Question

8£®ÈçͼËùʾ£¬ÐéÏßMOÓëˮƽÏßPQÏཻÓÚO£¬¶þÕ߼нǦÈ=30¡ã£¬ÔÚMO×óÉϲà´æÔڵ糡ǿ¶ÈΪE¡¢·½ÏòÊúÖ±ÏòϵÄÔÈÇ¿µç³¡£¬MOÓÒϲàij¸öÇøÓò´æÔڴŸÐӦǿ¶ÈΪB¡¢´¹Ö±Ö½ÃæÏòÍâµÄÔÈÇ¿´Å³¡£¨Í¼ÖÐδ»­³ö£©£¬´Å³¡µÄÒ»Ìõ±ß½çÔÚÖ±ÏßMOÉÏ£¬ÏÖÓÐÒ»ÖÊÁ¿Îªm¡¢µçÁ¿Îª+qµÄ´øµçÁ£×ÓÔÚÖ½ÃæÄÚÒÔËÙ¶Èv=$\frac{E}{B}$£¬ÇÒ·½ÏòÓëMO³É¦È½Ç´ÓMµãÉäÈë´Å³¡£¬ÓÖÏò×ó´ÓMOÉϵÄDµã£¨Í¼ÖÐδ»­³ö£©Éä³ö´Å³¡½øÈëµç³¡£¬×îºóµ½´ïOµã£¬²»¼ÆÁ£×ÓÖØÁ¦£®Çó£º
£¨1£©MDµÄ¾àÀëL£»
£¨2£©Á£×Ó´ÓMµãÔ˶¯µ½OµãËùÓõÄʱ¼ä
£¨3£©´Å³¡ÇøÓòµÄ×îСÃæ»ý£®

Answer 1

·ÖÎö £¨1£©Óɼ¸ºÎ֪ʶÇó³öÁ£×Ó¹ìµÀ°ë¾¶£¬ÓÉÅ£¶ÙµÚ¶þ¶¨ÂÉÇó³ö¾àÀëL£»
£¨2£©Á£×ÓÔڴų¡ÖÐ×öÔÈËÙÔ²ÖÜÔ˶¯£¬Ôڵ糡ÖÐ×öÀàƽÅ×Ô˶¯£¬ÓÉÔ²ÖÜÔ˶¯µÄÖÜÆÚ¹«Ê½ÓëÀàƽÅ×Ô˶¯ÖªÊ¶Çó³öÁ£×ÓµÄÔ˶¯Ê±¼ä£»
£¨3£©Óɼ¸ºÎ֪ʶÇó³ö´Å³¡ÇøÓòµÄ×îСÃæ»ý£®

½â´ð ½â£º£¨1£©Á£×ÓµÄÔ˶¯¹ì¼£ÈçͼËùʾ£¬

ÉèÁ£×ÓÔÚÔÈÇ¿´Å³¡ÖÐ×öÔÈËÙÔ²ÖÜÔ˶¯µÄ°ë¾¶ÎªR
ÓÉÅ£¶ÙµÚ¶þ¶¨Âɵãº$qBv=\frac{{m{v^2}}}{R}$£¬
Óɼ¸ºÎ¹ØϵµÃ£ºL=2Rsin¦È£¬
ÒÑÖª£ºv=$\frac{E}{B}$£¬
½âµÃ£ºL=$\frac{mE}{{q{B^2}}}$£»
£¨2£©ÉèÁ£×ÓÔÚÔÈÇ¿´Å³¡ÖÐ×öÔÈËÙÔ²ÖÜÔ˶¯µÄÖÜÆÚΪT£¬$T=\frac{2¦Ðm}{qB}$
ÓÉͼ¿ÉÖª£¬Á£×ӵijõËٶȵķ½ÏòÓë´Å³¡µÄ±ß½çÖ®¼äµÄ¼Ð½ÇÊÇ30¡ã£¬ÓÉÔ˶¯µÄ¶Ô³ÆÐÔ¿ÉÖª£¬Á£×ÓÔڴų¡ÖÐÔ˶¯µÄ¹ý³ÌÖеÄƫת½ÇÊÇ60¡ã£¬Á£×ÓÔÚÔÈÇ¿´Å³¡ÖÐÔ˶¯Ê±¼äΪt₁£º${t}_{1}=\frac{60¡ã}{360¡ã}T=\frac{1}{6}T$£¬
ÓɶԳÆÐÔ¿ÉÖª£¬Á£×Ó¹ýMOºó·½Ïò´¹Ö±Óڵ糡·½Ïò£¬ËùÒÔÁ£×Ó×öÀàƽÅ×Ô˶¯£¬ÉèÔ˶¯µÄʱ¼äΪt₂£¬
Ôò£ºx=vt₂
$y=\frac{1}{2}\frac{qE}{m}{t_2}^2$
Óɼ¸ºÎ֪ʶ¿ÉÖª£ºy=xtan¦È£¬
ÔòÁ£×Ó×ÔM½øÈë´Å³¡ÖÁOËùÓõÄʱ¼ät=t₁+t₂
´úÈëÊý¾Ý½âµÃ£ºt=$\frac{{£¨2\sqrt{3}+¦Ð£©}}{3}\frac{m}{qB}$£»
£¨3£©ÓÉÌâÒâ¿ÉÖª£¬´Å³¡·¶Î§µÄ×îСÃæ»ý¡÷SÊÇÁ£×ÓÔڴų¡ÖеĹ켣ÓëMDËùΧ³ÉµÄÃæ»ý£®
ÉÈÐεÄÃæ»ý£º$S=\frac{1}{6}¦Ð{R^2}$£¬
Èý½ÇÐεÄÃæ»ýΪ£º$S'=\frac{1}{2}{R^2}cos{30^0}=\frac{{\sqrt{3}}}{4}{R^2}$
ÓÖ¡÷S=S-S'£¬
ÁªÁ¢µÃ£º¡÷S=$£¨\frac{¦Ð}{6}-\frac{{\sqrt{3}}}{4}£©\frac{{{m^2}{E^2}}}{{{q^2}{B^4}}}$£»
´ð£º£¨1£©MDµÄ¾àÀëL=$\frac{mE}{{q{B^2}}}$£®
£¨2£©Á£×Ó×ÔMµãÉäÈë´Å³¡ÖÁµ½´ïOµãËùÓõÄʱ¼ät=$\frac{{£¨2\sqrt{3}+¦Ð£©}}{3}\frac{m}{qB}$£®
£¨3£©´Å³¡ÇøÓòµÄ×îСÃæ»ýΪ£º$£¨\frac{¦Ð}{6}-\frac{{\sqrt{3}}}{4}£©\frac{{{m^2}{E^2}}}{{{q^2}{B^4}}}$£®

µãÆÀ ×öºÃ´ËÀàÌâÄ¿µÄ¹Ø¼üÊÇ׼ȷµÄ»­³öÁ£×ÓÔ˶¯µÄ¹ì¼£Í¼£¬ÀûÓü¸ºÎ֪ʶÇó³öÁ£×ÓÔ˶¯µÄ°ë¾¶£¬ÔÙ½áºÏ°ë¾¶¹«Ê½ºÍÖÜÆÚ¹«Ê½È¥·ÖÎö£®