A cylinder is placed in uniform electric field $\overrightarrow{E}$ar, with its axis parallel to field. Show that the electric flux through the cylinder is zero.

(i) at a point near an infinitely large uniformly charged line charge. Explain why an infinite length is necessary for the result.

(ii) at a point near an infinitely large uniformly charged cylinder.

(iii) at a point outside a uniformly charged spherical shell.

(iv) at a point inside and outside a uniformly charged sphere.

(v) at a point outside and inside a charged sphere.

(vi) at a point near a uniformly charged infinitely large charge sheet

(vii) at a point near to a charged conductor.