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Thread: Divergence of vector field

  1. #1
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    Divergence of vector field

    If we consider the limit case of eg. shrinking a coin, surely at Volume=0 then the diameter of the coin will be 0? Since a coin of volume zero cannot have a diameter (to have a diameter it needs to have a volume of more than zero)?

    This random question arose when studying the divergence of a vector field which is defined over $\beta \rightarrow 0$ (the maximum linear dimension or diameter of the "control volume" surrounding a point $P=(x,y,z)$ in a region $R$) and strictly not the volume of the area surrounding $P$.



    Last edited by shakra; Sep 10th 2016 at 04:31 AM.
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  2. #2
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    Re: Divergence of vector field

    Quote Originally Posted by shakra View Post
    If we consider the limit case of eg. shrinking a coin, surely at Volume=0 then the diameter of the coin will be 0? Since a coin of volume zero cannot have a diameter (to have a diameter it needs to have a volume of more than zero)?
    This isn't true. Keep the coin constant diameter and shrink the thickness to 0.

    In the limit the volume goes to zero while the diameter remains constant.
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