Formula Solid Sphere (E-field Inside) Electric charge Radius
$$E(r) ~=~ \frac{Q}{4\pi \varepsilon_0 \, R^3} \, r$$ $$E(r) ~=~ \frac{Q}{4\pi \varepsilon_0 \, R^3} \, r$$
Electric field
$$ E $$ Unit $$ \frac{\mathrm V}{\mathrm m} $$ Radial outwards directed electric field at the field point \( r \) within a homogeneously electrically charged sphere.
Electric charge
$$ Q $$ Unit $$ \mathrm{C} $$ It is the amount of charge that is homogeneously distributed within the entire sphere.
Field point
$$ r $$ Unit $$ \mathrm{m} $$ Field point points from the center of the sphere to any point inside the sphere where the electric field \( E(r) \) is present.
Radius
$$ R $$ Unit $$ \mathrm{m} $$ Radius of the charged sphere.
Vacuum Permittivity
$$ \varepsilon_0 $$ Unit $$ \frac{\mathrm{As}}{\mathrm{Vm}} $$ The vacuum permittivity is a physical constant that appears in equations involving electromagnetic fields. It has the following experimentally determined value:$$ \varepsilon_0 ~\approx~ 8.854 \, 187 \, 8128 ~\cdot~ 10^{-12} \, \frac{\mathrm{As}}{\mathrm{Vm}} $$