  We propose a comprehensive theoretical formulation of magnetic penetration
depth, $\lambda(T)$, based on the microscopic calculations for a general
superconducting gap symmetry. Our findings admit the significant role of band
structure and Fermi surface topology together with the symmetry of
superconducting order parameter. We employ our findings pertaining to the
heavy-fermion superconductor CeCoIn$_5$ to explore both local and non-local
behaviors in response to an external magnetic field across varying
temperatures. Our calculations in the low-temperature regime offer compelling
macroscopic evidence of the nodal character within the superconducting state
with $d_{x^2-y^2}$ symmetry. Furthermore, our findings align with the
characteristics of London-type superconductivity, holding significant
implications for upcoming experiments.
