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Finding Potential (Spherical coordinates )

  1. Apr 28, 2014 #1
    1. . An electric dipole located at the origin in free space has a moment p = 3ax −2ay +az nC·m. Find V at r = 2.5, θ =30◦, φ =40◦.
    I find it difficult to solve when its in spherical co-ordinates.


    2.Relevent Eq
    V =P.(r-r')/( 4∏ε|r−r'|2)(|r-r'|)


    I am confused how to find a unit vector on spherical co-ordinate. ie |r-r'|


    This que is from william Hayt and page no 100.
     
  2. jcsd
  3. Apr 28, 2014 #2

    vanhees71

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  4. Apr 28, 2014 #3
    Thanks for the reply,but my que
    1)how to find unit vector in a spherical coordinate system?
    2) dipole p is in rectangular coordinate system and distancw vector is in spherical coordinate system.How do i multiply both with a dot product.?
    Haunts me.
    I spent a whole day and and went mad with vectors buzzin in my brain. I am preparing for an test this fundas are essential.please look into this
     
  5. May 2, 2014 #4

    rude man

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    You can express the observation point for V in cartesian coordinates, then use just the cartesian coordinartes. The observation point is totally defined for you in spherical terms.

    V = kp*r/r3

    where r is the vector from the origin to the point of observation, and r its magnitude.

    So you need to figure out how to express this potential in terms of your cartesian coordinate system, then do the dot-product with the dipole moment expression.

    Don't try to do a dot-product in a spherical system. You have to translate to cartesian first.
     
    Last edited: May 2, 2014
  6. May 2, 2014 #5

    rude man

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    Should say p = 3a i - 2a j + a k,
    ijk unit vectors
     
  7. May 2, 2014 #6
    yes and do the dot product and expand using ##V = \frac{\vec{p} . \vec r}{4 \pi \epsilon_0 r^3}##

    And for a dipole centrered at origin along z-axis for example, what can you say about azimuth dependence? Does the potential depend on ##\phi##?
     
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