Final answer:
The potential in the dielectric can be found by solving the form of Laplace's equation applicable for a cylindrical coordinate system with azimuthal symmetry, giving the general solution V(p) = A ln(p) + B. The constants A and B are determined by boundary conditions, including the properties of Teflon and system dimensions.
Step-by-step explanation:
The question involves finding the potential as a function of p in a dielectric using Laplace's equation, specifically in the context of a cylindrical configuration with a conductive inner core, a dielectric layer (in this case, Teflon), and an outer conductor. Solving such a situation typically requires setting up the appropriate form of Laplace's equation in cylindrical coordinates and finding a solution that satisfies the boundary conditions imposed by the geometry and materials of the system.
To begin, we recognize that the electric potential V in a region with no free charge density follows Laplace's equation, which, in cylindrical coordinates and assuming azimuthal symmetry (no dependence on angle), simplifies to:
d2V/dr2 + (1/r)dV/dr = 0
The general solution to this equation can be expressed as:
V(p) = A ln(p) + B
where A and B are constants determined by the boundary conditions. Since the question involves a teflon sheathed conductor, one must adjust these constants based on the electric characteristics of Teflon and the given dimensions of the system.