Final answer:
To calculate the electric potential at various points in a system with a charged inner sphere and an oppositely charged outer spherical shell, one must apply electrostatic principles, considering the spherically symmetric charge distribution and the effects of conductive materials.
Step-by-step explanation:
The electric potential V(r) for a charged sphere and a point inside and outside a spherical shell can be derived using the principles of electrostatics. For points outside the radius of the sphere (r ≥ rα), the sphere can be treated as a point charge at the center due to the spherically symmetric charge distribution. Therefore, the electric potential at the radius of the sphere (V(rα)) is given by the formula V(r) = k * q / r, where k is Coulomb's constant, q is the charge, and r is the distance from the center. For a metallic sphere with radius rα = 2.0 cm and charge +5.0 μC, surrounded by a spherical shell of inner radius rβ = 5.0 cm and charge -5.0 μC, we can calculate the electric potential at the sphere's surface and within the shell using this principle.
In between the two spheres, for rα < r < rβ, there is no net charge enclosed, and thus the electric potential remains constant at the value determined at the outer surface of the inner sphere. Inside the inner sphere, due to the conductive nature of the sphere, the electric potential remains the same as well. For points outside the outer shell, the combined charge of the system is zero, hence the electric potential is zero as if observed from infinity.