Question

14£®Á½¸ö´øµÈÁ¿ÕýµçµÄµãµçºÉ£¬µçÁ¿·Ö±ðΪq£¬¹Ì¶¨ÔÚͼÖÐa¡¢bÁ½µã£¬ab=L£¬MNΪabÁ¬ÏßµÄÖд¹Ïߣ¬½»Ö±ÏßabÓÚOµã£¬AΪMNÉϵÄÒ»µã£¬OA=$\frac{\sqrt{2}}{2}$L£®È¡ÎÞÏÞÔ¶´¦µÄµçÊÆΪÁ㣮һ´ø¸ºµçµÄÊÔ̽µçºÉq£¬½öÔÚ¾²µçÁ¦×÷ÓÃÏÂÔ˶¯£¬Ôò£¨¡¡¡¡£©

• A£® Èôq´ÓAµãÓɾ²Ö¹ÊÍ·Å£¬ÆäÔÚÓÉAµãÏòOµãÔ˶¯µÄ¹ý³ÌÖУ¬¼ÓËÙ¶ÈÏÈÔö´óºó¼õС
• B£® Èôq´ÓAµãÓɾ²Ö¹ÊÍ·Å£¬ÏȼÓËÙºó¼õËÙ£¬ÔÚOµãËٶȼõΪ0
• C£® qÓÉAµãÏòOµãÔ˶¯Ê±£¬Æ䶯ÄÜÖð½¥Ôö´ó£¬µçÊÆÄÜÖð½¥Ôö´ó
• D£® ÈôÔÚAµã¸øqÒ»¸öºÏÊʵijõËٶȣ¬Ëü¿ÉÒÔ×öÔÈËÙÔ²ÖÜÔ˶¯

Answer 1

·ÖÎö ¸ù¾ÝµÈÁ¿Í¬ÖÖµãµçºÉµç³¡Ïߵķֲ¼Çé¿ö£¬×¥×¡¶Ô³ÆÐÔ£¬·ÖÎöÊÔ̽µçºÉqµÄÊÜÁ¦Çé¿ö£¬È·¶¨ÆäÔ˶¯Çé¿ö£¬¸ù¾Ýµç³¡Á¦×ö¹¦Çé¿ö£¬·ÖÎöÆäµçÊÆÄܵı仯Çé¿ö£®

½â´ð ½â£ºA¡¢Á½µÈÁ¿ÕýµçºÉÖÜΧ²¿·Öµç³¡ÏßÈçÓÒͼËùʾ£¬ÆäÖÐa¡¢bÁ¬ÏßµÄÖд¹ÏßMNÉÏ£¬ÉèÈÎÒâµãPµ½OµÄ¾àÀëÊÇx£¬aµ½OµÄ¾àÀëÊÇ$\frac{L}{2}$£¬ÔòaÔÚP²úÉúµÄ³¡Ç¿£º${E}_{a}=\frac{kQ}{{r}^{2}}=\frac{kQ}{£¨\frac{L}{2}£©^{2}+{x}^{2}}$£®ÔÚ a¡¢bÁ¬ÏßµÄÖд¹ÏßMNÉϵķÖÁ¿£º${E}_{ax}={E}_{a}•cos¦È={E}_{a}•\frac{x}{\sqrt{{x}^{2}+{£¨\frac{L}{2}£©}^{2}}}$=$\frac{\frac{kQ}{{£¨\frac{L}{2}£©}^{2}+{x}^{2}}•x}{\sqrt{{x}^{2}+£¨\frac{L}{2}£©^{2}}}=\frac{kQx}{£¨{x}^{2}+\frac{{L}^{2}}{4}£©^{\frac{3}{2}}}$
Õ¹¿ªµÃ£º${E}_{ax}=\frac{kQx}{\sqrt{{x}^{6}+\frac{3{L}^{2}}{4}•{x}^{4}+\frac{3{L}^{2}}{16}•{x}^{2}+\frac{{L}^{6}}{64}}}$=$\frac{kQ}{\sqrt{{x}^{4}+\frac{3{L}^{2}}{4}{x}^{2}+\frac{{L}^{6}}{64{x}^{2}}+\frac{3{L}^{4}}{16}}}$
ÓÉÈýÏîʽ¶¨Àí£º$A+B+C¡Ý3•\root{3}{ABC}$µÃ$x=\frac{\sqrt{2}}{4}L$
ÓÉÓÚ$\frac{\sqrt{2}}{2}£¾\frac{\sqrt{2}}{4}$¹ÊÊÔ̽µçºÉËùÊܵĵ糡Á¦ÊDZ仯µÄ£¬qÓÉAÏòOµÄÔ˶¯Ê±µÄµç³¡Á¦ÏÈÔö´ó£¬ºó¼õС£¬ËùÒÔ¼ÓËÙ¶ÈÏÈÔö´ó£¬ºó¼õС£¬¹ÊAÕýÈ·£®
B¡¢Èôq´ÓAµãÓɾ²Ö¹ÊÍ·Å£¬Ò»Ö±×ö¼ÓËÙÔ˶¯£¬ÔÚOµãËÙ¶È×î´ó£»¹ÊB´íÎó£®
C¡¢´ÓAµ½O¹ý³Ì£¬µç³¡Á¦×öÕý¹¦£¬¶¯ÄÜÔö´ó£¬µçÊÆÄÜÖð½¥¼õС£¬¹ÊC´íÎó£®
D¡¢¸ºµçºÉÔÚAµãÊܵ½µÄµç³¡Á¦µÄ·½ÏòÊúÖ±ÏòÏ£¬¸ù¾ÝµÈÁ¿Í¬ÖÖµãµçºÉµÄµç³¡·Ö²¼µÄ¿Õ¼ä¶Ô³ÆÐÔ¿ÉÖª£¬ÈôÔÚAµã¸øqÒ»¸öºÏÊʵijõËٶȣ¬Ê¹ËüÔÚAµãÊܵ½µÄµç³¡Á¦Ç¡ºÃµÈÓÚÏòÐÄÁ¦£¬Ëü¿ÉÒÔÔÚÓëÁ½¸öµçºÉµÄÁ¬Ïß´¹Ö±µÄƽÃæÄÚ×öÔÈËÙÔ²ÖÜÔ˶¯£¬¹ÊDÕýÈ·£®
¹ÊÑ¡£ºAD

µãÆÀ ±¾Ì⿼²é¾²µç³¡µÄ»ù±¾¸ÅÄ¹Ø¼üÒªÊìϤµÈÁ¿Í¬ÖÖµãµçºÉµç³¡Ïߵķֲ¼Çé¿ö£¬ÔËÓö¯Äܶ¨Àí½øÐзÖÎö£®½â´ð¸ÃÌâµÄÄѶÈÔÚÓÚÈçºÎÅжϳöÖ±ÏßMNÉϵĵ糡ǿ¶È×î´óµÄµã£®