Electromagnetic Theory-Gauss Law and Applications (CSIR Physical Sciences): Questions 1 - 3 of 4

Consider a hallow charged shell of inner radius and outer radius. The volume charge density is (k is a constant) in the region. The magnitude of the electric field produced at distance is –

A static charge distribution gives rise to an electric field of the form, where and R are positive constants. The charge contained within a sphere of radius R, centered at the origin is: (December)

A solid of radius R has a charge density, given by; where is the radial coordinate and and R are positive constants. If the magnitude of the electric field at is times that at then the value of a is – (December)