Question

12£®ÈçͼËùʾ£¬Õý·½ÐÎÈÝÆ÷´¦ÓÚÔÈÇ¿´Å³¡ÖУ¬Ò»Êøµç×Ó´Ó¿×a´¹Ö±Óڴų¡ÑØab·½ÏòÉäÈëÈÝÆ÷ÖУ¬ÆäÖÐÒ»²¿·Ö´Óc¿×Éä³ö£¬Ò»²¿·Ö´Ód¿×Éä³ö£¬ÈÝÆ÷´¦ÓÚÕæ¿ÕÖУ¬ÔòÏÂÁнáÂÛÖÐÕýÈ·µÄÊÇ£¨¡¡¡¡£©

• A£® ´ÓÁ½¿×Éä³öµÄµç×ÓËÙÂÊÖ®±Èv_c£ºv_d=2£º1
• B£® ´ÓÁ½¿×Éä³öµÄµç×ÓÔÚÈÝÆ÷ÖÐÔ˶¯µÄʱ¼äÖ®±Èt_c£ºt_d=1£º2
• C£® ´ÓÁ½¿×Éä³öµÄµç×ÓÔÚÈÝÆ÷ÖÐÔ˶¯µÄ¼ÓËٶȴóС֮±Èa_c£ºa_d=$\sqrt{2}$£º1
• D£® ´ÓÁ½¿×Éä³öµÄµç×ÓÔÚÈÝÆ÷ÖÐÔ˶¯µÄ½ÇËÙ¶ÈÖ®±È¦Ø_c£º¦Ø_d=2£º1

Answer 1

·ÖÎö ´øµçÁ£×ÓÔÚÔÈÇ¿´Å³¡ÖÐ×öÔÈËÙÔ²ÖÜÔ˶¯£¬ÂåÂ××ÈÁ¦ÌṩÏòÐÄÁ¦£¬ÓÐBqv=m$\frac{{v}^{2}}{r}$£¬µÃ³ö°ë¾¶¹«Ê½r=$\frac{mv}{qB}$£¬¸ù¾Ý°ë¾¶¹ØϵµÃ³öÁ£×ÓµÄËٶȹØϵ£®ÔÙ¸ù¾Ý¼ÓËٶȹ«Ê½¿ÉÈ·¶¨Ô˶¯µÄ¼ÓËÙ¶ÈÖ®±È£®
´øµçÁ£×ÓÔËÐеÄÖÜÆÚT=$\frac{2¦Ðm}{qB}$£¬¸ù¾ÝÔ²ÐĽÇÇó³öÔËÐÐʱ¼ät=$\frac{¦È}{2¦Ð}$T£®´Ó¶øÇó³öÔ˶¯Ê±¼äÖ®±È£®

½â´ð ½â´ð£º½â£ºÉè´Å³¡±ß³¤Îªa£¬ÈçͼËùʾ£¬Á£×Ó´ÓcµãÀ뿪£¬Æä°ë¾¶Îªr_c£¬Á£×Ó´ÓdµãÀ뿪£¬Æä°ë¾¶Îªr_d£»

A¡¢ÓÉBqv=m$\frac{{v}^{2}}{r}$£¬µÃ³ö°ë¾¶¹«Ê½r=$\frac{mv}{qB}$£¬ÓÖÓÉÔ˶¯¹ì¼£Öª  r_c=2r_d  Ôòv_c£ºv_d=2£º1£¬¹ÊAÕýÈ·£»        
B¡¢ÓÉT=$\frac{2¦Ðm}{qB}$£¬¸ù¾ÝÔ²ÐĽÇÇó³öÔËÐÐʱ¼ät=$\frac{¦È}{2¦Ð}$T£®ÔËÐÐʱ¼ä t_d=$\frac{T}{2}$£¬t_c=$\frac{T}{4}$£®Ôòt_c£ºt_d=1£º2£¬¹ÊBÕýÈ·£®
C¡¢ÏòÐļÓËٶȣºa=$\frac{{v}^{2}}{r}$£¬Ôòa_c£ºa_d=2£º1£¬¹ÊC´íÎó£»
D¡¢¼ÓËٶȣº¦Ø=$\frac{¦È}{t}$£¬$\frac{{¦Ø}_{c}}{{¦Ø}_{d}}$=$\frac{\frac{\frac{¦Ð}{4}}{{t}_{c}}}{\frac{\frac{¦Ð}{2}}{{t}_{d}}}$=$\frac{{t}_{d}}{2{t}_{c}}$=1£º1£¬¹ÊD´íÎó£»
¹ÊÑ¡£ºAB£®

µãÆÀ ±¾ÌâÊôÓÚ´øµçÁ£×ÓÔڴų¡ÖеÄƫתÖеäÐÍÌâÄ¿£¬´ËÀàÌâµÄ¹Ø¼üÔÚÓÚÈ·¶¨Ô²Ðļ°Óɼ¸ºÎ¹ØϵÇó³ö°ë¾¶£®ÕÆÎÕ´øµçÁ£×ÓÔÚÔÈÇ¿´Å³¡ÖÐ×öÔÈËÙÔ²ÖÜÔ˶¯µÄ°ë¾¶¹«Ê½r=$\frac{mv}{qB}$£¬ºÍÖÜÆÚ¹«Ê½T=$\frac{2¦Ðm}{qB}$£®