A new, reduced-unknown integral equation for scattering by an inhomogeneous dielectric/magnetic structure is discretized using rectangular brick elements. The new integral equation involves only the electric field (3 scalar components) as the unknown quantity whereas traditional formulations employed both electric and magnetic fields for a total of 6 scalar components per cell. Edge-based linear shape functions are used for the expansion of the field inside the dielectric and a modified Galerkin's technique is employed for testing the integral equation. Results demonstrating the validity of the integral equation are presented.