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Thread: Laplace operator

  1. #1 Laplace operator 
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    I am studying electromagnetism but there is a concept that can not lead to the interpretation and it's Laplace operator o laplacian.



    I know the meaning of divergence for example, it's the flux of an scalar field in closed surface. The meaning of rotational is that, it's the circulation of the vector through a closed path where the direction of the rotational vector is the center of rotation. And finally the gradient is the rate of change of the scalar field whose direction is such that points in the direction of maximum variation.

    So, when I see these operators I can bring to a performance and understand the concepts of the fields. But I do not know what physical interpretation gives to the Laplacian
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  2. #2  
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    Quote Originally Posted by julian403 View Post
    I am studying electromagnetism but there is a concept that can not lead to the interpretation and it's Laplace operator o laplacian.



    I know the meaning of divergence for example, it's the flux of an scalar field in closed surface. The meaning of rotational is that, it's the circulation of the vector through a closed path where the direction of the rotational vector is the center of rotation. And finally the gradient is the rate of change of the scalar field whose direction is such that points in the direction of maximum variation.

    So, when I see these operators I can bring to a performance and understand the concepts of the fields. But I do not know what physical interpretation gives to the Laplacian
    Since the Laplacian of a vector field in Cartesian coordinates is the Laplacian of the components which are just functions and the Laplacian of a function is the divergence of the gradient then you can think of the vector Laplacian the same way. See Vector calculus identities - Wikipedia, the free encyclopedia
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  3. #3  
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    with the expresión



    the first term of the equation is the gradient of the divergence. So it is a vector whose magnitude is the rate of change of the cause scalar A vector whose direction is the maximum varaición this cause. . The second term it's the curl of the curl of the vector A.

    What is the physical meaning of the difference between the first tem vector with the second term vector?
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  4. #4  
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    Quote Originally Posted by julian403 View Post
    with the expresión



    the first term of the equation is the gradient of the divergence. So it is a vector whose magnitude is the rate of change of the cause scalar A vector whose direction is the maximum varaición this cause. . The second term it's the curl of the curl of the vector A.

    What is the physical meaning of the difference between the first tem vector with the second term vector?
    I don't know of a physical meaning to the Laplacian. You know what a Laplacian is, right? It appears in Maxwell's equations and in Newton's equation for the gravitational field. What do you think its physical meaning is there? As far as I'm aware of not all operators have an obvious physical meaning. In Newtonian mechanics the Laplacian shows up in Poisson equation



    Where G is the gravitational constant, is the gravitational potential and is the mass density. What do you believe the physical meaning of is in this equation?
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  5. #5  
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    I think laplacian talk about the causes of the vectors and scalar field. In that case it says that the cause of the gavitational potential is the mass density. For the



    It says that the charge density is the cause of electric potential. And taking the all expression . it talk about all causes, the scalar causes and the vectorial causes. For example



    The cause of vectorial potential is the density current.

    What the diferent between the divergencia which it talk about de scalar cause and the rotational which talks about scalar cause with the laplacian?

    I thinks that it's because the laplacian refers to the cause of cause. For example the cause of vectorial potential is the magnetic field and the cause of magnetic field is the density current so

    That's correct?
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  6. #6  
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    Quote Originally Posted by julian403 View Post
    I think laplacian talk about the causes of the vectors and scalar field....That's correct?
    In my opinion I think it's more accurate to think of it as a source rather than a cause. For example: we say that milk is a source of nutrition. We don't think of milk as causing nutrition.
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