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Консультация № 199931
20.12.2020, 13:11
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Здравствуйте! У меня возникли сложности с таким вопросом:Помогите пожалуйста
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Обсуждение
25.12.2020, 13:04
общий
это ответ
Здравствуйте, zhalykov.2015!
а) Векторное поле
называется соленоидальным, если его дивергенция равна нулю, то есть
В данном случае P = 7x - 9y + 7z + 2, Q = -8x + 6y - 3, R = 6x - 5y + 5z - 5 и
то есть поле не является соленоидальным.
б) Поток векторного поля F через поверхность [$963$], определяемый выражением
в случае замкнутой поверхности, ограничивающей некоторый объём V, по теореме Остроградского-Гаусса будет равен интегралу по объёму от дивергенции этого поля:
В данном случае div F = 18, а объём V представляет собой трёхгранную пирамиду с вершинами (0, 0, 0), (3, 0, 0), (0, 7, 0) и (0, 0, -7), ограниченную плоскостями x = 0, y = 0, z = 0 и 7x + 3y - 3z = 21. Тогда
в) Векторное поле
называется потенциальным, если его можно представить в виде градиента некоторого скалярного поля [$966$]:
Необходимым и достаточным условием потенциальности поля является
В данном случае P = 7x - 9y + 7z + 2, Q = -8x + 6y - 3, R = 6x - 5y + 5z - 5,
Так как
(остальные условия также не выполняются), то поле не является потенциальным.
а) Векторное поле
называется соленоидальным, если его дивергенция равна нулю, то есть
В данном случае P = 7x - 9y + 7z + 2, Q = -8x + 6y - 3, R = 6x - 5y + 5z - 5 и
то есть поле не является соленоидальным.
б) Поток векторного поля F через поверхность [$963$], определяемый выражением
в случае замкнутой поверхности, ограничивающей некоторый объём V, по теореме Остроградского-Гаусса будет равен интегралу по объёму от дивергенции этого поля:
В данном случае div F = 18, а объём V представляет собой трёхгранную пирамиду с вершинами (0, 0, 0), (3, 0, 0), (0, 7, 0) и (0, 0, -7), ограниченную плоскостями x = 0, y = 0, z = 0 и 7x + 3y - 3z = 21. Тогда
в) Векторное поле
называется потенциальным, если его можно представить в виде градиента некоторого скалярного поля [$966$]:
Необходимым и достаточным условием потенциальности поля является
В данном случае P = 7x - 9y + 7z + 2, Q = -8x + 6y - 3, R = 6x - 5y + 5z - 5,
Так как
(остальные условия также не выполняются), то поле не является потенциальным.
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