حلول التدريبات العملية 2 في الكهروستاتيكا

وبما أن القوة الكهربائية هي قوة حافظة، فإن شغلها يساوي التغيّر في طاقة الوضع للجسمين. 

نحسب بالتالي شغل القوة الكهربائية:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»W«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»U«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»W«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»U«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»U«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»W«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»U«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»U«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»W«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»U«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»U«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mi mathvariant=¨bold¨»K«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»Q«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»Q«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«/mrow»«msub»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mi mathvariant=¨bold¨»K«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»Q«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»Q«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«/mrow»«msub»«mi mathvariant=¨bold¨»r«/mi»«mo mathvariant=¨bold¨»§#8734;«/mo»«/msub»«/mfrac»«/mstyle»«/math»

عندما تصل كلا الكرتين إلى اللّانهاية، فإن طاقتهما الوضعية تساوي الصفر

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طريقة أخرى:

نستخدم قانون الشغل والطاقة، نتطرق إلى التغيّر في طاقة الجسمين. 

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تبدأ الكرتان بالتحرك من حالة السكون، وطاقة حركتهما في البداية تساوي صفرًا:

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mathvariant=¨bold¨»E«/mi»«mi mathvariant=¨bold¨»K«/mi»«/msub»«mn mathvariant=¨bold¨»2«/mn»«/msub»«/menclose»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»W«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»E«/mi»«mi mathvariant=¨bold¨»K«/mi»«/msub»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«msub»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»E«/mi»«mi mathvariant=¨bold¨»K«/mi»«/msub»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»W«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup»«mrow mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»V«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»`«/mo»«/mrow»«mn mathvariant=¨bold¨ 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mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«msup»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»547«/mn»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»W«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»478«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»119«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»597«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»J«/mi»«mspace linebreak=¨newline¨/»«/mstyle»«/math»

وإذا أخذنا بالحسبان إلى جميع المنازل بعد المنزلة العشرية، فإن قيمة الشغل المحسوب سيكون: 

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