A sphere of radius R carries charge density p proportional to the square of the distance from the centre such that `p = Cr^(2)`, where C is a positive constant. At a distance R`//`2 from the centre, the magnitude of the electric field is :

A sphere of radius R carries charge such that its volume charge density is proportional to the square of the distance from the centre. What is the ratio of the magnitude of the electric field at a distance 2 R from the centre to the magnitude of the electric field at a distance of R//2 from the centre?

A sphere of radius R_(0 carries a volume charge density proportional to the distance (x) from the origin, rho=alpha x where alpha is a positive constant.The total charge in the sphere of radius R_(0) is

A sphere of radius R has a charge density sigma . The electric intensity at a point at a distance r from its centre is

The potential at a distance R//2 from the centre of a conducting sphere of radius R will be

A Sphere of radius R_0 carries a volume charge density proportional to the distance (x) from the origin, rho=alphax where alpha is a positive constant. (a) Calculate the total charge in the sphere of radius R_0 . (b) The sphere is shaved off so as to reduce its radius. What should be the radius (R) of the remaining sphere so that it contains half the charge of the original sphere? (c) Find the electric field at a point inside the sphere at a distance r lt R. Give your answer for original sphere of radius R_0 as well as for the smaller sphere of radius R that was left after shaving off the original sphere.

A solid sphere of radius R has total charge Q. The charge is distributed in spherically symmetric manner in the sphere. The charge density is zero at the centre and increases linearly with distance from the centre. (a) Find the charge density at distance r from the centre of the sphere. (b) Find the magnitude of electric field at a point ‘P’ inside the sphere at distance r_1 from the centre.

A non-homogeneous cylinder of radius "R" carries a current I whose current density varies with the radial "distance "r" from the centre of the rod as J=sigma r where sigma is a constant.The magnetic field at a point "P" at a distance r