Final answer:
The question deals with finding the electric potential at a point above a uniformly charged circular disk, a topic in Physics at the College level. It involves integral calculus to integrate the potential contribution from each infinitesimal charge element on the disk.
Step-by-step explanation:
The subject of this question is Physics, particularly involving the concept of electric potential due to a charged object. The question is appropriate for College level study, as it requires understanding of electromagnetic theory and integral calculus to solve.
Finding the Electric Potential at Point P
To find the electric potential at point P(0,0,h) due to a uniformly charged circular disk in the x−y plane with charge density σ (C/m²), one has to integrate the contribution of potential (dV) from each infinitesimal charge element (dq) on the disk. The potential due to a point charge is given by V = k * dq / r, where k is Coulomb's constant, dq is the charge of the infinitesimal element, and r is the distance from the charge element to point P. Since the disk is uniformly charged, σ is constant, and the charge element can be expressed as dq = σ * dA, where dA is the area element of the disk.
To perform the integration, one would typically switch to cylindrical coordinates where dA = r*dr*dθ, with the limits of integration for r being from 0 to R (the radius of the disk) and for θ being from 0 to 2π (a full circle). The distance r from each infinitesimal area element to point P is √(r² + h²), leading to the integral expression for the potential at point P:
V = ∫∫ σ / (4πε₀) * r*dr*dθ / √(r² + h²)
The integration needs to be performed over both θ and r to find the total potential at point P.