3 2 exp - m v 2 2 kt v2 v = f( v)v, vv + v. (2 ) v p,.,.,. (3 ),,. 47
,.,.,,,,,., v. 6-8??? : v p,., v p,, v p. v,,, v = vd N 0 v = d N 0 v 2 n i v i i, n i i = v f ( v ) d v. 0 v 2 = v 2 f ( v ) d v. 0 v p, v v 2,,, 48
. :, ;, ;,. 6-9,.,? :,.,.,,,.,,, v p v v 2,, 0.,. 6-10,,? :,.,. ( ),,,, 49
., (, ).,,. : 6-11? (1 ) f ( v) d v ; ( 2) Nf ( v) d v ; (3 ) v 2 f ( v) d v ; v 1 (4) v 2 Nf( v) d v ; v 1 (5) v 2 v f( v)d v; v 1 (6) v 2 Nvf( v) d v. v 1 : f( v) v., v. (1 ) f ( v) d v = d N vv + d v N ;, v v + d v. (2 ) N f( v) d v = d N vv + d v. N 2 d N (3 ) v 2 N 1 f ( v ) d v = v 1. N (4 ) v 2 Nf ( v) d v v 1 = N 2 = N N v 1 v 2 N 1 d N = N v 1 v 2. ( 5) v 2 v f ( v) d v = v 1 N v 2 v f ( v) d v v 1 N v 1 v 2 50
.. (6 ) v 2 Nv f ( v) d v v 1 v 2 v 1 6-12? :,,.,.,,.,,.,,. 6-13,.,,,? :,,, p = nk T, = v Z = 1 2 nd 2 = p,,. T k T 2d 2,. p 6-14?,? :,., 51
: v r = 2 v,,.,,. 6-15,?? :,,., :,, ;, ;,.,,., A, A,.,., v,, (). 6-16, :, S A B S S, S 2.?. :,,,, 52
.,, v. ( Z )., S A B,,,.,.. 6-16, S,, y S,, S,., 2, A B. 6-16 53
. 7-1?? (1 ),. (2 ),. :,.,., : (a), ( ptv ),, T ; ( b), ; (c), ; ( d),..,.., : (a),,,, ; ( b),,,, 54
; (c),,., ( 1 ).,.,..( 2 ).,,. 7-2 : (1 ) ; (2 ). : ( 1),,,..,,,, Q = 0. Q = E + A, V < 0, A < 0, ;E > 0,. (2 ),,. V > 0, A > 0, ; T = 0, E = 0;, Q > 0,. 7-3?,?,??? : C = d Q : d T, 1 K. d Q 55
,,., 1 K, C. 1 mol. 7-3 :, d Q = 0, C m = 0 ;, d T = 0, C m = ;, C p, m > 0;, C V, m > 0; 7-3, 1 < n <,,,. 7-4, : (1 ) ; (2 ) ( ) ; (3 ). :,,, E 1 = E 2 = E 3 > 0;,, p - V, A 1 > A 2 > A 3, ; ( 2), Q 2 = 0.,, 56
7-4 (1 )( 3),. (2 ) ( ), Q 2 = 0. Q = E + A, E 2 = - A 2, A 2 < 0., E1 =E2 = E3 = - A2., Q 1 = E 1 + A 1 = - A 2 + A 1 < 0,., Q 3 = E 3 + A 3 = - A 2 + A 3 > 0,. : (1 ) ( ),,,.. (2 ) ( ),.. (3) ( ),,.. 7-5,?,? 57
: Q =E + A., T = 0, E = 0, : Q = A,.,, Q = 0, :E = - A.,,,. 7-6?? :,,,.,.,.,.,, ;,.. 7-7, p - V,,, 7-7,??? :,E = 0.p - V, A,,,. 58
: ;.,, Q. =. A Q, 7-7 = ( T 2 A Q = 1 - T 2 T 1 : - T 1 ),. 7-8 p - V,. 7-8., ( S abc d > S abcd ),,.? :. = A Q,,,, Q,. 59
7-8 = 1 - T2 T 1, A Q. 7-9,,,.,,?? :, Q 2, A, w = Q 2 A = Q 2 Q 1 - Q 2. 1,., w = T 2 T 1 - T 2.,,, Q 2, ; T 2., A,, 7-10,? :.: 1 2, 7-10 ( a) ( b). 60 (1 ) 7-10 ( a), 13241.
7-10 ( ),,. (2 ) 7-10 ( b ),, ( ),,.? 7-11, :.: AB 1, C 3 2, 1231, 7-11 ( a) ( b). (1 ) 7-11 ( a),, 2 3,,. (2 ) 7-11 ( b ),, 3 2,,. 61
7-11 7-12? :,, S 2 - S 1 = 1. : ; 2 d Q T., (1 ),, (2 ),, ; (3 ), ; (4 ),. 7-13,, : ( 1) ; ( 2) ; ( 3 ) 62
.??,? :,,,., ( 1), ( 2), ( 3),.,., (1 ) ; ( 2) ; ( 3). 7-14,,,,,? :.,,,,.,. V 1 2 7-15, p 1, V 1,,,.?? : p - V,,,,. 63
p - V,,.,. 7-15 7-16? (1 ),. (2 ),. : ( 1),,..,,,, 1.,.. (2 ),,,,.. 64
8-1,? :,,,,. 8-2,. (1 )... (2 ), E (3 ), r, E :, E, :, ;,,,., (1 ).,, q > 0,. (2 ).,, 65
, E. (3 ). E :, r, E,, E. 8-3 E = 1 q, 4 0 r0, E,,? : q r0,, q.,,. r 2 8-4, q 0, q 0 F. Fq 0?,? : 8-2., ( ).,.,. q0, q0,,,., q 0, Fq 0 ;, Fq 0.q 0,, Fq 0, F. 66
8-5 q, q? :.. q,..q,..,, q. 8-6,,. :, ( ),., ( ). 8-7 E,?,, E? : E, Ed S = q 0 = 0; q S = 0.,.,,, E. 8-8 Ed S = q 0, 67
E q? :. E d S, d S, d S,. : E S, q,. 8-9 (1 ) q, l. E? (2 ), E? 8-9 : ( 1) q, 3 2 l ( ),, E ( ) q., 0, ( 68
)., E q. 6 0 (2 ) q, 8,, q, 8-9. (1 ), E q, 6 0,, E q. 24 0 8-10,,? :. Ed S = q E, 0 : S E, d S, d S E d S ; d S E d S, E., S E Ed S = S Ed S = E d S = ES, E. S 8-10, 8-10,, E E.,,,., 69
, E, E.,,. 8-11 Ed l = 0,? :,. :, L,.Ed l = 0, ()., Ed S = q, 0,.,. 8-12 AB. (1 ) A B, ; (2 ) A B, ; (3 ) A B, ; (4 ) A B, ; (5 ) A B ; (6 ) A B. : AB, A B, V A - V B = A AB q 0 = B Ed l. A (1 ), V A < V B ; (2 ), V A > V B ; 70
(3 ), V A > V B ; (4 ), V A < V B ; (5 ), q 0 > 0, V A > V B ; (6 ), q 0 < 0, V A < V B. 8-13,, 10 5 V.?,,?? :,, 10 5 V,.,.,,.?? 8-14 ( 1 ), (2 ), : : E = - d V d n e n. (1 ),.,,. (2 ),,. 8-15. (1 ),? (2 ),? 71
(3 ),? (4 ),?? : E = - d V d n en. (1),, V = C, E = 0. :. (2 ) P V P = 0, P d V d n P, E P. :,. (3 ) P, P,. :,. (4 ),,.,. 72
9-1,??,,,? :,,..,..,.,.,.,.,,. 9-2 Q,?,????? :, Q,,, = 0 Q 4R 2 ( R )., Q > 0, 73
; Q < 0, (8-4).,, E, E,,,. 0,.,. q > 0,,. 9-2, R, Q r ( r > R ) q > 0, V R = Q 4 0 R + q 4 0 r > Q 4 0 R. 9-2 9-3 (1 ) ; (2 ), ; (3 ) ; (4 ). : ( 1),,,,. 74 (2 ) ( 1),.
Q > 0,,,. (3 ) (1 ) q < 0, Q > 0, q < Q,. (4 ) (1 ) q > 0, Q < 0, q < Q,. 9-4, A,, q 1 q 2, A., q( rr ), q 1 q 2? 9-4 :,,,, : q1 - q1 ; q2 - q2 ; A ( q1 + q2 ), + q2 = q1 4R 2,.,,., q1 q2,,.q 1 q 2 ( q 1 + q 2 ). 75
q( rr ),, A, ( q 1 + q 2 ),,,., q q 1 q 2, q 1 q 2. A q, : rr,, F = 1 ( q 1 + q 2 ) q. 4 0 r 2 9-5 q r P E = q r, 4 0 r 3, q P?, P? ( P.) : q. q,.., P., q, P q P. q,,, P q P. P, P r, P. q, P, 9-5., q,, P. 76
9-5. 9-6, (1 ),??? (2 ),? (3 ),? :,., (1 ),,... (2 ),,,,.,,,. (3 ),. 77
9-7 (1 ),? (2 ),? (3 ),? :, C. C,., (1 ).. (2 ). (3 ). 9-8,,,??,? :,,.,,, V R = q 4 0 R V r = q 4 0 r ( Rr)., C R = q V R = 4 0 R C r = q V r = 4 0 r ( Rr).,,,,., q R 4 0 R = q r 4 0 r, q R + q r = 2 q, 78
q R = 2 R R + r q, q r = 2 r R + r q. 9-9, ( ), d. :??? : S d : Sd,.,,.. q, d,, E = = q q ;, U = Ed = 0 0 S 0 S d ;, C = q U = S 0 d. 9-10 ( ),,? :. U d, E, q, C. 9-11,,?. :,,.,, ;,,,., 79
,.,,,., C 1 C.C 1 = C 2., C 2., C 2 C.C 2 = 2 C., W 1 = 1 2 C 1 U 2 = 1 4 CU2., W 2 = 1 2 C 2 U 2 = CU 2 = 4 W 1., C 2. 9-12 q, S 1 S 2, E D.,,? : q E 0,,,,. E, : E = E 0 + E., D E, D = E = ( E 0 + E ). S 1,.S 1 q, 80
9-12, S 1 E D.S 1, S 1 E 0 E S 1, S 1. S2,. S2 q,, S 2 E E = q, D 0 D = q.s 2,. q E 0 E,,. 9-13 ( 1), r,?? (2 ),,? : ( 1),.E = E 0 = U d, E 0 81
, E E 0 = 1.,,,, ( )., r, Q = r ( Q0 Q 0 ),,. r C0 C = Q U,, C = Q U = r U =., r. (2 ) Q0,,., E = E 0, E 0, E = 1. r E 0 r C = Q U, C = Q 0 Ed = r E 0 d = r C 0., Q 0, r. Q 0 Q 0 9-14 + q, E D.?? : + q, + q E 0 E,.. D = E D = 82
0 E,., P, D, E.:, : D = q 4r 3 r, r.e r, : E = D = q r; : E = D = 4 0 r r 3 0 q r. 4 0 r 3, : E = D = 0. q r, r 4 0 r 3 E D, 9-14., D ; E ( ), (). 9-14,,. 9-15 ( 1), 83
, Q 4 0 r R?? (2 ),,? ( Q, R, r.) :,,. Q. (1 ), V R = R E 1 d l = R Q d r = 4 0 r 2 Q 4 0 R Q 4 0 r R. (2 ), V R = R E 2 d l = R Q Q d r = 4 0 r r 2 4 0 r R. 9-16 E, 9-16 84 (1 ), ; (2 ). ED E D
? :,,. E, D = 0 E + P.. (1 ), E : E 0, E 1, E 2., E 0 E 1,, 0, E 0 2 E 1, 0., E= E 0 + E 1 = E., P = 0, D= 0 E= 0 E. (2 ), E., E 0 E 2 E 1,, E 0 = 0 E 1 = E 2 =. 0 0 E = E0 + E1 + E2 = E0, D= 0 E= 0 E0. 9-17 W = 1 2 q i V i 1 2 qv?, W = : W = 1 2 q i V i V i 85
q i, q i, q i V i,, 1 2. W = qv, V q q, qv q. E1 9-18 q 1 q 2 E = + E2, W =2 0 E 2 d V = V 1 1 0 = E 2 1 1 d V + V 2 + 0 E 1 E 2 d V. V V V 1 2 0 EEd V 2 0 E 2 2 d V (1 ) ; (2 ) q 1 q 2? (3 ) q 1 q 2,? : ( 1) q 1 q 2., q 1 q 2, q 1 q 2. (2 ) q 1 q 2. (3 ) q 1 q 2,,,. 86
10-1, 0,? :.,, = 0, 0. = E d S = 0 = 0, (E) = E = 0, E =, = = 0., 0 0, 0, = 0. 0 0 10-2,?? :. S,, d S = 0,,,,. 10-3 ( 10-3 (a) )AB, AB??. : A B U,, = E,.,, AB 87
, E = - U n e n, (10-3 ( b) ).,, AB. (a) ( b) 10-3 10-4 ( ), U,???,? 10-4 :,.,.,., R = l S,. 88
10-5,??? :,,.,,,,,,. 10-6? : :. :, ;,,.,,,.,.,.,.,. 10-7?? :, : B, A, E= A E k d l. B, ( ). 89
, A ( ) B,.U AB = V A - V B = B Ed l.. A,. ( ),,, ;,,. r i E R,. U AB = V A - V B = E - Ir i. 10-8 - P = I 2 R P = U2 R, R, R,? : P = I 2 R ; P = U2 R R R I, R U, R.,. U = IR,. 10-9,?? :.,, U, R, P.. 90
10-10 l S 2 l 1 2 S, : (1 )? (2 )? : ( 1),. (2 ),, R = l S. R 2 R 1 = l 2 S 1 l 1 S 2 = 4. 4. 10-11 U, r, l.. (1 ) U ; (2 ) r, l ; (3 ) l, r. : n v = en = I en S, S = r2. ( 1) S l, R. U, U = IR, I, v. (2 ) SU, l, R = l S, R, U = IR I 1 2, v 1 2. (3 ) lu, r, S 4, R 91
= l S, R 1, U = IR I 4 4, v. 10-12, O : V O = V A + V B + V C + V D 4. 10-12 :, V B = V D., BO OD.,, V O. 10-13,, ( ). :,. 10-13. 10-13 92
10-14? :,.,, = 3 2 kt, 0.1 ev, 1 ev.,,. 10-15 A B,,? : A B,., PN.,,,.,,.,,. 10-16 A B C,? :., A B C., 10-16 93
,,,,,. 94
11-1 B? : B, E.P B P,. q P F q, v P. P, BP vp, BP.,, B. 11-2, v x,, B.. F = 0; (1 ) ; (2 ) F z, ; (3 ) F - z, : F = qv B, (1 ) B x, B = Bi B = B( - i), 95
(2 ) B y, B = Bj, F = F max k, ; (3 ) B = B x i + B y ( - j), B x = B y = B 2, F = q v B = - 1 2 qbk = - 1 2 F max. 11-3 ( 1),? (2 ),? : ( 1) q v P, F = qv B q v v B. v,, F, P. (2 ) ( ),, E, qe,, E. 11-4,? :,..,,. F = qv B, v B, F = 0. 11-5? :,. 96
11-6 C S 1 S 2. : 11-6, C S 1 ( ) S2 S. : S S = S 1 + S 2. Bd S = 0, S Bd S = S 2 = S 2 1 Bd S + S 2 Bd S = 0, Bd S = -Bd S. S 1 S 1 S 1 S, S= S 1 + S 1. Bd S S = S 1 = S 1 1 Bd S + S 1 Bd S = 0, Bd S = - 1 = 2.. Bd S. S 1 11-6 11-7 I,? B? 97
: -, : B,, B, B. 11-8 R.: (1 )? (2 )? (3 )? : B = 0 q v r. r 4 r 3 ( ). 11-8 (1 ) v, v ; (2 ) v, ; (3 ),. 11-9 0 ni, 0 ni, 2? 1 2? :,. B = 0 ni, B 0 ni..,,.. 98 B 0 ni, 2
1 2. 11-10? : 8-10. Bd l = 0 I B, L. L, B, d l, d l B d l ; d l B d l, Bd l., :Bd l L =Bd l = L Bd l = BL = 0 I, B. L,.,., Bd l = 0 I, L B,, L.,., B, -. 11-11? :, 99
B 1 B 2,, B = B 1 + B 2. 11-12 11-12 I1 I2 8 A, L 1 L 2 L 3 Bd l.: (1 ) B? (2 ) L 2 B?? : : L 1 L 2 L 3 :Bd l = 0 I 1 ; L 1 :Bd l = 0 ( I 2 - I 1 ) = 0; L 2 :Bd l = 0 I 2. L 3 11-12 (1 ) B I1 I2 B 1 B 2, B = B 1 + B 2.., B. (2 ) L 2 : (1 ), B, Bd l, L2, Bd l. 11-13 q,,. 100 (1 ),
. (2 ), q - q,,. (3 ) q - q,,,. (4 ) v BF,,. (5 ) m,. : q B F = qv B, F v B,, F = qvbsin, v B 180. (1 ). q B, ( = / 2 ), F. (2 ). (3 ). (4 ).q, v BF,. (5 ). ( 0, ).,, ( ). 11-14, (1 )? ( 2)? (3 ),? :, F = qe + qv B., E, v B.,. 101
,.,,.,.,,. 11-15 11-15 ( a),, 2 v v,..,? : v B, F = qv B, 2 v,, v,.,, ( 2 ),,. 11-15 ( b). (a) ( b) 11-15 102
11-16 11-16, O xy,, v z,. 11-16 : 11-7.B z, v B.F = qv B, F = 0.. 11-8, B Id l, d F = Id lb,,, F = 0. 11-17? : F =Id lb = L Id l B = I LB, L d l = L, L L. 103
11-17, F = 0, L B, 11-17. 11-18,,,.????,? : M = pm B, pm = ISen.., pm M, p m B. p m B = 2,.. :,, p m B = 0 =. 104 = 0,
, p m B = 0. =,, p m B =. 105
12-1,,,,?,. :,.,. A B, A B,. A B,, ; B A, A. B. 12-2? :,., ;,.,. 12-3 B H. : : B, H. : B H :. B = B i, H = H i ; 106
H : H = B - M 0 H,. : Bd l = 0 L I i. I i ( ),. Hd l = L I i. I i,. B H : H = B - M. 0 : B 0 = 0 H ; : B = H = 0 r H, r ;, B = H,.. 12-4,. (1 ), H (2 ) H,. (3 ), B H. (4 ) L B. (5 ) L H. : ( 1).H, H,., H, 107
H. (2 ). H, H, H,. (3 ), M B., H = B - M 0 B H., 12-5. (4 ).11-6. (5 ).12-5. 12-5, M,. H B. 12-5 : B H : H = B - M. 0 M,. s ( ) M, M.,, s,. 108 B 1 = 0 s ( cos 2 - cos 2 1 ) 0 s = 0 M,
H 1 = B 1 - M0; 0 B 2 = B 3 0, H 2 = H 3 = B 2 - M0, M = 0 ; 0 B 4 = B 5 = B 6 = B 7 0 M, ; 2 H 4 = H 7 = B 4 - M M 0 2-0 = M 2, M = 0; H 5 = H 6 = B 5 - M M 0 2 - M = - M 2,.,, B H,., B H. 12-6,? :,, Bd S = 0. S,,. 12-7? :,, ;,,,. 12-8, 109
. :,, ;. 1, 2, B 1t = B 2 t., 0 0 r 1, r 1, B 1 t 0.. 12-9,,,? :,.,.,. 12-10. : 1.B - H, 1., p m., p m,,,, H, B., B - H,., B - H,, ;, ;, ;,, 110
,.. 111
13-1 13-1,,??,? (1 ), (a) ( b) ; (2 ), (c) ( d) (e) ; (3 ), ( f), ; (4 ), ( g) ; (5 ) 1 2, 1,,2, ( h ). 13-1 112
:,,.., (1 ) ( a) ( b) d d t = 0, E i = 0; d < 0 E i 0,. d t (2 ), ( c) ( d) ( e) (3 ) ( f) (4 ) ( g) d < 0, E i 0, ; d t d < 0, E d t i 0, ; d = 0, Ei = 0. d t d < 0, E d t i 0, ; d < 0, Ei 0,. d t (5 ) ( h), I 1, ;, I 1, d 21 d t d 2 1 d t < 0, E 21 0, > 0, E 21 0,. 13-2,,.? (1 )? (2 )? (3 ), :,,. 113
(1 ) I = d q d t I = E i R = 1 d R d t q = 1 R. R.,,. (2 ). d A = 1 R (E i ) 2 d t = 1 R 2 d d t = d d t d t d q, q.,,. (3 ),,,. 13-3,,,. :,,,.,.,.,,,. 13-4 13-4 R,? 114 : R,,
,. 13-4 13-5,.? :,, ( ), E = - d. d t,.,? E B,, t,,,.,,,.,,.,, 13-5 115
13-5., r,,. 13-6,,,,?,,. 13-6 :,, 116
,.,.,,.,.,. 13-7, 13-7.,,. 13-7 :,,,,,.,,. 13-8 B, 13-8. B, P B,. :, B,..,. P 117
13-8 B,, P B + B.B, B, P B.. B, P, B. 13-9 13-9, R,. L 1 L 2 B t? E? Ed l L1 Ed l?,? L2 L 1? L 2 ABC D? :,,. L 1, B0, B t 0; L 2, B = 0, B t = 0. 118 L 1 E 1 E 1 = - r 1 2 d B d t, r 1
13-9 L 1, d B d t > 0, E 1, r 1 ; L 2, E 2, E 2 = - R 2 d B 2 r d t, r L 2, E 2, r. L 1 : L 1 d B E 1 d l = - S 1 d t d S = - d B d t r2 1 0. L 1.L 1, E 1,,.,,. L 2 :, E 2 d l = L2 0.L 2,,,. L 2.DC AB, E 2 d l,, E 2 d l.da BC L 2 E 2 d l = A D E 2 d l - B C E 2 d l = 0, 119
E D A = E CB = R2 2 d B d t. DA BC., d B d t > 0, ABC D V A = V B > V D = V C, U AD = U BC = R2 2 d B d t. 13-10 13-10 ( a),, E = vb, E = 0??? : E = vb E = 0,.,.. ( 13-10 ( b ) ),, F e F m,, E = vb., F m F,., E = vb.,,,.,,,, E = 0., 120
,,. (a) ( b) 13-10 13-11,,. : E L = d = L d I d t d t, L = d. d I,.,.,.,,,, ( ).. 13-12 A B,,,,. A, B.: (1 )? (2 )? :, 121
. (1 ) L = 0 n 2 V, V = Sl = D2 4 l.a B,. A, B, n A > n B,, L A > L B. (2 ) = L R, L = 0 n 2 V, R = l S,, l, S. D, d, = L R = 0Dd 16, d., B. 13-13 (L, R ) E,,,? :,, I = 0. d I.,, d t t = 0. 13-14??. : L R, E I = E R 1 - e - R L t = I 0 1 - e - R L t. 122
t = 0, E L t = 0 = - L d I d t t = 0 = - Ee - R L t t = 0 = - E.,, I t = 0 = 0. L R,, d I,, d t t = 0,., L R.,.,. 13-15,?? :,.,.,.,,,.,,. 13-16,,?. : M,,. 123
,, Wm = 1 2 L1 I2 + 1 2 L2 I2 1 2 M I2. M = k L 1 L 2, 0k1., ( ),.k = 1; k = 0.,,. 13-17, C 1 C 2. S, C 1 C 2 U 1 U 2?, I 1 I 2? : S, C 1 C 2, U 1 0 U 20.,. t = 0,. I 1 = E, I R 2 = E. 1 R 2 13-17, t, I 1 = I 2 = 0, : U 1 = U 2 = E. 13-18, E = 10 V, R 0 = 10, R = 40, L = 20 H., I 1 I 2 I 3. 124 (1 ) S ; (2 ) S ;
(3 ), S. : ( 1) S,, I 3 t = 0 = I 3 0 1 - e - R L t t = 0 = 0. I 10 = I 2 0 = E R 0 + R = 10 10 + 40 A = 0.2 A. (2 ) S,. d I 3 d t.l,. I 2 = 0, I 1 = I 3 = E R 0 = 10 10 A = 1 A. = 0, t = 13-18 (3 ) I 1 = I 3 = E R 0 = 1 A S, L R. I 1 = 0, I 2 = - I 3 t = 0 = - E R 0 e - R L t t = 0 = - E R 0 L., I 1 = I 2 = I 3 = 0. = - 1 A,- I 2, 13-19,, 125
? : w m, B = N I 2r = B2. 2.,. 13-20 W m = 1 2 L I2 W m = 1 2? V. B 2 V 0 : W m = 1 2 LI2 L, I, I. W m = 1 2 B 2 V B 0 V, B. B, W m 1 = V B 2 d V. 2 0,.,.,,. B,.,. 126
14-1???? :,,,,. : I d = d D d t I = I c + I d., ( ).. : (1 ), ( ),. (2 ),.,,. (3 ) -.,,, -.. 127
,.,,,., : I d = d D d t E d = 0 t + P t. 14-2 D? : d D.D, d D, ; D, d D,. 14-3,? :, S, d,. U = U 0 cos t = E 0 dcos t. D = 0 E = 0 E 0 cos t, S D I d = d D d t U 0 S = DS = 0 cos t, d = - 0 U 0 S sin t = 0 U 0 S cos t +. d d 2, 2. 128
14-4,,,? :, R,,,. : Id = D t R2 = Ic. D S t, Hd l = L + d S. r ( r < R ) L 1 L 2 : L 1 ; L 2, 14-4., L 1 L 2,, r H, r; r. 14-4 :,, -. d E 14-5 0. d t : ( SI), dim 0 = dim q2 = Fr 2 ( IT) 2 MLT - 2 L 2 = I 2 L - 3 M - 1 T 4, 129
dim E = dim ES = dim FS q = MLT - 2 IT L 2 = ML 3 I - 1 T - 3,. d E dim 0 d t = I. 14-6,. : : S Dd S = q = V d V ( 1) Bd S = 0 ( 2) S, ( 2),. L L B Ed l = -d S ( 3) t S D Hd l = + d S ( 4) t, ( 3) -. - : S E B, H D + t t ; :.,. 14-7 0 S Ed S = q = d V V 0 E d S = q = S d V,? V 130
: E,. E,,. 14-8,Bd S = 0, Bd S = 0,, B? : B,. B,.,, S, B. 14-9. :. ( ), : (1 ),,. (2 ),. (3 ),. ;,. (4 ),. : 131
; E B, ;,, ; E B ( ), ;. 132
15-1 : (1 ). (2 ). (3 ). (4 ). : : ( ) ; : () ().,. : (1 ).,. (2 ).. (3 ).,. (4 ).. 15-2??,?,,? 133
: / 2,.,.,,, ;,,,.,. ( ), ; ( ),.,. ( ), ; ( ),. 15-3,? (1 ),,. (2 ),,. : ( 1).,, ;,,,. (2 ).,,.,,. 134
15-4 k m,, l 0,. 15-4 ( a),. : 15-4 (a) m :, (, = k m ).. Ox,, b, t x. 15-4 ( b), mgsin - kb = 0, mgsin - k x = m d2 x, d t 2 ( a) ( b) 15-4 135
d 2 x = - d t 2 k ( x - b) = - 2 ( x - b), m 2 = k,.x= x - b, m d 2 x = - 2 x. d t 2, b,. 15-5 k, 15-5 m,..,. 15-5 :,., 136
,,. m,, k., k. (a) f = f 1 = f 2 = - k x 2 = - k x, k= k 2. x. ( b) f = f 1 + f 2 = - kx - k x = - k x, k= 2 k. (c) f = f 1 + f 2 = - k x - kx = - k x, k= 2 k. ( d) f = f 1 = f 2 = - k x 2 = - k x, k= k/ 2. x= ( x - b), b m, kb = mg. (e) f = f1 + f2 = - k x - kx= - k x, k= 2 k. ( f) f = f 1 + f 2 = - kx - kx= - k x, k= 2 k. 15-6,,?,,? (1 ),,. (2 ),,. (3 ),,. : ( 1),.,,., 137
. T, T = 2 l g. a, a g., f - ma = f - m a 2 + g 2 = 0. f, a, a= a 2 + g 2,, T = 2 l a. (2 ), T.,,., f - mg - ma = f - m ( g + a) = 0, g = g + a,, T = 2 l g ;,,., f - mg + ma = f - m ( g - a) = 0, g = g - a,, T = 2 l g. (3 ) T e = 2 l g e, g e = G m e r 2 e r e, g e. T m = 2 l g m, g m = G m m r 2 m. m e. m m r m, m m 0.012 m e, r m 0.273 r e, g m 0.16 g e, T m 2.5 T e > T e. 138
r,. : v 2 = G m e r, r3 = G m e ; r g 2 r g r = G m e r 2. r4.210 4 km, g r 0.023 g e., T s 6.6 T e > T e., : T s ( ) > T m ( ) > T e ( ).? 15-7,, :. T = 2 m k, m,, k. (1 ), a,. (2 ),,. (3 ),,. 15-8,,,.,?? :,, = cos(t + ). 139
,,, = d d t t = 0 g l, l., t = 0,, = 0, t = 0 =. : = ( > 0 ), = 0. = cos g l t ( rad).,, d d t, = g l. 15-9 T 0 t = 0 15-9.,. 15-9 140
: ( a), 2, = 0 cos 2 T t + ; 2 ( b), 3-2 2, 0,, = 0 cos 2 T t - ; 2 ( c), = 0 cos 2 T t; ( d), = 0 cos 2 T t +. 15-10, l A = 2 l B.,. (1 )? ( 2) B, A? A B?? ( 3 ), A B? A B? : T = 2 l g, l A = 2 l B, T A = 2 T B. (1 ), 141
.,, 0. (2 ) B, t = T B 4 = 2 8 T A, B B t =, A 2 A t = 2 2 2 = 2, B.t, A 4,., A B. (3 )A B, t 1 t 1 = 2 + 1 2 B t 1 - A t 1 =, T A, = ( 2 + 1 ) l A g., A B, t 2 B t 2 - A t 2 = 2,, t 2 = ( 2 + 1 ) T A = 2 ( 2 + 1 ) l A g. 15-11 x - t 15-11.. : A T,,. 142 (a) ( b) t = 0, x 0 = A 2, v 0 > 0. 0 = - 3. x = Acos 2 T t -. 3
15-11 (c) t = 0, x 0 = - A 2, v 0 > 0. 0 = - 2 3. x = Acos 2 T t - 2. 3 t = 7 8 T, x t = 7 8 T = 0, v ( d) t = 7 8 T < 0. t = 7 8 T = 2 7 t = 7 8 T T 8 T + 0 = 2, 0 = - 5 4. t = 5 8 T, x t = 5 8 T = 0, v x = Acos 2 T t - 5. 4 = 2, > 0. = - t = 5 8 T t = 5 8 T 2, 143
= 2 5 t = 5 8 T T 8 T + 0 = - 2, 0 = - 4. x = Acos 2 T t -. 4 15-12,,? 15-12,,. 15-12 :,, ( 15-10 ).,, x,. 144 (a) ; ;. ( b) ; ;.
(c) ; ;. ( d) ; ;. (e) ; ;. ( f) ; ;. 15-13,,,,,,,?? :.,, ;,,,. T = 2 l g., l. T= 2 J mgh., J ; m, ; h,, h = l. R, m. J : J = 1 2 mr2 + m l 2. T= 2 J mgh = 2 ( R2 / 2 l) + l g, ( ). > T.,., J,. l, m 1, R, m 2. 145
, J 1 = 1 3 m 1 l 2 + 1 2 m 2 R 2 + m 2 l 2.,,., J 2 = 1 3 m 1 l 2 + m 2 l 2 < J 1. J T= 2, h, ( m 1 + m 2 ) gh J 1 > J 2.,,. 15-14,,.. :,,.,,,,.,,.,,,,. ( ), ; v, v. 15-15,,? : ( ) A = x 2 0 + v2 0 2 0 146
, x 0 v 0, T 0 = 2, 0. 0. A = m F 0 ( 2 0-2 ) 2 + 4 2 2, x 0 v 0,.,. = 1 T = 2 147
16-1 16-1 ( a),, ABC DEFGH I, T/ 4. :.,,, 16-1 ( b).,., T/ 4, / 4, 16-1 ( c). 16-1 148
16-2 : (1 ). (2 ). (3 ). : ( ), 16-2 A I. (1 ). 16-2 B D,., B D,, 16-2.,. (2 ).(1 ). 16-2 B H,,,,.,. (3 ). 16-2 A I.,.,, 2.. 16-3 u =,,? :.,., ( ),.u =, 149
... ( ), u. c. c u = n, n. 16-4,,?? :.,.,.,, u =,.,, ( ).,.. 16-5 y = Acos t -? y = Acos t - x u x u + 0 + 0, 0? y = Acos t - x u x u? + 0, x u? x = 0? t = 0? :.,. y = Acos t - x u + 0 A. t x t = 0 150
.,,., x u = t u x, 0. x x x = 0 u, - t x. y = Acos t - x u + 0, x = 0.x = 0, : x, x ;,., t = 0 x.t = 0, x,. 16-6?,? : ( ),,..,,,. 16-7 T u k, : 151
y = Acos 2 t T - y = Acos(t - kx ) y = Acos k( x - ut) x : 0 = 0, x y = Acos t - x u. ( * ) : = 2 = 2 1 T, u = ( * ) y = Acos 2 t T - x. k = 2, = 2 = 21, ut = T ( * ) y = Acos (t - k x). k = = u, cos( - ) = cos T ( * ) y = Acos k( x - ut). 16-8 u, a y = Acos t +, 16-8 2 b. : a ( ),, a ( O ) ( ),.. b, b (a) O a T 4. 152
16-8 O y( x, t) = Acos t - b x b y( O, t) = Acos t + T 4 x u = 2 y( x b, t) = Acos t - +, 2 + T 4 + = Acos t - 2 ( b) ( a). b x b y( x, t) = Acos t - = - 4 y( x b, t) = Acos t + += Acos t. 2 u x u +, x u +, 4 u += Acos t + 3 2. 153
(c) O a T 2. O y( x, t) = Acos t - b x b y( O, t) = Acos t - x u = - 4 y( x b, t) = Acos t + 4 u T 2 +, 2 - T 2 + = Acos t - 2 x u - = Acos t. 2 -, 2 ( d) x.o a T 4. O y( O, t) = Acos t - y( x, t) = Acos t + x u b x b = - 4 y( xb, t) = Acos t - 4 u T 4 +, 2 - T 4 + = Acos t + x 2 u, = Acos t -. 2 16-9 ( 1 ),,? (2 ),,?? : ( 1)., 154
,.. (2 ).,,.,. x y x y t 2 2.,,,. 16-10 ( 1 ),,,,? (2 ),? : p m I = 1 2 ua2 2 = 1 2 = ua. p 2 m u. I I = ( p m ) 2 (u ), ( p m ) 2 (u) (u ) = 1103 1430 (u ) 1.293331 = 3.34103. (1 ), p m p m = (u ) (u) = 1.7310-2 1. (2 ), I = (u ) = 3.3410 3 1. I (u) 16-11 1 db, : (1 )? 155
(2 )? : ( 1) IL = 10 lg I I 0. I L = 1 = 10 lg I I 0 I I = 100.1 1.26. - lg I I 0, (2 ). I = 1 2 I L = 1 = 10 lg I I 0 p 2 m u. - lg I I = 20lg p m 0 p m p m = 10 0.05 1.12. p m 16-12,, u 1 u 2, 1 2, A 1 A 2, x = 0 10 2 0,,. (1 ) A 1 A 2, ; (2 ) 1 2, ; (3 ) 1 0 20, ; (4 ) u 1 = - u 2,. : x y 1 y 2 = A 1 cos 2 1 t - = A 2 cos 2 2 t - : y = y 1 + y 2. 156 x u 1 x u 2 + 1 0, + 20 (1 )
. y = y 1 + y 2 = ( A 1 + A 2 ) cos 2 t -,.., A = x u + (2 ) y = y 1 + y 2 = 2 Acos ( 2-1 ) t - cos ( 2 + 1 ) t - 2 u - 1 x 2 u 1 2 + 1 x + u 2 u 1 = 2 Acos ( 2-1 ) t - Ax cos ( 2 + 1 ) t - Bx +. 2-1 u 2, B = 2 u 1 u 2 + 1 u 1,.,. (3 ). y = y 1 + y 2 = A cos 2 t -, A = 2 A cos 10-2 0, 2 = arctan sin( 1 0 - ) + sin( 20 - ) cos( 1 0 - ) + cos( 20 - ) x u +., = 2 x u 10-2 0 = 2 k, k = 0, 1, 2,, 2 A, (1 ). 10-2 0 = ( 2 k + 1 ), k = 0, 1, 2,,. (4 ). :. 157
y = y 1 + y 2 = 2 Acos 2 x cos 2 t +. u 16-13, : (1 ),,,? (2 ),,,? (3 ),,,? (4 ),,? :.,,,. (1 ),,,,,,. ( 2). (2 ),,,,,.,. (3 ),,,,,,,,. 158
,. (4 ),,.,. 16-14 (1 )? (2 ),,,? : ( 1),. :,,. :,,.,. (2 ),,.,, :, ;,.,,. 16-15, 16-15..,,.. :,.,.,,. 159
16-15,..,. ( :,2002). 16-16,, 16-16 (a)., T/ 4 ( T ). :,,,,.,,,. 16-6( b).t/ 4 16-6(c)16-6 ( d). 160
(a) ( b) (c) ( d) 16-16 161
17-1? : :...,.,,,,,. 17-2 S 1 S 2 : (1 ) S 1 S 2. (2 ) S 1 S 2. : S 1 S 2, S1 S2. ( 1), S 1 S 2,,.,, 162
. ( 2), S 1 S 2,.,, S 1 S 2, S 1 S2., 17-2.,. 17-2 17-3 17-3, : (1 ) ; (2 ) ; (3 ) S ; (4 ) S ; (5 ) S. : 17-3 ( a), S 163
, S 1 S 2. (1 ) S 1 S 2 ( ) d, () x = D d. (a) 17-3 (b) (2 ) a,,,,.dd, d/ a,,,. (3 ) S S( 17-3 (b) ), P, S S 1 S 2 P = ( S S 1 + r 1 ) - ( S S 2 + r 2 ), S,, (),. = m, m S ( ), P,. (4 ) S,, S 1 S 2. 164
( 5) S,,., (3 ),,.P, S, k ; S, k, SS P = - = [( S S 1 + r 1 ) - ( S S 2 + r 2 )] - [( SS 1 + r 1 ) - ( SS 2 + r 2 )] = [ S S 1 - S S 2 ] - [ SS 1 - S S 2 ] = S S 1 - S S 2 = 2.,,. S, 2 SS.,,,,,. 17-4,,?,? :,,.,,. ( ),.,,. 17-5 ( )?,, 165
.,,?? :, e,.,,.,. ( ) ( ).,,.,,,.,,. 17-6? :.,,. 17-7 17-7,,?,?,,? :,.,,,. 166,
17-7,,.,, (). 17-8, ( n 1 = 1.50 )( n 2 = 1.75 )., ( n 3 = 1.62 ), 17-8 ( a).,. (a) (b) 17-8 :, 167
,.,,. 17-8 (a),,,,,,.,,,,,. 17-8 ( b). 17-9,,,?? :., :,, ; ;,.,, ; ;,. 17-10,. ( ) G L,. ( ),, 168
,,,,. : L, L G, ; L R, L G,, ; L R, L G,, G,,,,. 17-10, L R,,,, ; L, R,,,.. 17-10 17-11, M 2, M 1 M 1, 17-11,? M 1 R (), 169
, M 2,? 17-11 : 17-7.M 1 M 2, M 2,.,, ; M1 M 1,, M 1 M 1,,. M 1 R, M 2,,. 17-12 (1 ),? (2 ),? :, ( ). 170
.,,. (1 ), 10 4 m10-4 m, 10-7 m.,,,,. (2 ), ( 10 3 m) (10 2 10 3 m) ( 110 2 m)( 10-4 1 m)..,,,,. 17-13,,? :..,,.,.,. 17-14 17-14, : (1 ) ; (2 ) ; (3 ) ; (4 ) S ; (5 ). 171
17-14 : :, ;,, ; : - < asin < ; x = 2.. : f a. (1 ) a, (2 ) a, (3 ),,. (4 ) L 1 S, L 1.. (5 ),,. 172
17-15,? :,,,.,,.,,.,,,.,, S 1 S 2,, a0.,, I 0, (, ).,,.,,, I = 4 I 0 cos 2., 2 4 I 0 ; x.,, 17-15 (a)., a,,,.,,,.,,. :,, ; x,., 17-15 ( b). 173
, da,, ; a,. 17-15 17-16?? :. 17-16, : (1 ),, ( a + b) = d = 1, ; N (2 ), a,,, ; 174
17-16 (3 ) N - 1, N - 2, N, ; (4 ), a + b a = d a, ;, (5 ), N, : R = kn. 17-17,? : a = b, a + b a. = 2.,, 17-18? :.,,,,,,., 175
,..,,.,. R = kn, k, N. d = a + b,, N d,. R = b d n n, d d d b. N d = b, b. 17-19, 1 200 600 90. (1) 7001 000 nm,??? (2 ),? :,., k = 1.,.. dsin = k, k = 1, sin = 1, M = d. k = 2 sin = 1, m = d 2. 176
;., m < < M d 2 < < d. d 1 = 110-3 1 200 d 2 = 110-3 600 d 3 = 110-3 90 : m = 833 nm, m = 1 667 nm, m = 1. 1110 4 nm, d 1 2 d 2 2 = 417 nm; = 833 nm; d 3 2 = 5.56103 nm. (1) 7001 000 nm, (2 ) 400760 nm, 17-20 17-20.? (a)( b). : 17-20 ( a) : ; ;., (a), a + b a = d a = 3, b = 2 a. ( b)(a),., ( b), a + b a = d a = 3, b = 2 a. (c), a. 177
17-20 17-21 17-21 (a), M, N.. M, N OO 360, N? N, M OO360, N?. : M, M, M,.N OO 360, M,., N 178 (a) 17-21
. N, M OO 360, M. M 360 N. t = 0, M N, N ( M ) OO 360 M ( N ), (b) N 17-21 17-21 ( b). 17-22, M N, N. M N C, M N, N?. C, : M, N, t = 0 C N, OO.t C N t. I 0, M I M, I M = 1 2 I 0., C I C = I M cos 2 2 - t = 1 2 I 0 sin 2 t. N I N = I C cos 2 t = 1 2 I 0 sin 2 tcos 2 t N, 4. = 1 8 I 0 sin 2 2 t = 1 16 I 0 (1 - cos 4t) 179
t = (2 k + 1 ) 4, k = 0,1,2,,, 1 8 I 0 ; t = k, k = 0, 1, 2,,,. 2, 17-22. 17-22 17-23 17-23 ( a),,?.. i 0 = arctan n, n. ii 0. : 17-23 ( b). 17-24,?? :, = 2 -.,. = arctan 1.33, 53, 37. ( ). 180
( a) ( b) 17-23 17-25,,.? :,,. 181
,.,,,. 17-26 17-26 ( a), ( ),? A B,, ( b),? B, B?? 17-26 : ( a),, o e.o, e.,. ( b), AB,, AB, A o B, ; A e B, A, B, e, ( e A B ).,. 182
B,., B o B e B o e., o, e. 17-27 17-27 ( a), ABCD 45, ABD AB, BCD. AB, o e, o e. : AB, ABD o e,,. BD,. BCD, o e, e o,., o e. 17-27 ( b). (a) ( b) 17-27 17-28 17-28 ( a),,., : ( 1) o? e?? ( 2) ab? 183
.( 3),,? : ( 1) o e ( n o > n e ), o e,, o e., a o, b e. (2 ), a(o ) (a ), b(e ) (b ).,, 17-28 ( b). (a) ( b) 17-28 (3 ),., o ;, e ;, o, e ;,. 17-29 (1 ) (a) ; ( b) ; ( c).. 184
(2 ) ( a) ; ( b) ; (c).. : ( 1) M,,, ;, ; ( ),. (2 ) M,,, ;,, M 1/ 4,,, ;,. 17-30, : 1/ 4. : M,.,. M N, ( ), M 45, N., 1/ 4.,,.,. 17-31 P 1 P 2 185
C,? : P 1 ; C ; P 2 P 2., :,,., P 1 P 2 C. 17-32 17-32 ( a) -., S. ( 1) S P 0 (, P 1 P 2 P 3 )? ( a) 17-32 (2 ) S 1 S 2 P 1 P 2,.P 0 45,? (3 ) P 3, P 0, (1 )? (4 ) ( 3), P 0 90 P 3 186
,? (5 ) ( 3), P 0,? :,, 1, I = A 2., I = 4 I 0 cos 2 2, I 0 P ( ).P. (1 ) S P 0 P 1 P 2 P 3, P 0, I 0 = I0 2. I = 4 I 0 cos 2 2 = 2 I 0 cos 2 2,. ( ) (2 ) S 1 S 2 P 0 45 P 1 P 2,, A 1 = A 2 = 2 2 A 0,, I 1 = I 2 = A 2 1 = A 2 0 2 = I 0 4, A2 0 = I 0 2, 17-32 ( b). : = k,, y, I = ( A 2 1 + A 2 2 ) 2 = I 0 2. = ( 2 k + 1) 4,, I = I 1 = I 2 = I 0 4. = ( 2 k + 1),, x, 2 187
( b) 17-32 I = I 0 2.,.,,,,. (3 ) P 0 P 3,., I y A 1 y = A 2 y = A 0 cos45 45= A 0 2 I 1 y = I 2 y = A 2 1 y = I 0 8. = 4 I 1 y cos 2 2 = I 0 2 cos2, 2, ( 1), ( 1) 4 I 1 y = 1 4 I 0 4. (4 ) ( 3) P 0 90P 3, y, 188
, ( 3), 17-32 (c). : (c) 17-32 I y = 4 I 1 y cos 2 2 = I 0 2 cos2 2,, = 2 +, = dsin., S 1 S 2.(3 ),,. (5 ) ( 3), P 0, P 1 P 2, I 0 2,, P 3 I 0 4., I = I 0 4 + I 0 4 = I 0 2. 189
18-1 A B,, A A, B B. : A B,?? :, M ( T ). M ( T )., ( ),.A B,,. A B,.A, ; B,.,, B A. 18-2?,?,? : ( )., 1,..,. 1, 190
, 1,,.,.,,,,...,,, ;,,,,..,,. 18-3,? :. 37(310 K), : T m = b ( b = 2.89710-3 mk) m = b T = 9. 34510-6 m,. 18-4,,,,,?,? :,.,, 191
.,.,,. 18-5 ( ),? : -, ( ) T 2 T 1 = 2, M 0 ( T ) = T 4, M 2 M 1 = T 2 T 1 4 = 2 4 = 16., 16. 18-6, : ( 1 ) 1 ; ( 2) 1,,? :,,, h= 1 2 m v2 m + A.( ),. I = N h. N. : (1 ) ( ), I 1. K N 1, 1, 1. 192 (2 ) ( ),
1. 1, N,. 18-7 : 4.12 ev, 4.50 ev, 4.20 ev, 2.50 ev, 2.30 ev. :,? : ( ) ( 760 400) nm,, h= h c, ( 1.643.11) ev., : h- A0.,. 18-8, :,? :,.,,.,,..,, (),..,, CCD, ( Charge - Coupled Device).,.,, ( ).CCD 193
., R - G - B,. 18-9 ( )?? : ( ) :, ;. ( ) :, ( ), ;,. 18-10 1, I 1 ; 2 1, I 2.I 2 > I 1, 1 2? : 18-6.., N 1 h 1 = N 2 h 2., I N : I 2 = N 2 I 1 N 1 1 > 2. = 1 > 0, 2 18-11 1, E k 1 ; 2, E k 2, E k 1 > E k 2, 1 2? 194
:,,., h 1 - E k 1 = h 2 - E k 2, E k 2 - E k 1 = h( 2-1 ) < 0, 2 < 1. 18-12? : X,,,,. : X 10 4, 3.1 ev, 1010 2 ev, 10-2 ev. X,,.: = - 0 = 2 h m 0 c sin2 2.,. 0 X,, X,., 0.,,,., ( ),,., 0.,,, 195 ev
.,,.,, 0.,, :, 0, 0.,. 18-13,? :.,.., ev, 1 ev.,,,,, ; X, 10 4 ev,,.,,.,,.,. 18-14, 196
? :. ( ), (X 10 4 10 5 ev, 1010 2 ev).,.,. 18-15,,,.? :., :,,,..,.,..,.,.,,,,. 18-16 (1 ),? (2 ) n. 197
: ( 1) = R 1-1 k 2 n 2 = T ( k) - T ( n), k n ( n > k). k nn k, n n = k, n- k, n = T ( n) - T ( n ) = R 1 n 2-1 n 2, n- n = 1, n > k.n, k, n n R 2 n 3., n = 30, 812. 6 m - 1 ; n = 350, 0. 5 m - 1 n.., (2 ) E n = - E 1 n 2, E 1 = me 4. E 8 2 0 h 2 n < 0 n.n E n, n, E n 0. E = E n - E n = 1 n 2-1 E n 2 1, n,e E = 2 n 3 E 1 n.,n = 30 E1 mev; n = 350 E6.310-4 mev.,,. 18-17, n = 4,? : 43, 42, 41, 32, 31, 21, 6. 18-18,, 198
1 2 3.? : = 1 = R 1 - k 2 1 n 2 1 2 3 1-3 1 2 = 1. 1 18-18 18-19 m, v. h= mc 2, = h m v, = c2 v. = v, v = c.,? : v u.,., u =,., u = = c2 v > c,., v ()c.? 18-20 : 199
..,. 200
1.,..,,,.,,. t N,., n, v 0. a b c, v 1, Z - 1. Z - 1 201
, v 0. v 1, x, t = x v 1,, v = v + v, v = v = v - v = v 0 - v 1. v, Z - 2, v. Z - 2 Z - 1, S 1 = bc, S 2 = ab, n 1 = n S 1 vcos n 2 = n S 2 vsin, t N 1 = ns 1 vcos x = ns v 1 1 xcot N 2 = ns 2 vsin x v 1 = ns 2 x, x : N = N 1 + N 2 = n S 1 xcot + n S 2 x. ( 1) 202 v 1 v = sin.
x,. v 1. x, S 2,., x, v1, cot.,,.,. v 0 Z - 3., t Z - 3 N 1 = ns 1 vcos x v 1 = ns 1 v 0 cos x v 1. N 2 = n S 2 vsin x v1 = n S 2 ( v 1 + v 0 sin ) x v1. x, N = N 1 + N 2 = nv 0 ( S 1 cos + S 2 sin ) t + ns 2 x, ( 2).,..,, (S 1 cos ), (S2 sin ). 203
v 0,, Z - 4.(2 ) ( - ), x : N = N1 + N2 = n S 1 v 0 cos x + S v 2 ( v 1 - v 0 sin ) x 1 = nv 0 S 1 cos t - nv 0 S 2 sin t + n S 2 x. ( 3) (3),,, ; ns 2 x - nv 0 S 2 sin t = ns 2 ( v 1 - v 0 sin ) t, v1 v 0 sin.: 1. ( v 1 - v 0 sin ) < 0,.,, S2 ( v 1 - v 0 sin ) t. v 1 Z - 4 2. ( v 1 - v 0 sin ) > 0,.,, S 2 ( v 1 - v 0 sin ) t. 3. ( v 1 - v 0 sin ) = 0,.,.,., ( 3). 2.,,. 204
,.,,,.. m, m r, v 2 = Gm, ( 1) r, 2 vd v = - G m r 2 d r, ( 2) E = - G m m + 1 r 2 m v2., d t, d A = d - G m m + 1 r 2 m = G m m d r + m vd v, ( 3) v2 r 2 (2 )( 3), d A = - 2 m vd v + m vd v = - mvd v. ( 4) d A < 0, d v > 0.,,.,., ( 2 ).,, -.( 4) :,.,,.,. 205
3..,.?,,.,.,.,,,.,.,,,,. :,,.,,,.Z - 5, O, r 1 r 2,., 1 2.2,, 2, 3., O r = r1 - r2. 2,,,, A 1 = mgr - r 2 m 2 rd r r 1 206
= mgr + 1 2 m 2 ( r 2 1 - r 2 2 ). Z - 5 3, = 0,,, : A 2 = - mgrcos 0., A = A 1 + A 2 = mgr (1 - cos 0 ) + 1 2 m 2 ( r 2 1 - r 2 2 ).,r > 0, ( 1 - cos 0 ) > 0, ( r 2 1 - r 2 2 ) > 0, A > 0.,,,. 4.,,.,., : 207
,??,?.,, :. :.,,.,.,,.,. K K.K K x u, t = 0,. F. d t, K d r = d r+ ud t, F A =Fd r, L K, F A=Fd L r=fd r L -Fud t t = A -Fud t, t, F u,,.,,.,. K A =Fd r = E k - E k0, L 208
E k = 1 2 m v2, E k0 = 1 2 m v2 0. K, A=Fd L r=m d v L d t = v m v v 0 d v = E k d r - E k0, E k = 1 2 m v 2, E k0 = 1 2 m v 2 0.,,,.,, : 1. : A = A + A = F i d r i = L E k i - E k0 i = E k - E k0,. 2.,,. 3.,...,,.,,. 209
.,., : : A = A + A = E k - E k0, : E = E k + E p : A = A + A = E - E 0,, A + A = 0, E = E 0 =..,, : K, A A, ; K, A A,.,. :,, m, u,. :,.m., m. mg, ; F N,,,., : 210
mgh = 1 2 m v2, h, v m., m,., L.Z - 6, F N L,, F N,. Z - 6,,, ;,,,. 5. L,.., ( z ), L L z, z,, L z 211 = J,
M z = d L z d t..,,,, Lz = J L = J. L = rp = rm v, ( 1) r, p r. L r p.. m, r.z - 7. v = r, Z - 7 (1 ), : L = rm v = rm ( r ), A( BC) = B( AC) - C( AB), ( 2) O L = mr 2 - mr ( r ). ( 3) r,, 212
L = m r 2, ( 4) O L. O, Z - 7, O (3 ) L= mr 2 - m r cos, ( 5), LL.,, L., L. z, Z - 8. d m, r l.. O, L = rv d m, r O d m. v = r, ( 2), Z - 8 L = [ r2 - ( r ) r ] d m. Z - 8 r = r z + r l, r 2 = r 2 z + r 2 l, r z = rcos, L = r2 d m - ( r ) rd m = ( r2 z + r 2 l )d m - rcos ( rz + rl ) d m = r2 zd m + r2 ld m -rcos r z d m - 213
rcos r l d m. r z, - rcos r z d m = - r2 zd m,, L = r2 ld m -rcos r l d m = r2 ld m - r zr l d m = r2 l d m - r z r l d m = J z + - r z r l d m = L z + L l., z, O L, L z = J z = r2 l d m, J z = r2 l d m, L z,,, z J z. L l - r l.,, L. L l = - r z r l d m, L l, - r z r l d m,- L l,, r l, z.d m O Z - 9. - r z r l d m z 214
,. Z - 9, z, L,., L, L. z, L l = - r z r l d m = 0, L = L z = J z,, L. z, Jz..,, J c L = J= J c,, L = J c., :. 1.,,., L. 215
2. L. L z = J M z = d L z d t, L, L z L. 3. z, L.,,. 4.,, L,. 5., L l,,. 6., Z - 10 K K,,.,? Z - 10 216
l 0.,,,,.?, K : l 0,, l, l< l 0,, K. K, l 0,, l, l< l 0,.,, K,? K :. : K, K, ;, K, K. K, ( O, t 0 ) ( x 1, t 1 ), K, ( O, t 0 ), ( x 1, t 1 ), Z - 11., t 0, x 1 = t 0 = 0. = x 1 + v t 1, 1-2 = v c., ( K),, 217
Z - 11 t 1 = t 0 = 0, x 1 = x 1 1-2, l= l 0 1-2.,, l = l 0 - l= l 0 ( 1-1 - 2 ), t= l v = l 0 v ( 1-1 - 2 )., K, t 0 = t 1 = 0,. K., t= - c 2 vx 1 = - 1-2 c 2 vl 0 < 0. 1-2 -, K. 218,
? t t: t > t,,,,,,,.,. 7. : K t, K t, t=t 1 - v 2 c 2 < t,, v, c., K, K.,, KK., :,,.,,,? :,,. :,,.?.,,,.. 219
, 1905,.,.,, :,,. : 1.,.,.,,.,,,.,. 2.,.,,,.,,, :,.,., :,,. 3..1966, 14 m,,.,.1975 1976,,,,. 220
,,,. 8., v p : T,,, v p v p,. v p p? = 1 2 mv2 p. ( 1), : T,,, p,. f ( ) = 2 ( k T ) - 3 2 1 2 exp - kt, d d f( ) = 0, v 2 p = 2 kt ( 1), m p = 1 2 k T, ( 2) = kt. ( 3), ( 2), ( 3).,,, v p, 221
= 1 2 m v2 p = k T,,, p, p = 1 2 k T?..,.. = 1 2 m v2 d= mvd v = 2 m 1 2 d v, d d v = 2 m 1 2 1 2.,,.,. p = 1 2 k T v = k T m < v p,, v p ;, v d v, vp d vp. d= m vd v, d, m vd v = mv p d v p, d v d v p = v p v = 2.,. 222 d N d N p = 1 2 f( v) d v = e - 2 = f( v p ) d v p 2e - 1 e 2 > 1..
9.,. 1 6, 1 4,?, : 1.,, : v 2 x = v 2 y = v 2 z = 1 3 v2, 1 6.,. n, v, x 1 6.d t, x d n,, vd t : d n = 1 6 n vd t, m,, 2 m v,, p = 2 m vd n d t = 2 1 6 n m v2 = 1 3 nm v2.,, v, 223
1 6 n v, = 1 3 v. 2. v,. :,, g( v i ) = f ( vx, vy, vz ) = g( vx ) g( vy ) g( vz ), m 2kT 1 2 exp - m v 2 i 2 k T ( i = x, y, z ). d t, x d n,, v x d t : d n = [ ng( v x ) d v x ] v x d t = nd t = nd t k T m J = d n d t = n k T m m 2k T m 2k T 1 2 m 2k T 1 2 0 1 2, = n 1 4 v x exp - 8 k T m mv 2 i 2 kt d v x 1 2 = 1 4 n v..,? :, ;, ;,.,,,, 224
v,,..,,,..,.,, 1 6 1 4. 10., p - V : pv n =,, n.. Z - 12 : Z - 12 225
: p =, n = 0 ; : pv =, n = 1; : d V = 0,, n = ; : pv Y =, n =.,, n. d p = 0 ( ), d T = 0 d E = 0 ( ), d V = 0 d A = 0 ( ), d S = 0 d Q = 0 ( ).,?, C m = d Q d T =, 1 - R C m - C V, m, n,. C m = d Q d T = C V, m - n 1 - n, n ( 1),. 226 C m n = 0 = C p, m = C V, m ( ), C m n = 1 = C T, m = ( ), R C m n = = C V, m = - 1 ( ), C m n = = C Q, m = 0 ( ). = C p, m C V, m.,,
,,., n,., n. n, C m, n, Z - 13., C m > 0,, Cm < 0,.,, p V.,,. Z - 13, p - V,, 4 8, Z - 14, 4 1 5, 2 6, 3 7, 4 8.1 mol, a,. a d p d V a = - n p a V a. 227
d V > 0, d A > 0 : 1. 1a5 : d T < 0,< n <, C m > 0. : d Q = C V, m - n 1 - n d T < 0; : d E = CV, m d T < 0. Z - 14,,,,,... 2. 2a6 : d T < 0,1 < n <, C m < 0. : d Q = C V, m - n 1 - n d T > 0; : d E = C V, m d T < 0.,,,,,..,. 3. 3a7 : d T > 0,0 < n < 1, C m > 0. : d Q = C V, m - n 1 - n d T > 0; : d E = C V, m d T > 0. 228
,,,,,..,. 4. 4a8 : d T > 0, n < 0, C m > 0. : d Q = C V, m - n 1 - n d T > 0; : d E = C V, m d T > 0.,,,,,..,., d V < 0, d A < 0,,, n, d T..,, :,. Z - 15 : 1 2 p - V AB.1, AB : p A V A = p B V B p A V n A = p B V n B, V A = V B, p A = p B, AB., 1,.,,.,,. 229
Z - 15 11.,.,?,?, ( ).,.,, Z - 16.. Z - 17,, Z - 16, Z - 17 : ( ), Z - 17 a, ( ),,, ;, ( ), b ; 230
,, ( ), c ;, ( ),,, d ; ( ),. Z - 16 Z - 17 231
A ( ), Q 2, Q 1, w = Q 2 A = Q 2 Q 1 - Q 2,, Q 1 = A + Q 2 = A( 1 + w ). w = 5, A = 1 J, Q 2 = 5 J, Q 1 = 6 J.,? A = 1 J, Q 2 = 5 J,,, Q 1 = 6 J,.,,,.,.,,, 6 J ( ),.,,,.,, : 1 J, 5 J, 6 J,., 6 J.,,. 232
12. Ed l = 0. L,,. V ( r ) r, E ( r),. : P,, P.,,, P ;, P,.,, :, ;, ;,?,?, : ( 1 ),, ; (2 ) P, V P ; ( 3 ). P, 233
V P = P 0 Ed l, P P 0. P 0 P 0, V P = P 0 P P 0, P Ed l = P 0 Ed l P + P 0 P P = V P - V0 = P 0 P V Ed l 0 = P 0 P Ed l., P V 0, V 0 = P 0 Ed l. P 0, P,. E E = - V n e n = - ( V - V 0 ) n e n Ed l + V 0.,. P 0,.,. V 0.,. V 0 = 0.,,.,,. 234, :, r P
V P = q 4 0 r ; r 0 P, P q 1 V P = 4 0 r - 1 r ; 0 r = 0, V P,. =,, ( ),,. r 0 r 0, V P = P 0 P Ed l = r 0 r 2 0 r d r = (ln r 2 0 - ln r ), 0 = 1, ln r 2 0 = 0, P 0 V P = -, VP = P 0 P ln r. 2 0 Ed l = r 0 d r = ( r0 - r), r 2 0 2 0 = 0, P, r 0. V P = - r. 2 0 =, V P,.,?., r 0 0, ;,,, 235
.,,,.., : E r, E = Kr - n, n = 0; n = 1; n = 2; n = 3, P V P = K r r n d r = K ( - n + 1 ) 1 r n - 1 r = (n1 ), (n > 1 ).,,, n > 1,,.,.,,,.,? :,.,, ;.,.,,., E 0 q,. 236
Z - 18 :..,, O x, q x.p 0, x P V P = P 0 P Ed l = P 0 Ed l + V 0, P, E, P 0 Ed l x P P 0, V 0 P P 0. P VP = P 0 P Ed l + V 0 = ( E 0 x - E 0 x ) + = q, E 0 x - 4 0 x + V 0 = 0, P V P = q 4 0 x - q 4 0 x + V 0 q 4 0 x - E 0 x. q 4 0 x - E 0 x + E 0 xq 4 0 x + V 0, P P 0, P. V 0 P 0 = 0, P 0, E 0 xq = 0, 4 0 x 237
x= q. 4 0 E 0,,. V = 0,., :.,,, ( ), V = 0. VV? V= V = 0? : V P = P 0 P Ed l = P 0 Ed l P + P 0 P V 0 = P 0 Ed l. P 0 Ed l 0 = P 0 P Ed l + V 0,,, P,, P P 0, P 0., :, P V 0. P,, E P P,, P 0 P, E P 0 E P, V 0 0.,,,, V V V 0.P, P, V 0, 238
, P 0 0, V 0 0, V V = 0,.,, V V. 13.,,.,, :, ;,,.,., () ( ),,. : W = 1 n 2 q i V i ; ( 1) i = 1 W = 1 d L, 2 L 1 2 S 1 d S, 2 V d V ; 239 ( 2)
W =w e d V = 1 2 V V DEd V ( 3) W = W + W. ( 4) :, 1. ( ). 2. ( ),,,,..,,,,. 3. ( ),.: (1 ),,.q 1 q 2 q 3,, ; q 1 q 2, q 3,.,,,. (2 ) W = qu. 1 2, U q q., q,. 240
(3 ), ( ),. :,., E,.,,. :, : = + =.,? 1. (2 )( 1), (a) ( 1) V i q i, q i, (2 ), d q. ( b) ( 1), ( ), ( 4) W. ( 2),, ; ( 2 ),,, ( 4). (c) ( 1) (2 ) d q. (2 ),,,,,. (2 ).,.,,, ( ),. 241
d q,.,,. 2., ( 2) (3 ). (2 ) ( 3),. 9-9,,., ( 2 ), (3 ).. 3., ( ), ( 2 ) ( 3 ).,.,. 4., (1 ).n V 0 ( x, y, z ), n, n. W = 1 n 2 q i V i i = 1 n + q i V 0 i. i = 1,., Q 1 Q 2 V 1 V 2., 242
(2 ), W = 1 2 Q1, Q 2 V = V 1 + V 2, Vd q= 1 ( V 2 1 + V 2 )d q 1 + 1 ( V Q1 2 1 + V 2 )d q 2 Q2 = 1 V 2 1 dq 1 + 1 V Q1 2 2 dq 2 Q2 + = W + W. : 1 V 2 2 d q 1 + 1 V Q1 2 1 d q 2 Q2 Q 1 = Q 2 = Q, U = V 1 - V 2, V 1 = - V 2 = 1 2 U, W = = 1 2 V 1 Q 1 + 1 2 V 2 Q 2 + 1 2 V 2 Q 1 + 1 2 V 1 Q 2 1 2 V1 Q1 + 1 2 V 2 Q2 + 1 2 V2 Q1-1 2 V2 Q1 = 1 2 ( V 1 - V 2 ) Q 1 + 0 = 1 2 QU.,, ( 2), ( 3). 14.,.,,? ( Robert Goddard) 1909,., 243
., 20 70,,,.,,,,., :,., :, ( EMS, Electro Magnetic System), ;, ( EDS, Electro Dynamic System ),..,, ;,, ( ),.,. EMS, T.T, ( ),, Z - 19.,, ;,.,, 1 cm.,.,. 244 EDS,,,
Z - 19 EMS, U,,,.Z - 20 EMS.,,, 80 km h,,,,.,,.,.,., Z - 20 EDS 245
,,,.,,,.Z - 21.,.,, ;,. Z - 21.,,, ;.,. EMS. 15. : 246
E = - d d t ( 1) E = Ed l + v Bd l ( 2).,,.(2 ), (1 ).,,,.,,,,. (1 ),,.,,,. :,.,., d d t. = Bd S S, d B, d t., :,,, ( 1 ).,,, ( 1 ).,. (2 ).,, ; 247
,.,., E ( v B)., (2 ),., ( 1) (2 ). : B, t., ( 1) E = - d d t = - d d t S Bd S. ( 1.1), L, ( 2) E = - (1 ) ( 2), d d t S B Ed l = -d S, t S S B t d S + v Bd l, ( 2.1) B Bd S = t d S - v Bd l. ( 3) Z - 22, t L 1, t + t L 2,, S 1 S 2 L 1 L2. t, B ( ) B 1 B 2.t L 1 S 1 S Z - 22 248
1 =B 1 d S 1, S 1 t + t L 2 S 2 2 =B 2 d S 2, S 2 t, B 2 2 2 =B 1 + B 1 t t d S 2 S 2 d dt = lim t0 B 1 ds 2 2 - S 1 2 = lim t t t0 B 2 = B 1 + B 1 t t, B 1 =B 1 d S 2 + S S 2 2 B 1 t tds 2 S 2 + t0 lim t t td S 2, B 1 ds 1 S 1 - t0 lim t, L 1 t S 3 S 1 S 2 S.,, B 1 d S =B 1 d S 1 -B 1 d S 2 +B 1 d S 3 = 0, S S S S 1 2 3, ( 4) lim t 0 B 1 d S 2 S 2 t B 1 d S 1 S 1 = lim t0 + B 1 d S 3 S 3 t t0, S 2 S 1, (4 ). ( 4), ( 4. 1) lim t0 S 2 B 1 t td S 2 t B 1 = t d S 1, ( 4.2) S 1 249
(4.1 ) ( 4.2) (4 ), d d t = lim t0 B 1 d S 3 S 3 t B 1 + t d S 1, ( 4.3) S 1 d S 3 = vd td l 1,t0, L 2 L 1, S 3 L 1, lim t0 B1 d S3 S 3 t =B 1 ( v d l 1 ), L 1 a ( bc) = - bac, B 1 ( v d l 1 ) = L 1 -v B 1 d l 1, L 1, ( 4.3) d d t = d d t S B Bd S = t d S - v Bd l. L, ( 3),, (1 ) ( 2)., ( 1) (2 ), (1 )., : 1. :,., (1 ). 2..,,,,, ( 1), (2 ),. : ;. 250 3.. d d t S
., d l,,,. : Z - 23, B, OA,. t GOAG, t + t, GOA AG. d 0, E0. ( 1 ) d t (2 ). OA,. Z - 23 Z - 24, B,., P P., t AP 1 P 2 B,. t + t AP 1 PP 2 B. P 1 PP 2., 0, E0., ( 2 ). 251
,, t AP 1 P 2 B, t + t AP B., E.,, d l,,. Z - 24,, (2 ),., ( 2)?. : Z - 25, B, l. B, t v B,?,,,?,, (1 ),. 252
Z - 25 (2.1 ) E =Ed l L +v Bd l = E + E, L : E = vbl, E = r B 2 t, L l 2 E d l =E cos d x - = - l 2 l 2 l 2 E= bl B 2 t + vbl. r B b 2 t r d x = bl B 2 t, :,,, ( 1) (2 ),,,. :,. : E = - B t, F = q( E + v B),,. 253
16....,.,,, p ( primary wave),, s ( secondary wave),., 8..,,., p s,, p s.,., p s, ;, p s,, 2900 km, p, s, : (core), p, s ( ), ( mantle),, 5000 km, s, Z - 26.,,., p s,., 254
Z - 26,.,,,,.,. 17.,,,,..?, 2?. 255
,. EH ( s) ( p), E s E p H s H p, E p E s, Z - 27 (a ) ( b)., s p, (123 ). Z - 27 i n 1 n 2, i, n 2 r. r s = E s1 E s1 e - i s r p = E p1 E p1 e - i s p.z - 28 p s s p. Z - 28, ( Z - 27 ) : 256 1., p.
E s1 E p1 E s1 E p1, E 1 E 1,,., n 1 < n 2, i0 i90,, E 1 E 1,,. 2. p s,,,.n 1 < n 2, i = 0 p = 0, E p1, Z - 28 ( a), i = 0, E p1, E p1 ; s =, E s1, E s1.. Z - 28 (a) ( b ) n 1 < n 2 ( ) (c) ( d ) n 1 > n 2 ( ) 257
3., p, p s,,., n 1 < n 2, i 0 i B 90, p i B 0, s, Z - 28 (a) ( b). 0 < i < i B, p, () ; i B < i < 90, p s, p i 90,.,. n 1 > n 2,, p s, Z - 28 (c) ( d ) : 0 < i < i B, s 0, p, p Z - 27, E p1 (, ), ; i, i B < i < i c ( i c ), p s ; i > i c, r, Z - 28,,. 4.,, 2, n 3 n 2 n 1 i.,,, s p,. 2, 258
,.Z - 29 (a) ( b), 1 2 ( p s ),, 2. Z - 29, : 1. i 0 i90.,,. 2., n 3 n 2 n 1., n 3 = n 1, n 2 < n 1 n 2 > n 1, 2 ; n 3 > n 2 > n 1 n 3 < n 2 < n 1, 2. [ n 3 > n 2, n 2 < n 1 ; n 3 > n 1 ], [ n 3 > n2, n2 < n1 ; n3 < n1 ] [ n3 < n2, n2 > n1 ; n3 > n1 ] [ n3 < n 2, n 2 > n 1 ; n 3 < n 1 ],,.., 1 2 2 : 259
2 n 3 > n 1 0i < i 1B, i 2B i < 90 n 3 < n 2 n 2 > n 1 n 3 < n 1 n 3 < 0i < i 2B n 3 = 0i < i 2B n 3 > 0i < i 2B, i 1B i < i 2c n 3 > n 2 n 2 < n 1 n 3 < n 1 0i < i 2B, i 1B i < i 1c n 3 > n 1 0i < i 1B, i 2B i < i 1c, i 1 B i 2 B, i 1c i 2 c, = n 1 n 2 n 2 1 + n 2 2. 18.,,?,,,,..,. ( ),,.,,.,,,.( ),,.,,. 260
, a b A(e) i ( i + i)(z - 30 ),., ( ).,,.,,,,.,,. Z - 30,,? : i a b A,, Z - 30. ( i = 10), i 1 2 n e (, M., E. ). l = 25 cm, D = 0.25 cm, 261
i D l = 110-2 rad.n = 1.50,= 550 nm, e n ( 2i) 2 2.0 mm.,,.,,,.,, 2 mm ( ),,.,?, :,,., ( 400760) nm, = 550 nm, 150 nm, m = 2 ( ), m = 2 = 5502 150 nm2 m., 2 en m.n = 1.50, e m 0.7 m. 2 n :,,.,, ( ), ;,, ( ), ( ) ;,.., 262
,.,,,,,. 19.,.,,.,,.,,,.,,,.,? : d, ( ) f, n, n = 1.,.,, nsin = n sin, = n.,, 263
= n= 1. 22 n = 1.22 d d,., d = 2.5 mm, = 550 nm, 1., l = 25 cm, y = l0.1 mm..z - 31,,,., :,,. D, Z - 31 264
R = 1.22 D,, R = 1 = R D 1. 22. M = R, R, R ( ),, = R, M = R = = D R R d., ( ) M, ; M,,,., M.,, y., Z - 32, y y, y y ( ),., : nysin u = ny sin u,, n= 1, u., y= 0.61 sin u. 265
Z - 32 y = ny sin u = 0. 61 nsin u N.A.= nsin u. = 0. 61 nsin u N.A.. y, R = 1 y = N.A. 0.61. M : y y, M = y y = yn.a. 0. 61., y = 0.1 mm, = 550 nm,, M300N.A.. ( ) ( 500 1000 ) N.A.,,,,. 20., ( ),. : h= 1 2 m v2 m + A, A, 1 2 mv2 m 266
.,, h A, 0 = A h. h,.., h 0, n ( ) nh?, nh= 1 2 m v2 m + A, n..,,,,,., 10 24,.,,. 1960,. 1964 1975,.,,,. (): (1 ) n,. (2 ) n, nh= 267
1 2 m v2 m + A,. (3 )...,.,.,.,,,,.( ), ( ) 410-1 9 J, 2.510-19 J 2.710-19 J,,.,..,,,,., 5.110-1 9 J,.,,.,,.,..,,, ( ).. 268