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Консультация № 184658
03.12.2011, 00:56
58.76 руб.
0
1
1
Здравствуйте! Прошу помощи в следующем вопросе:
дано векторное поле а(вектор)=P(x,y)*i(вектор)+Q(x,y)*j(вектор)
1)проверить,что это поле является потенциальным
2)найти потенциал поля u=u(x,y)
3)найти уравнение линий равного потенциала и изобразить линии равного потенциала на чертеже
4)составить уравнение векторных линий поля а(вектор) и изобразить векторные линии на том же чертеже,указав стрелками направление векторных линий
5)вычислить линейные интеграл ∫a*dl от А до В
векторное поле:1/2*i+2*[$8730$]y*j ;т.А(-6;1) ,т.В(4;9)
Заранее благодарен за помощь!
дано векторное поле а(вектор)=P(x,y)*i(вектор)+Q(x,y)*j(вектор)
1)проверить,что это поле является потенциальным
2)найти потенциал поля u=u(x,y)
3)найти уравнение линий равного потенциала и изобразить линии равного потенциала на чертеже
4)составить уравнение векторных линий поля а(вектор) и изобразить векторные линии на том же чертеже,указав стрелками направление векторных линий
5)вычислить линейные интеграл ∫a*dl от А до В
векторное поле:1/2*i+2*[$8730$]y*j ;т.А(-6;1) ,т.В(4;9)
Заранее благодарен за помощь!
Обсуждение
04.12.2011, 21:27
общий
это ответ
Здравствуйте, G-buck!
Поле плоское.
1
Поле потенциально, так как ротор равен 0.
2
За путь интегрирования примем ломаную ОАВ: О(0,0), А(х,0), В(х,у)
Вдоль ОА y=dy=0:
Вдоль АВ dx=0:
3
4
Семейство векторных линий определяется дифференциальным уравнением:
На рисунке линии равного потенциала сплошные, а векторные линии - штриховые.
5
Поле плоское.
1
Поле потенциально, так как ротор равен 0.
2
За путь интегрирования примем ломаную ОАВ: О(0,0), А(х,0), В(х,у)
Вдоль ОА y=dy=0:
Вдоль АВ dx=0:
3
4
Семейство векторных линий определяется дифференциальным уравнением:
На рисунке линии равного потенциала сплошные, а векторные линии - штриховые.
5
5
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