Dipolar magnetic field by static current loop in exponential metric

Abstract We investigated the dipolar magnetic field generated by a static current loop around a compact gravitational source described by the exponential metric. Starting from Maxwell’s equations, we derived the expression for the electromagnetic vector potential in this spacetime and obtained analytical solutions. The angular dependence of the vector potential is expressed through Legendre polynomials, while the radial part is represented by the hypergeometric function of the first kind. The integration constants were determined by enforcing the continuity of the vector potential at the location of the source and by substituting the solution back into Maxwell’s equations. The resulting magnetic field is uniform in the interior region, resembling the Wald solution, whereas in the exterior region it assumes a dipolar structure. Moreover, the external magnetic field strength decreases with increasing radial distance. We have investigated the effect of introducing a dipole magnetic field on the motion of charged particles around the compact object. Our results show that the presence of this magnetic field alters the particle dynamics and causes the radius of the innermost stable circular orbit (ISCO) to move outward compared with the case of a neutral particle.