Final answer:
The electric field at a distance of 0.05 m from the outside surface of the shell is approximately 3598 N/C.
Step-by-step explanation:
The electric field at a distance of 0.05 m from the outside surface of the shell can be found using the principles of electrostatics. Since the spherical shell is uncharged and the charge is placed at the center, there is no electric field inside the shell. Therefore, we only need to consider the electric field outside the shell.
The electric field at a point outside a uniformly charged spherical shell is the same as the electric field produced by a point charge located at the center of the shell. The electric field produced by a point charge can be calculated using Coulomb's law:
E = k * (q / r^2)
Where E is the electric field, k is Coulomb's constant (approximately 8.99 x 10^9 Nm^2/C^2), q is the charge, and r is the distance from the charge.
In this case, the charge is +10.0 nC (1 nC = 10^-9 C) and the distance from the charge is 0.05 m. Plugging these values into the electric field equation, we get:
E = (8.99 x 10^9 Nm^2/C^2) * ((10.0 x 10^-9 C) / (0.05 m)^2)
Calculating this, we find that the electric field at a distance of 0.05 m from the outside surface of the shell is approximately 3598 N/C.