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Gradient in spherical coordinates

  1. Feb 18, 2017 #1
    <Mentor note: moved from a technical forum and therefore without template>


    So I´m trying to understand how to use the equation for finding the gradient in spherical coordinates, just going from cartesian to spherical seemed crazy. Now I´m at a point where I want to try out what I have read and I immediately run into problems, which clearly tells me I have no idea what I´m doing.

    Problem I was trying to solve:
    Given a scalarfield β = A/r where r = (x^2+y^2+z^2)^1/2 and A is a konstant, calculate the gradient in spherical coordinates.

    ∇β = ∂β/∂r ir + 1/r ∂β/∂θ iθ + 1/rsinθ ∂β/∂φ iφ

    When I thought the solution was pretty simply and then I go to the back of my book to check the result and I´m not even close.
    How on earth does the result become negative? it is also negative in Cartesian coordinates which don´t understand either.
    Well that is basicly my frustration, how does this become negative?
     
    Last edited by a moderator: Feb 18, 2017
  2. jcsd
  3. Feb 18, 2017 #2

    BvU

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    If something becomes smaller, the derivative is negative !
    From your ##\nabla\beta## in spherical coordinates, all that remains is the ##\partial \over \partial r## and the exponent of ##r## in ##\beta## is -1
     
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