charged sphere

$E(r) = \frac{Q}{4 \pi \epsilon r^2}$

$\varphi (r) = - \int E (r) \textrm{d} r = \frac{Q}{4 \pi \epsilon} \frac{1}{r} + K$

for r<a:

$\varphi (r) = \frac{Q}{4 \pi \epsilon} \frac{1}{r} + K = konst$