Final answer:
To calculate the electric potential V(h) inside a parallel-plate capacitor, find the electric field E using the surface charge density from the given free charge Q1, and then multiply E by the height h to get V(h).
Step-by-step explanation:
To calculate the electric potential V(h) inside a parallel-plate capacitor at a height h from the bottom plate, we can use the formula V = E × h, where E is the electric field between the plates. From the information provided, E can be calculated using the surface charge density σ and the electric constant ε₀ (E = σ /ε₀).
Given the free charge Q₁ = 8.0 × 10^-10 C and knowing the capacitance equation for a parallel-plate capacitor without dielectric in a vacuum, the surface charge density σ can be determined and consequently, the electric field E. Once E is known, V(h) = E × h can be expressed in terms of the given electron charge e and height h.
In this case, the potential at the bottom plate is taken to be zero, so we can express V(h) as V(h) = E(h) * d, where E(h) is the electrical field as a function of height.
If we know the magnitude of the electrical field as a function of height, we can substitute it in the equation to find the electric potential at any given height.