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Math Help - potential

  1. #1
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    potential

    Find the potential inside and outside a uniformly charge sphere of radius  R and whose total charge is  q . Use infinity as your reference point.

    So  V(r) = -\int_{\infty}^{r} \bold{E} \cdot d \bold{l} . What is the electric field inside the sphere?

    Then outside the sphere  \bold{E} = \frac{1}{4 \pi \epsilon_{0}} \frac{q}{r^2} \bold{r} . Then  V(r) = -\int_{\infty}^{r} \bold{E} \cdot d \bold{l} = \frac{q}{4 \pi \epsilon_{0}} \frac{1}{r} .

    For inside the sphere how would you compute the potential?
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  2. #2
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    Quote Originally Posted by heathrowjohnny View Post
    Find the potential inside and outside a uniformly charge sphere of radius  R and whose total charge is  q . Use infinity as your reference point.

    So  V(r) = -\int_{\infty}^{r} \bold{E} \cdot d \bold{l} . What is the electric field inside the sphere?

    Then outside the sphere  \bold{E} = \frac{1}{4 \pi \epsilon_{0}} \frac{q}{r^2} \bold{r} . Then  V(r) = -\int_{\infty}^{r} \bold{E} \cdot d \bold{l} = \frac{q}{4 \pi \epsilon_{0}} \frac{1}{r} .

    For inside the sphere how would you compute the potential?
    Read Example 4.1: Electric field of a uniformly charged sphere and http://physics.bu.edu/~duffy/semeste...l_spheres.html.
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    Quote Originally Posted by heathrowjohnny View Post
    Find the potential inside and outside a uniformly charge sphere of radius  R and whose total charge is  q . Use infinity as your reference point.

    So  V(r) = -\int_{\infty}^{r} \bold{E} \cdot d \bold{l} . What is the electric field inside the sphere?

    Then outside the sphere  \bold{E} = \frac{1}{4 \pi \epsilon_{0}} \frac{q}{r^2} \bold{r} . Then  V(r) = -\int_{\infty}^{r} \bold{E} \cdot d \bold{l} = \frac{q}{4 \pi \epsilon_{0}} \frac{1}{r} .

    For inside the sphere how would you compute the potential?
    Gauss' Law usually works well...

    -Dan
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