**Derivation of Electric Field of an Infinite Solid Non-Conducting Cylinder (Outside)**

To derive the electric field of an infinite solid non-conducting cylinder outside the cylinder, we can use Gauss's Law. Gauss's Law states that the electric flux through a closed surface is equal to the total charge enclosed divided by the permittivity of the medium.

**1. Gaussian Surface Selection:**
Let's consider a Gaussian surface in the form of a cylindrical surface with radius 'r' and length 'L', placed outside the infinite solid non-conducting cylinder.

**2. Symmetry Consideration:**
Due to the symmetry of the infinite solid cylinder, the electric field lines will be perpendicular to the Gaussian surface and have the same magnitude at all points on the surface. This allows us to consider the electric field as constant over the Gaussian surface.

**3. Calculation of Electric Flux:**
The electric flux through the Gaussian surface can be calculated as the product of the electric field and the area of the surface. Since the electric field is constant over the surface, the flux simplifies to E multiplied by the surface area, which is 2πrL.

**4. Applying Gauss's Law:**
According to Gauss's Law, the electric flux through the closed surface is equal to the total charge enclosed divided by the permittivity of the medium. In this case, the total charge enclosed is zero since the cylinder is non-conducting and does not have any net charge.

**5. Calculation of Electric Field:**
Setting the electric flux equal to zero, we can solve for the electric field:
E * 2πrL = 0

Since L is a constant, we can simplify the equation to:
E * r = 0

Thus, the electric field outside the infinite solid non-conducting cylinder is zero. This means that there is no electric field present outside the cylinder.

**Conclusion:**
In conclusion, the electric field outside an infinite solid non-conducting cylinder is zero. This is because the net charge enclosed by the Gaussian surface is zero, resulting in no electric flux through the surface. Therefore, the electric field outside the cylinder is nullified.