A non-conducting spherical ball of radius R contains a spherically symmetric charge with volume charge density `rho=kr^(n)` where r is the distance form the centre of the ball and n is a constant what should be n such that the electric field inside the ball is directly proportional to square of distance from the centre?

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 :

The electrostatic potential inside a charged spherical ball is given by phi=ar^2+b where r is the distance from the centre and a, b are constants. Then the charge density inside the ball is:

The electrostatic potential inside a charged spherical ball is given by phi = ar^(2) + b , where r is distance from the center of the ball, a and b are constants. Calculate the charge density inside the ball.

A solid sphere of radius R is charged with volume charge density p=Kr^(n) , where K and n are constants and r is the distance from its centre. If electric field inside the sphere at distance r is proportional to r^(4) ,then find the value of n.

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 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 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)

The region between two concentric spheres of radii 'a' and 'b', respectively (see figure), have volume charge density rho=A/r , where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, is: