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Vector Calculus Problem - Griffith Textbook

  1. Dec 17, 2012 #1
    I have a problem in the Griffith textbook (Introduction to Electrodynamics), Question 1.21, where it asks what is the meaning of the vector (A.∇)B, my simplistic approach would be to calculate the divergence of A which should be a scalar and multiply it out by Bx,By,Bz) to compute the x component of the expression. However in the solution manual (available by searching Introduction to Electrodynamics Solutions and clicking on the Scribd link) it seems to be the other way around.

    I just don't understand why this is, can someone clarify please?
     
  2. jcsd
  3. Dec 18, 2012 #2

    jedishrfu

    Staff: Mentor

    I think this is the directional derivative. It gives the change of a field B in the direction A.

    See wikipedia for details:

    http://en.wikipedia.org/wiki/Del
     
  4. Dec 18, 2012 #3

    lurflurf

    User Avatar
    Homework Helper

    (A.∇)B and B(∇.A) are not equal because that operator acts to the right so in
    (A.∇)B
    B is differentiated while in
    B(∇.A)
    A is differentiated
     
  5. Dec 18, 2012 #4
    Thanks all. Its quite clear now.
     
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