حلول التدريبات العملية 2 في الكهروستاتيكا

نحسب التغيّر في كمية الشحنة في كل من الكرتين:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»Q«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»Q«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»Q«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»33«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»9«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»(«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨»10«/mn»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»9«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ stretchy=¨true¨»)«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»33«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»9«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»9«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»33«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»9«/mn»«/mrow»«/msup»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»C«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»Q«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»Q«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»Q«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»66«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»9«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»(«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨»10«/mn»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»9«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ stretchy=¨true¨»)«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»66«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»9«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»9«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»33«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»9«/mn»«/mrow»«/msup»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»C«/mi»«/math»

يمكن ملاحظة أن شحنة الكرة 1 تقل بـ «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»33«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»9«/mn»«/mrow»«/msup»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»C«/mi»«/mstyle»«/math» وشحنة الكرة 2 تزداد بـ - «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»33«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»9«/mn»«/mrow»«/msup»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»C«/mi»«/mstyle»«/math».

لذلك يمكن تحديد أن كمية الشحنة Q التي تمر من الكرة 1 إلى الكرة 2 هي:    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»33«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»9«/mn»«/mrow»«/msup»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»C«/mi»«/mstyle»«/math» .