An insulating solid sphere of the radius R is carged in a non - uniform manner such that the volume charge density `rho=(A)/(r )`, where A is a positive constant and r is the distance from the centre. The potential difference between the centre and surface of the sphere is

A solid non conducting sphere of radius R has a non-uniform charge distribution of volume charge density, rho=rho_(0)r/R , where rho_(0) is a constant and r is the distance from the centre of the sphere. Show that : (i) the total charge on the sphere is Q=pirho_(0)R^(3) (ii) the electric field inside the sphere has a magnitude given by, E=(KQr^(2))/R^(4)

A solid non conducting sphere of radius R has a non-uniform charge distribution of volume charge density, rho=rho_(0)r/R , where rho_(0) is a constant and r is the distance from the centre of the sphere. Show that : (i) the total charge on the sphere is Q=pirho_(0)R^(3) (ii) the electric field inside the sphere has a magnitude given by, E=(KQr^(2))/R^(4)

A solid non conducting sphere of radius R has a non-uniform charge distribution of volume charge density, rho=rho_(0)r/R , where rho_(0) is a constant and r is the distance from the centre of the sphere. Show that : (i) the total charge on the sphere is Q=pirho_(0)R^(3) (ii) the electric field inside the sphere has a magnitude given by, E=(KQr^(2))/R^(4)

A system consits of a uniformly charged sphere of radius R and a surrounding medium filled by a charge with the volume density rho=alpha/r , where alpha is a positive constant and r is the distance from the centre of the sphere. Find the charge of the sphere for which the electric field intensity E outside the sphere is independent of R.

A solid sphere of radius R has a charge Q distributed in its volume with a charge density rho=kr^a , where k and a are constants and r is the distance from its centre. If the electric field at r=(R)/(2) is 1/8 times that r=R , find the value of a.