- #1
alejandrito29
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Homework Statement
Capacitor parallel plates separation $$d$$, potencial diference $$V_0$$, at the center there is a semi sphere of radius $r_0$.
Find the potencial as function of position if $$d>>r_0$$
Homework Equations
I think that relevant equation are Gauss Law
The Attempt at a Solution
Mi proposed of solution is
$$V_{plates}= \sigma /\epsilon_0 z $$
for $$r<|r_0|$$
Gauss Low
$$E 4/3 \pi r^2 = \sigma 4/3 \pi r_0^2$$
$$E= \sigma r_0^2 /\epsilon_0 r^{-2} \hat{r} $$
$$ V_{sp} = \sigma r_0 /\epsilon_0 ( r_0/r-1) = \sigma r_0 /\epsilon_0 ( r_0/\sqrt{x^2+y^2+z^2}-1) $$
And for $$r>|r_0|$$
$$ V=V_{plates}+V_{sp}$$
Help please