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Magnetic field due to magnetic dipole

  1. Jul 19, 2015 #1
    It is NOT a homework question. I am doing my revision and get stuck at this question.

    I am confused with the angle θ shown in this link:

    Professor who wrote this solution stated that θ is the angle between unit vector z and unit vector r, but as what i understand, the angle between two unit vectors (in this question) is cos(180-θ) = -cos(θ) but it is different with the solution shown in the link. (Help me, I am so confused!)

    And also one more question. Why is the integration of area taken from 0 to b? If it is, aren't we taking a integration of disk, then? but in the question, it says it is a loop.

    Can someone please explain it briefly?
    Last edited: Jul 19, 2015
  2. jcsd
  3. Jul 19, 2015 #2


    Staff: Mentor

    The professor is simply using the geometric definition of the dot product:
    ##\vec{a} \cdot \vec{b} = ||\vec{a}||\;||\vec{b}|| \; \cos(\theta)##
    See: https://en.wikipedia.org/wiki/Dot_product#Geometric_definition

    Since ##\hat{z}## and ##\hat{r}## are both unit vectors their magnitudes are both 1 and so ##\hat{z} \cdot \hat{r} = \cos(\theta)##.
  4. Jul 19, 2015 #3
    Thank you very much for your reply!
    I still want to make sure one more thing here.
    So, θ is the angle between these two unit vectors? or angle 180 degree subtract with the angle between unit vectors?
  5. Jul 19, 2015 #4


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    Staff: Mentor

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