Question

16£®ÈçͼËùʾ£¬×ø±ê¿Õ¼äÖÐÓг¡Ç¿ÎªE=$\frac{{m{v_0}^2}}{qL}$µÄÔÈÇ¿µç³¡ºÍ´Å¸ÐӦǿ¶ÈΪBµÄÔÈÇ¿´Å³¡£¬xÖÐΪÁ½ÖÖ³¡µÄ·Ö½çÃ棬ͼÖÐÐéÏßΪ´Å³¡ÇøÓòµÄÉϱ߽磬ÏÖÓÐÒ»ÊøÖÊÁ¿Îªm£¬µçºÉÁ¿ÎªqµÄ´øÕýµçÁ£×Ӵӵ糡ÖÐ×ø±êλÖã¨O£¬-L£©´¦£¬ÒÔ³õËÙ¶ÈV₀ÑØyÖáÕý·½Ïò¿ªÊ¼Ô˶¯£¬²»¼ÆÁ£×ÓÖØÁ¦£¬ÒÑÖªÁ¿Îª£ºm¡¢q¡¢V₀¡¢B¡¢L£¬Çó£º
£¨1£©´øµçÁ£×ÓµÚÒ»´ÎÔ˶¯µ½xÖáʱµÄËٶȴóСºÍ·½Ïò£®
£¨2£©ÒªÊ¹´øµçÁ£×ÓÄÜ´©Ô½´Å³¡ÇøÓò¶ø²»ÔÙ·µ»Øµ½µç³¡Öдų¡µÄ¿í¶Èd×î´óΪ¶àÉÙ£¿
£¨3£©ÔÚÁ£×ÓµÚÒ»´ÎÔ˶¯µ½xÖá´¦ÉèÖÃÒ»¸öËÙ¶ÈÉ¢ÉäÆ÷C£¬É¢ÉäÆ÷C²»¸Ä±äÁ£×ÓËٶȴóС£¬¿ÉʹÁ£×ÓËٶȷ½Ïò±ä³ÉÈÎÒâ·½Ïò£¬¶ÔÓÚ½øÈë¸Ã´Å³¡ÖеÄÁ£×Ó£¬Ö»¿¼ÂÇÔÚÖ½ÃæÄڵĸ÷ÖÖÈëÉä·½Ïò£¬Èô´Å³¡¿í¶ÈΪD=$\frac{{\sqrt{2}}}{Bq}m{v_0}$£¬ÓÐһЩÁ£×ÓÄܴӴų¡Éϱ߽ç·É³ö£¬ÇóÆä´©Ô½´Å³¡µÄ×î¶Ìʱ¼ä£®

Answer 1

·ÖÎö £¨1£©Á£×ÓÔڵ糡ÖÐ×öÀàƽÅ×Ô˶¯£¬¸ù¾ÝÑØyÖá·½Ïò×öÔÈËÙÖ±ÏßÔ˶¯Çó³öÔڵ糡ÖеÄÔ˶¯Ê±¼ä£¬½áºÏËÙ¶Èʱ¼ä¹«Ê½ºÍÅ£¶ÙµÚ¶þ¶¨ÂÉÇó³öÑØxÖá·½ÏòÉϵķÖËٶȣ¬Í¨¹ýƽÐÐËıßÐζ¨ÔòÇó³öËٶȵĴóСºÍ·½Ïò£®
£¨2£©¸ù¾Ý°ë¾¶¹«Ê½Çó³öÁ£×ÓÔڴų¡ÖÐÔ˶¯µÄ¹ìµÀ°ë¾¶£¬×¥×¡ÁÙ½çÇé¿ö£¬½áºÏ¼¸ºÎ¹ØϵÇó³ödµÄ×î´óÖµ£»
£¨3£©Ôڴų¡Öиù¾ÝÂåÂ××ÈÁ¦ÌṩÏòÐÄÁ¦£¬ÁÐʽȡ³ö°ë¾¶£¬»­³ö¹ì¼£Ô²»¡£¬¸ù¾Ý¼¸ºÎ¹ØϵÇó³öÔ²»¡Ëù¶ÔÓ¦µÄÔ²ÐĽǣ¬´Ó¶øÇó³ö¶ÔÓ¦µÄ×î¶Ìʱ¼ä£®

½â´ð ½â£º£¨1£©Á£×ÓÔڵ糡ÖÐÔ˶¯µÄʱ¼äΪ£ºt=$\frac{L}{{v}_{0}}$£¬
µÚÒ»´ÎÔ˶¯µ½xÖáˮƽ·½ÏòÉϵķÖËÙ¶ÈΪ£º${v}_{x}=\frac{qE}{m}t$=$\frac{{v}_{0}^{2}}{L}•\frac{L}{{v}_{0}}$=v₀£¬
¸ù¾ÝƽÐÐËıßÐζ¨ÔòµÃ£ºv=$\sqrt{{v}_{x}^{2}+{v}_{0}^{2}}=\sqrt{2}{v}_{0}$
·½ÏòÓëxÖá³É45¶È½Ç£»
£¨2£©Á£×ÓÔڴų¡ÖÐÔ˶¯µÄ°ë¾¶Îª£ºr=$\frac{mv}{qB}=\frac{\sqrt{2}m{v}_{0}}{qB}$£¬
¸ù¾Ý¼¸ºÎ¹Øϵ֪£ºd=r+rsin45¡ã=$\frac{\sqrt{2}m{v}_{0}}{qB}$£¨1$+\frac{\sqrt{2}}{2}$£©
£¨3£©Á£×ÓÔڴų¡ÖÐÔ²ÖÜÔ˶¯µÄʱ¼ät=$\frac{¦È}{2¦Ð}T$£¬ÒªÊ¹Á£×ÓÔ˶¯Ê±¼ä×î¶Ì£¬ÊÇ¿ÉÖª£¬¶ÔÓ¦Ô²ÖܽǦÈ×îС£¬Óɼ¸ºÎ¹Øϵ×÷³öÁ£×ÓµÄÔ˶¯¹ì¼£ÈçͼËùʾ

¸ù¾ÝÂåÂ××ÈÁ¦ÌṩԲÖÜÔ˶¯ÏòÐÄÁ¦£¬ÓУº$q{v}_{0}B=m\frac{{v}_{0}^{2}}{R}$
¿ÉµÃÁ£×ÓÔ²ÖÜÔ˶¯µÄ°ë¾¶Îª£ºR=$\frac{m{v}_{0}}{qB}$£¬Á£×ÓÔ˶¯µÄÖÜÆÚΪ£ºT=$\frac{2¦ÐR}{{v}_{0}}=\frac{2¦Ð\frac{m{v}_{0}}{qB}}{{v}_{0}}=\frac{2¦Ðm}{qB}$
Èçͼ£¬Á£×ÓÔڴų¡ÖÐÔ˶¯µÄʱ¼ä×î¶Ì£¬¶ÔÓ¦¼¸ºÎ¹ØϵÓУºd=Rsin$\frac{¦È}{2}$
´úÈë$d=\frac{\sqrt{2}}{qB}m{v}_{0}$¿É½âµÃ£º$¦È=\frac{¦Ð}{2}$
ËùÒÔÁ£×ÓÔڴų¡ÖÐÔ˶¯µÄ×î¶Ìʱ¼äΪ£º${t}_{min}=\frac{¦È}{2¦Ð}T=\frac{\frac{¦Ð}{2}}{2¦Ð}•\frac{2¦Ðm}{qB}$=$\frac{¦Ðm}{2qB}$
´ð£º£¨1£©´øµçÁ£×ÓµÚÒ»´ÎÔ˶¯µ½xÖáʱµÄËٶȴóСΪ$\sqrt{2}{v}_{0}$ºÍ·½ÏòÓëˮƽ·½Ïò³É45¡ã½Ç£»
£¨2£©ÒªÊ¹´øµçÁ£×ÓÄÜ´©Ô½´Å³¡ÇøÓò¶ø²»ÔÙ·µ»Øµ½µç³¡Öдų¡µÄ¿í¶Èd×î´óΪ$\frac{\sqrt{2}m{v}_{0}}{qB}$£¨1$+\frac{\sqrt{2}}{2}$£©£»
£¨3£©´©Ô½´Å³¡µÄ×î¶Ìʱ¼äΪ$\frac{¦Ðm}{2qB}$£®

µãÆÀ ±¾Ì⿼²éÁË´øµçÁ£×ÓÔڵ糡ºÍ´Å³¡ÖеÄÔ˶¯£¬ÕÆÎÕ´¦ÀíÀàƽÅ×Ô˶¯µÄ·½·¨£¬ÒÔ¼°ÕÆÎÕÁ£×ÓÔڴų¡ÖÐÔ˶¯µÄ°ë¾¶¹«Ê½£¬½áºÏ¼¸ºÎ¹Øϵ½øÐÐÇó½â£®