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

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 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 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 value of distance r_m at which electric field intensity is maximum 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 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)]

A ball of radius R carries a positive charge whose volume charge depends only on the distance r from the ball's centre as: rho=rho_(0)(1-(r)/(R)) Where r_(0) is a constant. Take epsilon to be permittivit of the ball. Calculate the maximum electric field intensity at a point (inside or outside the ball) due to such a charge distribution.

A ball of radius R carries a positive charge whose volume density depends according only on a separation r from the ball's centre as rho = rho_(0) (1 - r//R) , where rho_(0) is a constant. Asumming the permittivites of the ball and the enviroment to be equal to unity find : (a) the magnitude of the electric field strength as a function of the distance r both inside and outside the ball : (b) the maximum intensity E_(max) and the corresponding distance r _(m) .