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Relationship of curl and cross product.

  1. Mar 8, 2015 #1
    Hi all, I am very confused on how to define the vector product or cross product in a physical sense. I know the vector product is a psuedovector, and that it is the area of a parallelogram geometrically. However, I know it used used to describe rotation in physics. As with torque, magnetism and angular momentum. I was wondering how the curl operator plays a role in determining the vectors direction in a cross product or vector product, and why its magnitude is its parallelograms area. I understand the curl operator, but for some reason cannot directly connect it to a cross product to understand it.
    much thanks
  2. jcsd
  3. Mar 9, 2015 #2


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    Science Advisor

    In modern notation, the curl of A is written ##\nabla \times \mathbf{A}##.
    It is the cross product of the "del" operator ##\nabla## with the vector. The "del" operator is basically shorthand for
    ##\nabla = \frac{\partial}{\partial x}\hat{e}_x + \frac{\partial}{\partial y}\hat{e}_y + \frac{\partial}{\partial z}\hat{e}_z##

    You should verify when you calculate the cross product between "del" (treated like a vector) and A, you get curl A. (Del is actually a vector operator.)
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