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Laplacian is vector or scalar?

  1. Oct 8, 2012 #1
    Here's the link that I read for Laplacian-


    It looks as if the laplacian is scalar but the point is we know that

    ∇x∇xA= ∇(∇.A) - ∇2A

    This means that laplacian should be vector in nature which contradicts what was given in the link mentioned above.

    Would be happy if you could clear my doubt as I am new to EMF.

    Thanks a lot.
  2. jcsd
  3. Oct 8, 2012 #2
    The Laplacian of a scalar field is a scalar field, and the Laplacian of a vector field is a vector field.

    Edit: because it preserves scalars vs. vectors, it is common to refer to it as a scalar operator.
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