two long,charged,concentric cylinders have radii of 3.0 and 6.0 cm. The charge per unit length is 5.0*10^-6 C/m on the inner cylinder and -7*10^-6 C/m on the outer cylinder. Find the electric field at (a)r=4cm (b) r =8 cm,where r is the radial distance from the common central axis.

it is a basic question of the GAUSS LAW. Simply apply the Gauss Law at the two cylindrical gausian surfaces having its axis same as the cylinders and the radius 4 and 8 cms respectively.  In case of second the total charge wud be -2 micro coulumb. See  the length of the hollow cylinde does not matter . Hope u understand why!!!!!!!!1

Hi

Acc to gauss law, electric field wud be only because of the charge enclosed.

 Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field. Gauss's law states that:

In integral form  the equation is:

In this case , for r=4cm , electric field will be only because of the inner cylinder , bcoz as we draw the gaussian surface outside the inner cylinder but inside the outer cyl, the charge enclosed is just 5x10^-6 . So, in the gauss law, put q enclosed equal to 5x10^{-6 .}  .

In second case, draw gaussian surface outside the second cyl, hence net charge enclosed is now the sum of the two charges , hence the net q enclosed is ( -2x 10^-6 ), use this in the eq and find E.