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3
Ñîäåðæàíèå
Ââåäåíèå ....................................................................................... 5
ÃËÀÂÀ1. Ïîëíàÿ ñèñòåìà óðàâíåíèé Ìàêñâåëëà .................. 7
§1. Çàêîí ñîõðàíåíèÿ ýëåêòðè÷åñêîãî çàðÿäà ........................... 7
§2. Òåîðåìà Ãàóññà (IV óðàâíåíèå Ìàêñâåëëà) ..................... 10
§3. Ïîëíûé òîê (òîê ïðîâîäèìîñòè è òîê ñìåùåíèÿ) ............. 12
§4. Îïûò Ýðñòåäà (I óðàâíåíèå Ìàêñâåëëà) ........................... 13
§5. Îïûò Ôàðàäåÿ (II óðàâíåíèå Ìàêñâåëëà) ......................... 15
§6. III óðàâíåíèå Ìàêñâåëëà ..................................................... 16
§7. IV óðàâíåíèå Ìàêñâåëëà (ïîâòîðíûé âûâîä) ................... 17
§8. V, VI è VIII óðàâíåíèÿ Ìàêñâåëëà .................................... 18
§9. Ïîëíàÿ ñèñòåìà óðàâíåíèé Ìàêñâåëëà ............................. 19
§10. Âåêòîðíûé è ñêàëÿðíûé ïîòåíöèàëû ............................... 20
§11. Óðàâíåíèå Äàëàìáåðà ........................................................ 23
§12. Âûâîä óðàâíåíèÿ Äàëàìáåðà
äëÿ ñêàëÿðíîãî ïîòåíöèàëà ............................................... 24
§13. Àíàëèç óðàâíåíèé Äàëàìáåðà
äëÿ âåêòîðíîãî è ñêàëÿðíîãî ïîòåíöèàëîâ ...................... 25
§ 14. Ãðàíè÷íûå óñëîâèÿ
äëÿ âåêòîðîâ ýëåêòðîìàãíèòíîãî ïîëÿ ............................ 29
ÃËÀÂÀ 2. Ýëåêòðîñòàòèêà ......................................................... 36
§1. Ìåõàíè÷åñêèå ñèëû â ýëåêòðîñòàòèêå .................................. 39
§2. Ýíåðãèÿ âçàèìîäåéñòâèÿ ñèñòåìû òî÷å÷íûõ çàðÿäîâ ......... 40
§3. Ýíåðãèÿ íåïðåðûâíî ðàñïðåäåë¸ííûõ çàðÿäîâ ................... 41
ÃËÀÂÀ 3. Ïîñòîÿííûé òîê ........................................................ 45
§1. Âåêòîðíûé ïîòåíöèàë ........................................................... 48
§2. Âçàèìîäåéñòâèå ýëåìåíòîâ ëèíåéíûõ òîêîâ ....................... 51
§3. Ýíåðãèÿ ìàãíèòíîãî ïîëÿ ïîñòîÿííîãî òîêà ...................... 53
Ñîäåðæàíèå
Ââåäåíèå ....................................................................................... 5
ÃËÀÂÀ1. Ïîëíàÿ ñèñòåìà óðàâíåíèé Ìàêñâåëëà .................. 7
§1. Çàêîí ñîõðàíåíèÿ ýëåêòðè÷åñêîãî çàðÿäà ........................... 7
§2. Òåîðåìà Ãàóññà (IV óðàâíåíèå Ìàêñâåëëà) ..................... 10
§3. Ïîëíûé òîê (òîê ïðîâîäèìîñòè è òîê ñìåùåíèÿ) ............. 12
§4. Îïûò Ýðñòåäà (I óðàâíåíèå Ìàêñâåëëà) ........................... 13
§5. Îïûò Ôàðàäåÿ (II óðàâíåíèå Ìàêñâåëëà) ......................... 15
§6. III óðàâíåíèå Ìàêñâåëëà ..................................................... 16
§7. IV óðàâíåíèå Ìàêñâåëëà (ïîâòîðíûé âûâîä) ................... 17
§8. V, VI è VIII óðàâíåíèÿ Ìàêñâåëëà .................................... 18
§9. Ïîëíàÿ ñèñòåìà óðàâíåíèé Ìàêñâåëëà ............................. 19
§10. Âåêòîðíûé è ñêàëÿðíûé ïîòåíöèàëû ............................... 20
§11. Óðàâíåíèå Äàëàìáåðà ........................................................ 23
§12. Âûâîä óðàâíåíèÿ Äàëàìáåðà
äëÿ ñêàëÿðíîãî ïîòåíöèàëà ............................................... 24
§13. Àíàëèç óðàâíåíèé Äàëàìáåðà
äëÿ âåêòîðíîãî è ñêàëÿðíîãî ïîòåíöèàëîâ ...................... 25
§ 14. Ãðàíè÷íûå óñëîâèÿ
äëÿ âåêòîðîâ ýëåêòðîìàãíèòíîãî ïîëÿ ............................ 29
ÃËÀÂÀ 2. Ýëåêòðîñòàòèêà ......................................................... 36
§1. Ìåõàíè÷åñêèå ñèëû â ýëåêòðîñòàòèêå .................................. 39
§2. Ýíåðãèÿ âçàèìîäåéñòâèÿ ñèñòåìû òî÷å÷íûõ çàðÿäîâ ......... 40
§3. Ýíåðãèÿ íåïðåðûâíî ðàñïðåäåë¸ííûõ çàðÿäîâ ................... 41
ÃËÀÂÀ 3. Ïîñòîÿííûé òîê ........................................................ 45
§1. Âåêòîðíûé ïîòåíöèàë ........................................................... 48
§2. Âçàèìîäåéñòâèå ýëåìåíòîâ ëèíåéíûõ òîêîâ ....................... 51
§3. Ýíåðãèÿ ìàãíèòíîãî ïîëÿ ïîñòîÿííîãî òîêà ...................... 53
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