Question

Two axis aligned very long,thin shell cylinders have radii R1 and R2 with R1 < R2, A unform charge per unit length of λ is placed on the inner cylinder. Find the electric field, charge, and potential everywhere. Now, assume that the outer cylinder is grounded, repeat the calculation.

Answer 1

The electric field of a infinite line uniform charge is observed by Gauss'law

i am using another symbols for your question

lets take R1=r & R2=R

fast you have to consider gaussian surface with r  radius ,the electric field has the same magnitude at every point of the cylinder and is directed outward.

Considering a Gaussian surface in the form of a cylinder at radius r > R, the electric field has the same magnitude at every point of the cylinder and is directed outward. The electric flux is then just the electric field times the area of the cylinder.

The electric field of an infinite cylinder of uniform volume charge density can be obtained by a using Gauss' law. Considering a Gaussian surface in the form of a cylinder at radius r > R, the electric field has the same magnitude at every point of the cylinder and is directed outward. The electric flux is then just the electric field times the area of the cylinder.

The electric field inside an infinite cylinder of uniform charge is radially outward (by symmetry), but a cylindridal Gaussian surface would enclose less than the total charge Q. The charge inside a radius r is given by the ratio of the volumes:

the electric flux is given by

and the electric field is

Note that the limit at r= R agrees with the expression for r >= R.

if outer surface is grounded then potential is 0 for outer surface and get some potential due to resistance of cylinder you got inner potential you only have to replace to . is permitivety of cylinder