µç¶¯Á¦Ñ§¿¼ÊÔÖصã ÁªÏµ¿Í·þ

·¢²¼Ê±¼ä : ÐÇÆÚËÄ ÎÄÕµ綯Á¦Ñ§¿¼ÊÔÖصã¸üÐÂÍê±Ï¿ªÊ¼ÔĶÁca8a061daaea998fcc220e90

Á·Ï°Ìâ

£¨Ò»£© µ¥Ñ¡Ì⣨ÔÚÌâ¸ÉºóµÄÀ¨ºÅÄÚÌîÉÏÕýÈ·Ñ¡ÏîÇ°µÄÐòºÅ£¬Ã¿Ìâ1·Ö£© 1£®¸ß˹¶¨Àí

???dS=

s????Q?0ÖеÄQÊÇ £¨ £©

¢Ù ±ÕºÏÇúÃæSÍâµÄ×ܵçºÉ ¢Ú ±ÕºÏÇúÃæSÄÚµÄ×ܵçºÉ ¢Û ±ÕºÏÇúÃæSÍâµÄ×ÔÓɵçºÉ ¢Ü ±ÕºÏÇúÃæSÄÚµÄ×ÔÓɵçºÉ 2£®¸ß˹¶¨Àí

?s??dS=

Q?0ÖеÄEÊÇ

? ( )

¢Ù ÇúÃæSÍâµÄµçºÉ²úÉúµÄµç³¡Ç¿¶È ¢Ú ÇúÃæSÄڵĵçºÉ²úÉúµÄµç³¡Ç¿¶È ¢Û ¿Õ¼äËùÓеçºÉ²úÉúµÄµç³¡Ç¿¶È ¢Ü ¿Õ¼äËùÓо²Ö¹µçºÉ²úÉúµÄµç³¡Ç¿¶È

3£®ÏÂÁÐÄÄÒ»¸ö·½³Ì²»ÊôÓÚ¸ß˹¶¨Àí £¨ ¢Ù

????d?S=

Qs? ¢Ú

0???1S??dS=

?dV?

0?V???¢Û ¨Œ?E=-?B??t ¢Ü??E=?? 04.¶Ôµç³¡¶øÑÔÏÂÁÐÄÄÒ»¸ö˵·¨ÕýÈ· £¨ ¢Ù ¿âÂض¨ÂÉÊÊÓÃÓڱ仯µç´Å³¡ ¢Ú µç³¡²»¾ß±¸µþ¼ÓÐÔ ¢Û µç³¡¾ßÓеþ¼ÓÐÔ ¢Ü µç³¡µÄÉ¢¶ÈºãΪÁã

5£®¾²µç³¡·½³Ì ?E??d?Ll= 0 £¨ ¢Ù ½öÊÊÓÃÓÚµãµçºÉÇé¿ö ¢Ú ÊÊÓÃÓڱ仯µç´Å³¡ ¢Û L½öΪ³¡ÖÐÒ»ÌõÈ·¶¨µÄ»Ø· ¢Ü LΪ³¡ÖÐÈÎÒ»±ÕºÏ»Ø·

?6£®¾²µç³¡·½³Ì¨Œ?E= 0 ( )

¢Ù ±íÃ÷¾²µç³¡µÄÎÞÐýÐÔ ¢Ú ÊÊÓÃÓڱ仯µç´Å³¡ ¢Û ±íÃ÷¾²µç³¡µÄÎÞÔ´ÐÔ ¢Ü ½ö¶Ô³¡Öиö±ðµã³ÉÁ¢

7£®¶ÔµçºÉÊغ㶨ÂÉÏÂÃæÄÄÒ»¸ö˵·¨³ÉÁ¢ ( )

¢Ù Ò»¸ö±ÕºÏÃæÄÚ×ܵçºÉ±£³Ö²»±ä ¢Ú ½ö¶ÔÎȺãµçÁ÷³ÉÁ¢ ¢Û ¶ÔÈÎÒâ±ä»¯µçÁ÷³ÉÁ¢ ¢Ü ½ö¶Ô¾²Ö¹µçºÉ³ÉÁ¢ ??B?d?8£®°²Å໷·¶¨Àí

Ll= ?0I ÖеÄ?Ϊ £¨ ¢Ù ͨ¹ýLËùΧÃæµÄ×ܵçÁ÷ ¢Ú ²»°üÀ¨Í¨¹ýLËùΧÇúÃæµÄ×ܵçÁ÷ ¢Û ͨ¹ýLËùΧÇúÃæµÄ´«µ¼µçÁ÷ ¢Ü ÒÔÉÏ˵·¨¶¼²»¶Ô

9£®ÔÚ¼Ù¶¨´ÅºÉ²»´æÔÚµÄÇé¿öÏ£¬ÎȺãµçÁ÷´Å³¡ÊÇ £¨ ¢Ù ÎÞÔ´ÎÞÐý³¡ ¢Ú ÓÐÔ´ÎÞÐý³¡ ¢ÛÓÐÔ´ÓÐÐý³¡ ¢Ü ÎÞÔ´ÓÐÐý³¡

10£®¾²µç³¡ºÍ¾²´Å³¡£¨¼´ÎȺãµçÁ÷´Å³¡£©µÄ¹ØϵΪ £¨ ¢Ù ¾²µç³¡¿Éµ¥¶À´æÔÚ£¬¾²´Å³¡Ò²¿Éµ¥¶À´æÔÚ ¢Ú ¾²µç³¡²»¿Éµ¥¶À´æÔÚ£¬¾²´Å³¡¿Éµ¥¶À´æÔÚ ¢Û ¾²µç³¡¿Éµ¥¶À´æÔÚ£¬¾²´Å³¡²»¿Éµ¥¶À´æÔÚ ¢Ü ¾²µç³¡²»µ¥¶À´æÔÚ£¬¾²´Å³¡Ò²²»¿Éµ¥¶À´æÔÚ

£©

£©

£©

£©

£©

£©11£®ÏÂÃæÄÄÒ»¸ö·½³ÌÊÊÓÃÓڱ仯µç´Å³¡ £¨ £©

¢Ù ¨Œ?B=?0J ¢Ú¨Œ?E=0 ¢Û??B=0 ¢Ü ??E=0

12£®ÏÂÃæÄÄÒ»¸ö·½³Ì²»ÊÊÓÃÓڱ仯µç´Å³¡ £¨ £©

???B?¢Ù ¨Œ?B=?0J ¢Ú¨Œ?E=- ¢Û¨Œ?B=0 ¢Ü ¨Œ?E=

?t?0?????????13£®Í¨¹ý±ÕºÏÇúÃæSµÄµç³¡Ç¿¶ÈµÄͨÁ¿µÈÓÚ ( )

¢Ù

?V?????(??E)dV ¢Ú?(??E)?dl ¢Û ?(??E)dV ¢Ü?(??E)dS

LVS14£®Í¨¹ý±ÕºÏÇúÃæSµÄ´Å¸ÐӦǿ¶ÈµÄͨÁ¿µÈÓÚ ( )

¢Ù

?V(??B?)dV ¢Ú ?(??B?)?dl? ¢Û ?B??dS? ¢Ü 0

LS15£®µç³¡Ç¿¶ÈÑرպÏÇúÏßLµÄ»·Á¿µÈÓÚ ( )

¢Ù

?(??E?)dV ¢Ú ?????VS(??E)?dS ¢Û?V(??E)dV ¢Ü?S(??E)dS

16.´Å¸ÐӦǿ¶ÈÑرպÏÇúÏßLµÄ»·Á¿µÈÓÚ ( )

¢Ù ????????L(??B)?dl ¢Ú ?S(??B)?dS ¢Û?SB?dS ¢Ü?V(??B)dV

17. λÖÃʸÁ¿r?µÄÉ¢¶ÈµÈÓÚ ( )

¢Ù0 ¢Ú3 ¢Û1 ¢Ür

18.λÖÃʸÁ¿r?rµÄÐý¶ÈµÈÓÚ ( )

??¢Ù0 ¢Ú3 ¢Ûrrr ¢Ür3

19.λÖÃʸÁ¿´óСrµÄÌݶȵÈÓÚ? ( )

?¢Ù0 ¢Ú 1rrr ¢Û r ¢Ür3

20.?(a??r?)=? (ÆäÖÐa?Ϊ³£Ê¸Á¿) ( )

?¢Ù r? ¢Ú 0 ¢Û rr ¢Üa?

21.?1r=£¿ ( )

??¢Ù 0 ¢Ú -r ¢Û r?3 ¢Ü r?rr

22.?? rr3=£¿ ( )

?¢Ù 0 ¢Ú rr ¢Û r? ¢Ü1r

23.?? r?r3=£¿£¨ÆäÖÐr?0£© ( )

¢Ù0 ¢Ú 1 ¢Û r ¢Ü1

24.??[E?sin(k?????r0¢ÙE??sin(k?r)] µÄֵΪ£¨ÆäÖÐE0ºÍkΪ³£Ê¸Á¿£© ( )

?r?)¢ÚE????????????0?k0?rcos(k?r)¢ÛE0?kcos(k?r)¢ÜE0?rsin(k?r25. ??[E?sin(k??r)]µÄֵΪ£¨ÆäÖÐE?)

??00ºÍkΪ³£Ê¸Á¿£© ( )

2

????????????????¢Ùk?E0sin(k?r)¢ÚE0?rcos(k?r)¢Ûk?E0cos(k?r)¢ÜE0?ksin(k?r)

26.¶ÔÓÚ¸ÐÓ¦µç³¡ÏÂÃæÄÄÒ»¸ö˵·¨ÕýÈ· ( )

¢Ù¸ÐÓ¦µç³¡µÄÐý¶ÈΪÁã ¢Ú¸ÐÓ¦µç³¡É¢¶È²»µÈÓÚÁã

¢Û¸ÐÓ¦µç³¡ÎªÎÞÔ´ÎÞÐý³¡ ¢Ü¸ÐÓ¦µç³¡Óɱ仯´Å³¡¼¤·¢

27.λÒƵçÁ÷ ( )

¢ÙÊÇÕæʵµçÁ÷£¬°´´«µ¼µçÁ÷µÄ¹æÂɼ¤·¢´Å³¡ ¢ÚÓë´«µ¼µçÁ÷Ò»Ñù£¬¼¤·¢´Å³¡ºÍ·Å³ö½¹¶úÈÈ ¢ÛÓë´«µ¼µçÁ÷Ò»Æ𹹳ɱպϻ·Á¿£¬ÆäÉ¢¶Èºã²»ÎªÁã ¢ÜʵÖÊÊǵ糡Ëæʱ¼äµÄ±ä»¯ÂÊ

28.λÒƵçÁ÷ºÍ´«µ¼µçÁ÷ ( )¶¨ÏòÒƶ¯µÄ½á¹û ¢Ú¾ù¿ÉÒÔ²úÉú½¹¶úÈÈ

¢Û¾ù¿ÉÒÔ²úÉú»¯Ñ§Ð§Ó¦ ¢Ü¾ù¿ÉÒÔ²úÉú´Å³¡

29.ÏÂÁÐÄÄÖÖÇé¿öÖеÄλÒƵçÁ÷±ØȻΪÁã ( )

¢Ù·Ç±ÕºÏ»Ø· ¢Úµ±µç³¡²»Ëæʱ¼ä±ä»¯Ê± ¢ÛÔÚ¾øÔµ½éÖÊÖÐ ¢ÜÔÚµ¼ÌåÖÐ

30.ÂóÊÏ·½³ÌÖÐ??E????B??tµÄ½¨Á¢ÊÇÒÀ¾ÝÄÄÒ»¸öʵÑ鶨ÂÉ ( )

¢ÙµçºÉÊغ㶨ÂÉ ¢Ú°²ÅඨÂÉ ¢Ûµç´Å¸ÐÓ¦¶¨ÂÉ ¢Ü¿âÂض¨ÂÉ

31.Âó¿Ë˹Τ·½³Ì×éʵ¼ÊÉÏÊǼ¸¸ö±êÁ¿·½³Ì ( ) ¢Ù4¸ö ¢Ú6¸ö ¢Û8¸ö ¢Ü10¸ö

32.´ÓÂó¿Ë˹Τ·½³Ì×é¿ÉÖª±ä»¯µç³¡ÊÇ ( )

¢ÙÓÐÔ´ÎÞÐý³¡ ¢ÚÓÐÔ´ÓÐÐý³¡ ¢ÛÎÞÔ´ÓÐÐý³¡ ¢ÜÎÞÔ´ÎÞÐý³¡

33.´ÓÂó¿Ë˹Τ·½³Ì×é¿ÉÖª±ä»¯´Å³¡ÊÇ ( )

¢ÙÓÐÔ´ÎÞÐý³¡ ¢ÚÓÐÔ´ÓÐÐý³¡ ¢ÛÎÞÔ´ÓÐÐý³¡ ¢ÜÎÞÔ´ÎÞÐý³¡

34.ÏÂÁÐ˵·¨ÕýÈ·µÄÊÇ ( )

¢ÙÊø¸¿µçºÉÖ»³öÏÖÔڷǾùÔȽéÖʱíÃæ ¢ÚÊø¸¿µçºÉÖ»³öÏÖÔÚ¾ùÔȽéÖʱíÃæ ¢Û½éÖʽçÃæÉϲ»»á³öÏÖÊø¸¿µçºÉ ¢ÜÒÔÉÏ˵·¨¶¼²»¶Ô

35.½éÖʵľùÔȼ«»¯ÊÇÖ¸ ( )

¢Ù¾ùÔȽéÖʵļ«»¯ ¢ÚÏßÐÔ½éÖʵļ«»¯

¢Û¸÷ÏòͬÐÔ½éÖʵļ«»¯ ¢Ü½éÖÊÖд¦´¦¼«»¯Ê¸Á¿Ïàͬ 36.Êø¸¿µçºÉÌåÃܶȵÈÓÚ¢Ù0 ¢Ú??P? ( )

¢Û-??P? ¢Ün??(P??2?P1)

37.Êø¸¿µçºÉÃæÃܶȵÈÓÚ¢Ù0 ¢Ú??P? ( )

¢Û-??P? ¢Ü-n??(P??2?P1) 38.¼«»¯µçÁ÷ÌåÃܶȵÈÓÚ ( )

¢Ù0 ¢Ú??M?? ¢Û??M? ¢Ü?P?t

39.´Å»¯µçÁ÷ÌåÃܶȵÈÓÚ ( )

3

¢Ù¾ùÊǵç×Ó

???????M¢Ù??M ¢Ú??M ¢Û ¢Ün?(M2?M1)

?t???40.B??0(H?M) ( ) ???41.D??0E?P ( )

¢Ù½öÊÊÓÃÓÚ¸÷ÏòͬÐÔ½éÖÊ ¢Ú½öÊÊÓÃÓÚ¾ùÔȽéÖÊ ¢ÛÊÊÓÃÓÚÈκνéÖÊ ¢Ü½öÊÊÓÃÓÚÏßÐÔ½éÖÊ ¢ÙÊÊÓÃÓÚÈκνéÖÊ ¢Ú½öÊÊÓÃÓÚ¾ùÔȽéÖÊ

¢Û½öÊÊÓÃÓÚÌú´Å½éÖÊ ¢Ü½öÊÊÓÃÓÚ¸÷ÏòͬÐÔ½éÖÊ

??B??H42. ( )

¢ÙÊÊÓÃÓÚÈκνéÖÊ ¢Ú½öÊÊÓÃÓÚ¸÷ÏòͬÐÔ½éÖÊ

¢Û½öÊÊÓÃÓÚÌú´Å½éÖÊ ¢Ü½öÊÊÓÃÓÚ¸÷ÏòͬÐÔ·ÇÌú´Å½éÖÊ

43.D???E? ( )

¢Ù½öÊÊÓÃÓÚ¸÷ÏòͬÐÔÏßÐÔ½éÖÊ ¢Ú½öÊÊÓÃÓڷǾùÔȽéÖÊ

¢ÛÊÊÓÃÓÚÈκνéÖÊ ¢Ü½öÊÊÓÃÓÚÌú´Å½éÖÊ

44.¶ÔÓÚ½éÖÊÖеĵç´Å³¡ ( )

¢Ù£¨E????¢Ú£¨D?£¬H£¬B?£©ÊÇ»ù±¾Á¿£¬£¨D£©ÊÇ»ù±¾Á¿£¬£¨E?£¬B£¬H?£©ÊǸ¨ÖúÁ¿

¢Û£¨E?£¬B?£©ÊÇ»ù±¾Á¿£¬£¨D?£¬H?£©ÊǸ¨ÖúÁ¿

£©ÊǸ¨ÖúÁ¿¢Ü£¨D?£¬H?£©ÊÇ»ù±¾Á¿£¬£¨E?£¬B?

£©ÊǸ¨ÖúÁ¿ 45. µç³¡Ç¿¶ÈÔÚ½éÖÊ·Ö½çÃæÉÏ ( )

¢Ù·¨Ïß·½ÏòÁ¬Ðø£¬ÇÐÏß·½Ïò²»Á¬Ðø ¢Ú·¨Ïß·½Ïò²»Á¬Ðø£¬ÇÐÏß·½Ïò²»Á¬Ðø ¢Û·¨Ïß·½ÏòÁ¬Ðø£¬ÇÐÏß·½ÏòÁ¬Ðø ¢Ü·¨Ïß·½Ïò²»Á¬Ðø£¬ÇÐÏß·½ÏòÁ¬Ðø 46.´Å¸ÐӦǿ¶ÈÔÚ½éÖÊ·Ö½çÃæÉÏ ( )

¢Ù·¨Ïß·½ÏòÁ¬Ðø£¬ÇÐÏß·½Ïò²»Á¬Ðø ¢Ú·¨Ïß·½Ïò²»Á¬Ðø£¬ÇÐÏß·½Ïò²»Á¬Ðø ¢Û·¨Ïß·½ÏòÁ¬Ðø£¬ÇÐÏß·½ÏòÁ¬Ðø ¢Ü·¨Ïß·½Ïò²»Á¬Ðø£¬ÇÐÏß·½ÏòÁ¬Ðø 47.µçλÒÆʸÁ¿ÔÚ½éÖÊ·Ö½çÃæÉϵķ¨Ïò·ÖÁ¿ ( )

¢ÙÁ¬Ðø ¢Ú?p?0ʱÁ¬Ðø ¢Û?f?0ʱÁ¬Ðø ¢ÜÈκÎÇé¿ö϶¼²»Á¬Ðø 48.´Å³¡Ç¿¶ÈÔÚ½éÖʵķֽçÃæÉϵÄÇÐÏò·ÖÁ¿ £¨ ¢ÙÁ¬Ðø ¢Ú??0ʱÁ¬Ðø ¢Û??f?M?0ʱÁ¬Ðø ¢ÜÈκÎÇé¿ö϶¼²»Á¬Ðø 49£®¹ØÓڴų¡µÄÄÜÁ¿ÏÂÃæÄÄÒ»ÖÖ˵·¨ÕýÈ· ( )

¢Ù³¡ÄÜÔÚ¿Õ¼ä·Ö²¼²»Ëæʱ¼ä±ä»¯ ¢Ú³¡Äܽö´æÔÚÓÚÓÐÏÞÇøÓò ¢Û³¡ÄÜ°´Ò»¶¨·½Ê½·Ö²¼ÓÚ³¡ÄÚ ¢Ü³¡Äܽö´æÔÚµ¼ÌåÖÐ

50.²£Ó¡Í¤Ê¸Á¿?¢ÙÖ»ÓëE?S ( )

´¹Ö± ¢ÚÖ»ÓëH?´¹Ö± ¢ÛÓëE?ºÍH?¾ù´¹Ö± ¢ÜÓëE?ºÍH?¾ù²»´¹Ö±

51£®ÔÚÎȺãµçÁ÷»òµÍƵ½»±äµçÁ÷Çé¿öÏ£¬µç´ÅÄÜÊÇ ( )

¢Ù ͨ¹ýµ¼ÌåÖеç×ӵĶ¨ÏòÒƶ¯Ïò¸ºÔØ´«µÝµÄ ¢Ú ͨ¹ýµç´Å³¡Ïò¸ºÔØ´«µÝµÄ ¢Û ÔÚµ¼ÏßÖд«²¥ ¢Ü ÏÖÔÚÀíÂÛ»¹²»ÄÜÈ·¶¨

52£®¾²µçÊƵÄÌÝ¶È £¨ ¢Ù ÊÇÎÞÔ´³¡ ¢Ú µÈÓڵ糡ǿ¶È ¢Û ÊÇÎÞÐý³¡ ¢ÜÊÇÒ»¸ö³£Ê¸Á¿ 53£®ÔÚ¾²µçÎÊÌâÖУ¬´øÓеçºÉµÄµ¼Ìå £¨ ¢ÙÄÚ²¿µç³¡²»ÎªÁã ¢Ú ±íÃæ²»´øµç ¢Û ±íÃæΪµÈÊÆÃæ ¢ÜÄÚ²¿Óо»µçºÉ´æÔÚ

4

£©

£©

£©