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_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 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 spherical region of space has a distribution of charge such that the volume charge density varies with the radial distance from the centre r as rho=rho_(0)r^(3),0<=r<=R where rho_(0) is a positive constant. The total charge Q on sphere 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?

Metallic sphere of radius R is charged to potential V. Then charge q is proportional to

A sphere of charges of radius R carries a positive charge whose volume chasrge density depends only on the distance r from the ball's centre as rho=rho_0(1-r/R), where rho_0 is constant. Assume epsilon as theh permittivity of space. the maximum electric field intensity is

A sphere of charges of radius R carries a positive charge whose volume chasrge density depends only on the distance r from the ball's centre as rho=rho_0(1-r/R), where rho_0 is constant. Assume epsilon as theh permittivity of space. The magnitude of electric field as a function of the distance r inside the sphere is given by

A sphere of charges of radius R carries a positive charge whose volume chasrge density depends only on the distance r from the ball's centre as rho=rho_0(1-r/R ), where rho_0 is constant. Assume epsilon as theh permittivity of space. The magnitude of the electric field as a functiion of the distance r outside the balll is given by