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Консультация № 197077
13.11.2019, 18:40
0.00 руб.
0
1
1
Дано векторное поле
_ _ _ _
F(M)=(8x + 3y + 3z - 9)i + (-2x - 2y - 2z - 9)j + (8x + 6y - 4z - 3)k
и пирамида с вершинами в точках
O(0,0,0), A(-8,0,0), B(0,-5,0), C(0,0,-9);
_
a) проверить, является ли векторное поле F(M) соленоидальным;
б) по теореме Остроградского-Гаусса найти поток векторного
_
поля F(M) через полную поверхность пирамиды OABC в
направлении внешней нормали;
_
в) проверить, является ли поле F(M) потенциальным;
_
г) по теореме Стокса найти циркуляцию поля F(M) по
треугольнику ABC в направлении, которое из начала
координат видится по часовой стрелке. Сделать чертеж.
_ _ _ _
F(M)=(8x + 3y + 3z - 9)i + (-2x - 2y - 2z - 9)j + (8x + 6y - 4z - 3)k
и пирамида с вершинами в точках
O(0,0,0), A(-8,0,0), B(0,-5,0), C(0,0,-9);
_
a) проверить, является ли векторное поле F(M) соленоидальным;
б) по теореме Остроградского-Гаусса найти поток векторного
_
поля F(M) через полную поверхность пирамиды OABC в
направлении внешней нормали;
_
в) проверить, является ли поле F(M) потенциальным;
_
г) по теореме Стокса найти циркуляцию поля F(M) по
треугольнику ABC в направлении, которое из начала
координат видится по часовой стрелке. Сделать чертеж.
Обсуждение
23.11.2019, 18:16
общий
это ответ
Здравствуйте, mustang289!
а) Векторное поле
называется соленоидальным, если его дивергенция равна нулю, то есть
В данном случае P = 8x + 3y + 3z - 9, Q = -2x - 2y - 2z - 9, R = 8x + 6y - 4z - 3 и
то есть поле не является соленоидальным.
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 = 8x + 3y + 3z - 9, Q = -2x - 2y - 2z - 9, R = 8x + 6y - 4z - 3,
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 = 8x + 3y + 3z - 9, Q = -2x - 2y - 2z - 9, R = 8x + 6y - 4z - 3 и
то есть поле не является соленоидальным.
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 = 8x + 3y + 3z - 9, Q = -2x - 2y - 2z - 9, R = 8x + 6y - 4z - 3,
Так как
(остальные условия также не выполняются), то поле не является потенциальным.
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