Response of Homogeneous Conducting Sphere in Non-Integer Dimensional Space

Abstract

In this paper, we have investigated electric potential and field analytically for homogeneous conducting sphere by solving the Laplacian equation in fractional dimensional space. The laplacian equation in fractional space describes complex phenomena of physics. The separation variable method is used to solve the Laplace differential equation. The mathematical formulae governing the interaction of a low-frequency source of electric current with a spherical anomaly are derived in fractional dimensional space. These formulae are used to determine the apparent resistivity and induced-polarization response. The potential due to the current point source in fractional space is derived using Gegenbauer polynomials. The electric field inrensity of the homogeneous conducting sphere is calculated using the electric potential due to a current point source outside the sphere. The results are compared analytically with classical results by setting the fractional parameter α=3.