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 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 charge 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

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 value of distance r_m at which electric field intensity is maximum is given by

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 ball of radius R carries a positive charge throughout its volume, such that the volume density of charge depends on distance r from the ball's centre as rho = rho _(0) ( 1- ( r )/®) , where rho_(0) is a constant. Assuming the permittivity of ball to be one , find magnitude of electric field as a function of distance r, both inside and outside the ball. Strategy : The field has a spherical symmetry . For a point outside the ball ( r gt R ) phi =oint vec(E). bar(dA) = E xx 4 pi r^(2) By Gauss law , phi= ( Q)/( epsilon_(0)) implies E_(out) = (Q)/( 4pi epsilon_(0)r^(2)) , where Q is total charge For a point inside the ball ( r lt R ) phi = oint vec(E) . bar(dA) = E xx 4 pi r^(2) By Gauss law, phi = ( q_(enc))/(epsilon_(0)) implies E_("in")= ( q_(enc))/( 4pi epsilon_(0)r^(2)) where q_(enc)= charge in a sphere of radius r ( lt R) To find the enclosed charge , consider a spherical shell of radius r and thickness dr Its volume dV = 4pi r^(2) dr Charge dq = rho dV implies dq= rho _(0) (1-(r )/(R)) 4pi r^(2) dr implies q= int _(0)^(r ) rho _(0) ( 1- (r)/( R )) 4pi r^(2) dr = rho _(0)4pi [ int_(0)^(r ) r^(2) dr - int_(0)^(r ) (r^(3))/(R) dr ]= rho _(0) 4pi [ ( r^(3))/( 3) - (r^(4))/( 4R)]

In a spherical region the densiy varies inversely with the distance from ther centre Gravitational field at a distance r from the centre is .

A spherical shell of radius R has a uniformly distributed charge ,then electric field varies as

The electrostatic potential of a uniformly charged thin spherical shell of charge Q and radius R at a distance r from the centre

A solid non-conduction cylinder of radius R is charge such that volume charge density is proporation to r where r is distance from axis. The electric field E at a distance r(r lt R) well depend on r as.