When scattering intensity is plotted against the dimensionless quantity qR, where q is the magnitude of the scattering wave vector and R is the radius of the particle, in log-log scale the scattering curve shows a power-law structure which defines characteristic crossovers. This work reveals some new relationships between the power-law structure and the particle properties. In this work, computer simulation results from T-matrix, Mie theory, and discrete dipole approximation methods are used to study the far field intensity and the internal field of the particles. Scattering by both weakly and strongly refractive particles are studied. For weakly refractive randomly oriented spheroidal particles, how the phasor cancellation-based tip volume method can be applied to predict the scattering envelope is demonstrated. The relationship between backscattering enhancement and the curvature of the weakly refractive particles is explained. In strongly-refractive particles when the phase shift parameter is high, regions with higher field amplitudes start to appear. These regions are recognized as the hot spot regions. In this work, a proper definition is given to the hot spot region. The relationships between the hot spot region and the power-law structure, between the hot spot region and the particle morphology, and between the power-law structure and the particle morphology are extensively studied for scattering by spherical particles. A new semi-quantitative phasor analysis method is introduced, and the new method is used with color-coded phasor plots to identify how different regions of the particle contribute to the scattering pattern to get an insight into the physics behind the scattering. How different regions of the particle contribute to the second crossover (SC) and the backscattering enhancement is presented. Relationships between the SC, particle size, and relative refractive index of the particle are derived. It was identified that the scattering angle at the SC depends only on the relative refractive index of the particle. How the findings of this work can be applied to solve the inverse electromagnetic scattering problem for a single non-absorbing spherical particle is also discussed.