Using the Gauss theorem, determine the electric field strength of:
a) inside and outside a uniformly charged sphere, if the total charge of the
sphere is Q;
b) a uniformly charged infinite filament, if the charge of the unit length of the
filament is ρ;
c) a uniformly charged infinite plane, if the surface charge density of the plane
is σ;
d) inside and outside a uniformly charged a charged sphere of radius R, if
the bulk charge density is ρ; draw a graph of the electric field strength as a
function of the distance to the center of the ball;
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e) inside and outside a uniformly charged infinite cylinder of radius R, if the
bulk charge density is ρ. the charge density inside the cylinder is ρ; draw a
graph of the dependence of the electric field strength on the distance to the
cylinder axis;
f) outside and inside a uniformly charged infinite plate of thickness h, if the
volume charge density in the plate is ρ; draw a graph of the dependence of the
electric field strength on the distance to the central plane of the plate.