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Differences between solenoidal and rotational vector fields?

  1. Dec 25, 2015 #1
    In my electromagnetic theory book, there is a classification of vector fields, one of the 4 different type vector fields is "solenoidal and irrotational vector field" (both divergence-free and curl-free).

    If solenoidal and rotational vector fields are same thing, then it means the vector field is "rotational and irrotational vector field" at the same time. But we just want to indicate it is divergence and curl free.

    Is it the reason why synonym names(solenoidal and rotational) are used, to avoid confusion, or do they have different meanings?
     
  2. jcsd
  3. Dec 25, 2015 #2

    andrewkirk

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    Solenoidal means divergence-free. Irrotational means the same as Conservative, which means the vector field is the gradient of a scalar field. The term 'Rotational Vector Field is hardly ever used. But if one wished to use it, it would simply mean a vector field that is non-conservative, ie not the gradient of any scalar field.
    Solenoidal and Rotational are not the same. The zero vector field is both Solenoidal and Irrotational.
     
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