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Evaluating Scalar Field

  1. Oct 29, 2013 #1
    1. The problem statement, all variables and given/known data
    Evaluate the scalar field ##f(r, \theta, \phi)= \mid 2\hat{r}+3\hat{\phi} \mid## in spherical coords.


    2. Relevant equations
    Law of Cosines?

    ##\mid \vec{A} + \vec{B} \mid = \sqrt{A^2+B^2+2ABCos(\theta)}##

    3. The attempt at a solution

    I'm not sure the law of cosines is exactly what I'm suppose to use but so far it is the only thing that I've found that seems to fit the way the problem is presented.

    If this is the correct way then:
    ##\mid 2\hat{r}+3\hat{\phi} \mid=\sqrt{2^2+3^2+12cos(\theta)}##


    Am I doing this correctly?
     
  2. jcsd
  3. Oct 29, 2013 #2

    pasmith

    User Avatar
    Homework Helper

    The [itex]\theta[/itex] which occurs in this expression is not the spherical coordinate [itex]\theta[/itex]. This is obviously going to be a source of confusion, so you need to find a different letter for the angle between [itex]\vec A[/itex] and [itex]\vec B[/itex], such as [itex]\alpha[/itex]:
    [tex]
    \|\vec{A} + \vec{B}\| = \sqrt{A^2 + B^2 + 2AB\cos \alpha}
    [/tex]

    However I think the intended method is to start from
    [tex]
    \|2 \hat r + 3 \hat \phi\|^2 = (2 \hat r + 3 \hat \phi) \cdot (2 \hat r + 3 \hat \phi)
    [/tex]

    Now all you need is the angle [itex]\alpha[/itex] between [itex]\hat r[/itex] and [itex]\hat \phi[/itex].
     
  4. Oct 29, 2013 #3
    I made a mistake. The question should be: ##\mid 2\hat{r} +3\hat{\theta} \mid##
     
  5. Oct 29, 2013 #4
    I'm not sure how I would go about finding the angle between the two vectors in spherical. I could probably switch them to Cartesian but is there a simpler way via spherical?
     
  6. Oct 29, 2013 #5

    vanhees71

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    Science Advisor
    2016 Award

    Spherical coordinates are orthogonal coordinates! Thus [itex]\hat{r}[/itex] and [itex]\hat{\phi}[/itex] are orthogonal with unit norm...
     
  7. Oct 29, 2013 #6
    So just 90° then?
     
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