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Differential equation in physics

  1. Dec 8, 2005 #1

    i have a problem with spherical coordinates however i understand partial differentials.

    Basically a thin spherical layer of radius R is uniformly charged with surface charge density. Show by Calculating the electrostatic potential (x,y,z) produced by the layer that electrostatic potential is unifrom anywhere inside the sphere.Use spherical coordiantes.It also says a differential area da=R^2sin()d()d(/) can be obtained from the volume dv=R^2 sin()Rd()d(/)=dAdR


    I know how to calculate the moment of inertia using spherical coordinates however i dont know how to start off the question. Am i suppose to calculate the are or the volume and what equation do i put into the triple integral.Very confusing?:bugeye:
  2. jcsd
  3. Dec 8, 2005 #2


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    The equation for the potential is a volume integral over the charge distribution. In this case, you only have surface charge, so this turns into a surface integral of the surface charge density divide dy |r-r'|, where r is the position you are calculating the potential at and r' is the position of the charge (you integrate over r'). In this case, because of the spherical symmetry, you could use Gauss's law to solve this problem in one line. If you don't know Gauss's law, or aren't allowed to use it, you can still simplify the problem considerably by noting that you only need to consider r along the polar axis (phi=0), since the potential shouldn't depend on theta or phi.
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