Obtain Coulomb's law from Gauss's law. Indicate the additional information you require for their derivation.

(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.