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GhostStudent
Apr17-11, 10:24 AM
1. The problem statement, all variables and given/known data

Hello all;
i am trying to calculate the potential, inside a non conductive sphere of radius equal to a, in a point at a distance r from the center of the sphere.

2. Relevant equations
i know that:
http://i.imgur.com/lLXjw.png
where E and s are vectors;
and that the Eletric field inside the sphere is:
http://i.imgur.com/bLOuE.png


3. The attempt at a solution

since the distance r is:
0<r<a
i changed the limits so that:
http://i.imgur.com/HaUIV.png

but here comes the part were i am stuck:
i found:
http://i.imgur.com/ltF89.png
but the correct answer, so far, should be
http://i.imgur.com/g3KkV.png
which means that the first integral [ http://i.imgur.com/QHClG.png ] should be equal to zero, but i can't seem to understand why

thx in advance.
p.s.:
please tell me if the images are not showing up.

kuruman
Apr17-11, 09:56 PM
It is not clear why you have two line integrals. You should use

\varphi(r)-\varphi(a)=-\int^{r}_{a}\vec{E}\cdot \vec{ds}

GhostStudent
Apr18-11, 08:26 AM
i guess i was thinking more on terms of the path i should take, that's why my first integral ranges from 0 to a (size of the sphere), but since r is greater than 0 and smaller than a (because its inside the sphere, away from both the center and the surface) i changed the ranges.

dont know if i made it clear or not.

also, i was going to apply that equation, like you said, directly, but when my teacher demonstrated a similar problem in class, he also used those limits, so i guess i got a little mixed up.

thx man