Question

4£®ÖÊÆ×ÒÇÊÇÓÃÀ´²â¶¨´øµçÁ£×ÓÖÊÁ¿ºÍ·ÖÎöͬλËصÄÖØÒª¹¤¾ß£¬ÈçͼËùʾ£¬µçÈÝÆ÷Á½¼«°åÏà¾àΪd£¬Á½°å¼äµçѹΪU£¬¼«°å¼äÔÈÇ¿´Å³¡µÄ´Å¸ÐӦǿ¶ÈΪB₁£¬·½Ïò´¹Ö±Ö½ÃæÏòÍ⣮һÊøµçºÉµçÁ¿Ïàͬ¡¢ÖÊÁ¿²»Í¬µÄ´øÕýµçµÄÁ£×Ó£¬ÑصçÈÝÆ÷µÄÖÐÏßƽÐÐÓÚ¼«°åÉäÈëµçÈÝÆ÷£¬ÑØÖ±ÏßÔÈËÙ´©¹ýµçÈÝÆ÷ºó½øÈëÁíÒ»´Å¸ÐӦǿ¶ÈΪB₂µÄÔÈÇ¿´Å³¡£¬´Å³¡·½Ïò´¹Ö±Ö½ÃæÏòÍ⣮½á¹û·Ö±ð´òÔڸйâƬÉϵÄa¡¢bÁ½µã£¬Éèa¡¢bÁ½µãÖ®¼ä¾àÀëΪ¡÷x£¬Á£×ÓËù´øµçºÉÁ¿Îªq£¬ÇÒ²»¼ÆÖØÁ¦£¬Çó£º
£¨1£©Á£×ÓÔڴų¡B₁ÖÐÖ±ÏßÔ˶¯Ê±ËÙ¶ÈvµÄ´óС£¿
£¨2£©´òÔÚa¡¢bÁ½µãµÄÁ£×ÓµÄÖÊÁ¿Ö®²î¡÷m£¿

Answer 1

·ÖÎö £¨1£©¸ù¾ÝÁ£×Ó×öÔÈËÙÖ±ÏßÔ˶¯£¬¿ÉÅжÏÁ£×ӵĵ糡Á¦ºÍÂåÂ××ÈÁ¦ÏàµÈ£¬¼´¿ÉµÃÖªÁ£×ÓµÄËٶȣ®
£¨2£©´øµçÁ£×ÓÔÚÔÈÇ¿´Å³¡B₂ÖÐ×öÔÈËÙÔ²ÖÜÔ˶¯£¬ÓÉÂåÂ××ÈÁ¦ÌṩÏòÐÄÁ¦£¬½áºÏ¼¸ºÎ¹Øϵ¼´¿ÉÇó³öÁ½µãµÄÁ£×ÓµÄÖÊÁ¿Ö®²î¡÷m£®

½â´ð ½â£º£¨1£©Á½¼«°å¼äµç³¡Ç¿¶È£ºE=$\frac{U}{d}$
Á£×ÓËùÊܵ½µç³¡Á¦ºÍÂåÂ××ÈÁ¦ÊÇƽºâÁ¦£¬¼´Îª£ºqvB₁=qE£¬
ËùÒԵ糡Óë´Å³¡µÄ¹ØϵΪ£ºv=$\frac{E}{{B}_{1}}$=$\frac{U}{d{B}_{1}}$£»
£¨2£©´øµçÁ£×ÓÔÚÔÈÇ¿´Å³¡B₂ÖÐ×öÔÈËÙÔ²ÖÜÔ˶¯£¬
Ôò£º$qv{B}_{2}=\frac{m{v}^{2}}{r}$
´òÔÚa´¦µÄÁ£×ÓµÄÖÊÁ¿£º${m}_{1}=\frac{q{B}_{2}{r}_{1}}{v}$
´òÔÚb´¦µÄÁ£×ÓµÄÖÊÁ¿£º${m}_{2}=\frac{q{B}_{2}{r}_{2}}{v}$
ÓÖ¡÷x=2r₁-2r₂
ÁªÁ¢µÃ£º¡÷m=m₁-m₂=$\frac{q{B}_{2}¡÷x}{2v}=\frac{q{B}_{1}{B}_{2}d¡÷x}{2U}$
´ð£º£¨1£©Á£×ÓÔڴų¡B₁ÖÐÖ±ÏßÔ˶¯Ê±ËÙ¶ÈvµÄ´óСÊÇ$\frac{U}{d{B}_{1}}$£»
£¨2£©´òÔÚa¡¢bÁ½µãµÄÁ£×ÓµÄÖÊÁ¿Ö®²î¡÷mÊÇ$\frac{q{B}_{1}{B}_{2}d¡÷x}{2U}$£®

µãÆÀ ÔÚËÙ¶ÈÑ¡ÔñÆ÷ÖУ¬Á£×ÓµÄÊÜÁ¦Ìص㣺ͬʱÊܵ½·½ÏòÏà·´µÄµç³¡Á¦ºÍÂåÂ××ÈÁ¦×÷Óã»Á£×ÓÄÜÔÈËÙͨ¹ýÑ¡ÔñÆ÷µÄÌõ¼þ£ºµç³¡Á¦ºÍÂåÂ××ÈÁ¦Æ½ºâ£¬Ö»ÓÐËÙ¶ÈΪ$\frac{E}{B}$ µÄÁ£×Ó²ÅÄÜÑØÖ±ÏßÔÈËÙͨ¹ýÑ¡ÔñÆ÷£®