Response of Homogeneous Conducting Sphere in Non-Integer Dimensional Space: Response of Homogeneous Conducting Sphere

Saeed  Ahmed; M  Akbar; M Imran  Shahzad

doi:10.53560/PPASA(58-4)755

Authors

Saeed Ahmed Department of Earth Sciences, Quaid-i-Azam University, Islamabad, Pakistan
M Akbar Department of Electronics, Quaid-i-Azam University, Islamabad, Pakistan
M Imran Shahzad Department of Applied Physics, Federal Urdu University of Arts, Science and Technology, Islamabad, Pakistan

DOI:

https://doi.org/10.53560/PPASA(58-4)755

Keywords:

Laplacian Equation, Electric Potential, Fractional Dimensional Space, Separation Variable Method, Resistivity, Induced

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.

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Response of Homogeneous Conducting Sphere in Non-Integer Dimensional Space