A space is filled up with a charge with volume desnsity `rho = rho_(0) e^(-alpha r^(3))`, where `rho_(0)` and `alpha` are positive constansts, `r` is the distance from the centre of this system. Find the magnitude of the electric field strength vector as a function of `r`. Investigate the obtained expresssion for the small and large values of `r, i.e.,` at `alpha r^(3) lt lt 1` and `alpha r^(3) gt gt 1`.

A solid sphere of radius R has a volume charge density rho=rho_(0) r^(2) (where rho_(0) is a constant ans r is the distance from centre). At a distance x from its centre (for x lt R ), the electric field is directly proportional to :

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 system consits of a ball of radus R carrying spherically symmetric charge and the surrounding space filled with a charge of volume density rho = alpha//r , wehre alpha is a constant, r is the distance from the centre of the ball. Find the ball's the charge at whcih the magnitude of the electric field strength vector is independent of r outside the ball. How high is this strength ? The permittives of the ball and the surrounding space are assumed to be equal to unity.

A system consists of a ball of radius R carrying a uniformly distributed charge q and the surrounding space filled with a charge of volume density rho = alpha//r , where alpha is a constant and r is the distance from the centre of the ball. Find the charge on the ball for which the magnitude of electric field strength outside the ball is constant? The dielectric constant of the ball and the surrounding may be taken equal to unity.

A ball of radius R carries a positive charges whose volume density at a point is given as rho=rho_(0)(1-r//R) , Where rho_(0) is a constant and r is the distance of the point from the center. Assume the permittivies of the ball and the enviroment to be equal to unity. (a) Find the magnitude of the electric field strength as a function of hte distance r both inside and outside the ball. (b) Find the maximum intensity E_("max") and the corresponding distance r_(m) .

A ball of radius R carries a positive charges whose volume density at a point is given as rho=rho_(0)(1-r//R) , Where rho_(0) is a constant and r is the distance of the point from the center. Assume the permittivities of the ball and the enviroment to be equal to unity. (a) Find the magnitude of the electric field strength as a function of the distance r both inside and outside the ball. (b) Find the maximum intensity E_("max") and the corresponding distance r_(m) .

A solid sphere of radius R has a mass distributed in its volume of mass density rho=rho_(0) r, where rho_(0) is constant and r is distance from centre. Then moment of inertia about its diameter is