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Homework Help: Finding the value of the element dq

  1. Sep 11, 2009 #1
    1. The problem statement, all variables and given/known data
    Hi guys, i need a bit of help with the following question. Ok the question states the following, explain why the element of charge, dq, located within an infinitesimally thin spherical shell or radius r is equal to rho(r)*4*pi*(r)^2dr, where dr is the thickness of the shell.

    2. Relevant equations

    3. The attempt at a solution
    ok i know that total charge is equal to charge density multiplied by volume, which is equal to rho*4/3pi*r^2. Hence if i were to find dq, i would have to differentiate with respect to r, dq/dr and solve for dq... thus dq/dr=rho(r)*dv/dr
    where dv/dr=4*pi*r^2, therefore if i solve for dq i should get dq=rho(r)*4*pi*r^2*dr...

    ok i have no idea if that was right or not... any help here would be greatly appreciated and also why dont we differentiate rho(r)
    Last edited: Sep 11, 2009
  2. jcsd
  3. Sep 12, 2009 #2
  4. Sep 14, 2009 #3
    yeah i kinda need help with a question very similar to this..... i have the same basic idea as warror_1 but im still unsure as to how to explain it
  5. Sep 14, 2009 #4


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    Homework Helper

    Yes, that approach is right. And we do don't differentiate rho because it's a constant, not a function.

    As for explaining it, you don't need to; the OP's equations prove what the question asked to prove, so they're perfectly sufficient. For a more intuitive explanation, think of adding an extra layer of thickness dr on top of a sphere of radius r. If you flatten out the sphere onto a map, it would have an area of 4pi*r^2; with the extra layer, it would be 4pi*(r+dr)^2. If dr is small, there's no difference in their size, so now you have two layers of equal shape and area separated by distance dr. The volume of contained in that is 4pi*r2dr, so the contained charge must be rho*4pi*r2dr
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