charged sphere with dielectric housing

kouleskremicitymsklem1  D(r) = \frac{Q}{4 \pi} \frac{1}{r^2}

Q = \rho \frac{4}{3} \pi r^3

D(r) = \frac{\rho \frac{4}{3} \pi r^3}{4 \pi r^2} = \frac{\rho r}{3}

E(r) = \frac{D(r)}{\epsilon_0 \epsilon_r} = \frac{\rho r}{3 \epsilon_0 \epsilon_r}

D(r) = \frac{\rho \frac{4}{3} \pi a^3}{4 \pi r^2} = \frac{\rho a^3}{3 r^2}

E(r) = \frac{D(r)}{\epsilon_0 \epsilon_r} = \frac{\rho a^3}{3 \epsilon_0 r^2}

 

 

kouleelektrickypotencial2

 

kouleelektrickaintenzita_2dgraf_3b kouleelektrickalndukce_2dgraf_3c
D = \frac{Q}{4 \pi} \frac{1}{r^2}

 

kouleelektrickapolarizace_2dgraf_3d kouleelektrickypotencial_2dgraf_3a