An infinitely long conducting cylindrical rod of radius 1.59mm is surrounded by an infinitely long conducting cylindrical shell with an inner radius 3.62mm, and an outer radius 6.5mm . The figure gives you an idea of what it looks like.

Now Gauss's law works in cases of symmetry, but there are real world complications. Therefore we are going to look at a length 3.39m of both cylinders. The inner cylinder has a charge of 2.81nC uniformly distributed along that length and the outer shell has a charge of 4.97nC uniformly distributed along that length.

Therefore we will be able to ignore the ends of the cylinders because E and A are perpendicular there.

What is E(r), the radial component of the electric field at a point 0.41mm from the center of the inner rod?

What is the charge on the inner surface of the outer shell?

What is the charge on the outer surface of the cylindrical shell?

What is the radial component of the electric field, E(r), at a point 2.66 mm from the center of the inner cylinder?

What is the radial component of the electric field, E(r), at a point 4.9 mm from the center of the inner cylinder?

What is the radial component of the electric field, E(r), at a point 8.47 mm from the center of the inner cylinder?