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Spherically symmetric charge density

  1. Sep 24, 2014 #1
    1. The problem statement, all variables and given/known data

    Imagine a spherically symmetric charge density p(r)=Cr for r<=a, p(r)=0 for r>a.
    a) Find the electric field E(r) and potential V(r). Are they continuous at r=a?
    b) Suppose additional charge is placed uniformly on the surface at r=a with surface density sigma. Find E(r) and V(r). Are they continuous at r=a? Explain.

    2. Relevant equations

    gausses law

    3. The attempt at a solution

    So for part a to find the electric field I think I integrate from 0 to r with the integrand being Cr4pi r^2 dr and then add the integral from 0 to a of 0*4 pi r ^2 dr. And i get Cpir^4 ? is this correct? How can I get the potential and to know if they are continuous? I am guessing they are not?!?!

    Also I am lost on part b - please help.
     
  2. jcsd
  3. Sep 25, 2014 #2

    vanhees71

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    Science Advisor
    2016 Award

    Hm, I'd rather use the local laws, which are almost always so much more powerful than the integral laws.

    Here, however, you can also use the integral law due to the very symmetric situation. Write down the relevant equation. You got already one side of this equation correct. Now you have to think about the other side of the equation, i.e., to check, which quantities you need and how you can get them from this equation, taking into account the spherical symmetry of the problem. Finally you can think about the potential.

    Of course, there's also a direct solution for the electrostatic potential for a given static charge distribution, but the question sounds as if you should not ;-)).
     
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