Final answer:
To determine the electric field at the surface of the cylinder around the charged filament, calculate the linear charge density and use Gauss's Law. The filament's finite length is approximated as infinite since the cylinder is centrally located and short. The answer would depend on the charge per unit length, which can't be calculated here without more detail option a is correct.
Step-by-step explanation:
Finding the Electric Field at the Surface of a Cylinder
To find the electric field at the surface of the cardboard cylinder surrounding the uniformly charged filament, one can use Gauss's Law. The key to solving this problem is to treat the filament as a line of charge with a uniform linear charge density, λ, given by the total charge divided by the length of the filament. After calculating λ, we can apply Gauss's Law by using a cylindrical Gaussian surface coaxial with the filament.
However, since the filament is only 6.70 m long and the cylinder is quite short (1.90 cm) and situated at the center, we can approximate this situation with an infinitely long charged cylinder (for the purposes of the problem). This allows us to state that the electric field at the surface of the cardboard cylinder depends only on the charge per unit length of the filament and is independent of the radius of the cylinder.
Note: The exact answer requires more detailed information on the positioning and dimensions. As the specific charge distribution is not provided for calculation in this scenario, the student should refer to their physics textbook or notes for the technique to calculate the electric field using Gauss's Law around uniformly charged objects with cylindrical symmetry.