Question

9£®ÈçͼËùʾ£¬ÖÊÁ¿Îªm¡¢µç×èΪRµÄµ¥ÔѾØÐÎÏß¿òÖÃÓڹ⻬ˮƽÃæÉÏ£¬Ïß¿ò±ß³¤ab=L¡¢ad=2L£®ÐéÏßMN¹ýad¡¢bc±ßÖе㣮һ¸ùÄܳÐÊÜ×î´óÀ­Á¦F₀µÄϸÏßÑØˮƽ·½Ïò˩סab±ßÖеãO£®´Óijʱ¿ÌÆð£¬ÔÚMNÓÒ²à¼ÓÒ»·½ÏòÊúÖ±ÏòϵÄÔÈÇ¿´Å³¡£¬´Å¸ÐӦǿ¶È´óС°´B=ktµÄ¹æÂɾùÔȱ仯£®Ò»¶Îʱ¼äºó£¬Ï¸Ïß±»À­¶Ï£¬Ïß¿òÏò×óÔ˶¯£¬ab±ß´©³ö´Å³¡Ê±µÄËÙ¶ÈΪv£®Çó£º
£¨1£©Ï¸Ï߶ÏÁÑÇ°Ïß¿òÖеĵ繦ÂÊP£»
£¨2£©Ï¸Ï߶ÏÁѺó˲¼äÏß¿òµÄ¼ÓËٶȴóСa¼°Ïß¿òÀ뿪´Å³¡µÄ¹ý³ÌÖа²ÅàÁ¦Ëù×öµÄ¹¦W£»
£¨3£©Ïß¿ò´©³ö´Å³¡¹ý³ÌÖÐͨ¹ýµ¼Ïß½ØÃæµÄµçÁ¿q£®

Answer 1

·ÖÎö £¨1£©¸ù¾Ý·¨À­µÚµç´Å¸ÐÓ¦¶¨ÂÉÓëµç¹¦Âʱí´ïʽ£¬¼´¿ÉÇó½â£»
£¨2£©ÒÀ¾ÝÅ£¶ÙµÚ¶þ¶¨ÂÉÓ붯Äܶ¨Àí£¬¼´¿ÉÇó½â£»
£¨3£©ÒÀ¾Ý°²ÅàÁ¦±í´ïʽ£¬½áºÏ±ÕºÏµç·ŷķ¶¨ÂÉ£¬¼°µçÁ¿±í´ïʽ£¬¼´¿ÉÇó½â£®

½â´ð ½â£º£¨1£©¸ù¾Ý·¨À­µÚ¶¨ÂÉ£ºE=$\frac{¡÷∅}{¡÷t}$=$\frac{¡÷B}{¡÷t}{L}^{2}$=kL²£»  
µç¹¦ÂÊ£ºP=$\frac{{E}^{2}}{R}$=$\frac{{k}^{2}{L}^{4}}{R}$  
£¨2£©Ï¸Ï߶ÏÁÑ˲¼ä°²ÅàÁ¦£ºF_A=F₀£¬Ïß¿òµÄ¼ÓËÙ¶Èa=$\frac{{F}_{A}}{m}$=$\frac{{F}_{0}}{m}$  
Ïß¿òÀ뿪´Å³¡¹ý³ÌÖУ¬Óɶ¯Äܶ¨Àí£ºW=$\frac{1}{2}$mv²£»
£¨3£©ÉèϸÏ߶ÏÁÑʱ¿Ì´Å¸ÐӦǿ¶ÈΪB₁£¬ÔòÓУºILB₁=F₀£¬
ÆäÖÐI=$\frac{E}{R}$=$\frac{k{L}^{2}}{R}$  
ÏßȦ´©³ö´Å³¡¹ý³Ì£º$\overline{E}$=$\frac{¡÷∅}{¡÷t}$=$\frac{{B}_{1}{L}^{2}}{¡÷t}$  
µçÁ÷$\overline{I}$=$\frac{\overline{E}}{R}$ 
ͨ¹ýµÄµçÁ¿£ºq=$\overline{I}$¡÷t  
½âµÃ£ºq=$\frac{{F}_{0}}{kL}$ 
´ð£º£¨1£©Ï¸Ï߶ÏÁÑÇ°Ïß¿òÖеĵ繦ÂÊ$\frac{{k}^{2}{L}^{4}}{R}$£»
£¨2£©Ï¸Ï߶ÏÁѺó˲¼äÏß¿òµÄ¼ÓËٶȴóС$\frac{{F}_{0}}{m}$¼°Ïß¿òÀ뿪´Å³¡µÄ¹ý³ÌÖа²ÅàÁ¦Ëù×öµÄ¹¦$\frac{1}{2}$mv²£»
£¨3£©Ïß¿ò´©³ö´Å³¡¹ý³ÌÖÐͨ¹ýµ¼Ïß½ØÃæµÄµçÁ¿$\frac{{F}_{0}}{kL}$£®

µãÆÀ ¿¼²é·¨À­µÚµç´Å¸ÐÓ¦¶¨ÂÉ£¬Óë±ÕºÏµç·ŷķ¶¨ÂÉ£¬¼°°²ÅàÁ¦±í´ïʽµÄÄÚÈÝ£¬×¢Òâ»áÍƵ¼µçÁ¿×ۺϱí´ïʽ£¬Àí½â¶¯Äܶ¨ÀíµÄÔËÓã®