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Homework Help: Compute voltage inside sphere of uniform charge

  1. Jan 23, 2014 #1
    1. The problem statement, all variables and given/known data
    Problem 2.21 from Introduction to Electrodynamics, David J. Griffiths, Third Edition.

    Find the potential inside and outside a uniformly charged solid sphere who's radius is R and whose total charge is q. Use infinity as your reference point.

    2. Relevant equations
    Given: q, R, r'(r inside sphere)
    Variable: r
    ∫E da =q/ε0
    V = -∫[itex]^{r}_{∞}[/itex]E dl

    3. The attempt at a solution
    Outside of sphere:
    |E|∫s r2sinΘdΘdø = (1/ε0)q
    E = (q)[itex]\widehat{r}[/itex]/(4π εor2)
    V = -∫[itex]^{r}_{∞}[/itex]E dr =q/4πε0r

    The above is pretty straight forward. On the other hand, the Voltage inside the sphere completely illudes me. From the answer book, I know that is an A - B type problem but can't seem to get my mind around the concept. I know that the Voltage is a function of the radius but the E field is not zero as in a hollow sphere. How is the basic equation for the E field inside the sphere derived?
    Last edited: Jan 23, 2014
  2. jcsd
  3. Jan 23, 2014 #2


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    Homework Helper

    charge inside the gaussian surface at r<R is proportional to the Volume enclosed: rho V_inside
    where rho = q/(4/3 pi R^3)
  4. Jan 23, 2014 #3


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    2017 Award

    Staff: Mentor

    For a radius r>R, consider the sphere with a smaller radius (smaller than r) and the hollow sphere with a larger radius (larger than r) as separate objects. How can you calculate their field contributions?
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