A sphere of radius R contains charge density `rho(r )=A (R-r )`, for `0 lt r lt R`. The total electric charge inside the sphere is Q.
The electric field inside the sphere is

A sphere of radius R contains charge density rho(r )=A (R-r ) , for 0 lt r lt R . The total electric charge inside the sphere is Q. The electric outside the sphere is (k=1/(4pi in_(0)))

A sphere of radius R contains charge density rho(r )=A (R-r ) , for 0 lt r lt R . The total electric charge inside the sphere is Q. The value of A in terms of Q and R 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)

An insulating solid sphere of radius R has a uniformly positive charge density rho . As a result of this uniform charge distribution there is a finite value of electric potential at the centre of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinity is zero. Statement-1: When a charge 'q' is taken from the centre to the surface of the sphere, its potential energy changes by (qrho)/(3 in_(0)) Statement-2 : The electric field at a distance r (r lt R) from the centre of the the sphere is (rho r)/(3in_(0))

A solid metal sphere of radius R has a charg +2Q. A hollow spherical shell of radius 3R placed concentric with the frist sphere has net charge -Q. Find the electric field between the sphere at a distance r from the centre of the inner sphere. [R lt r lt 3R] .

An insulating solid sphere of radius R has a uniformaly positive charge density rho . As a result of this uniform charge distribution there is a finite value of electric potential at the centre of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinity is zero. Statement-1: Wgen a charge 'q' is taken from the centre to the surface of the sphere, its potential energy charges by (qrho)/(3 in_(0)) Statement-2 : The electric field at a distance r (r lt R) from the centre of the the sphere is (rho r)/(3in_(0))

An insulating solid sphere of radius R has a uniformaly positive charge density rho . As a result of this uniform charge distribution there is a finite value of electric potential at the centre of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinity is zero. Statement-1: Wgen a charge 'q' is taken from the centre to the surface of the sphere, its potential energy charges by (qrho)/(3 in_(0)) Statement-2 : The electric field at a distance r (r lt R) from the centre of the the sphere is (rho r)/(3in_(0))

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.