  In this paper, we check in detail the validity of the widely adopted point
source approximation for nearby cosmic-ray (CR) sources. Under an energy
independent escape model for CRs from the sources, we show that for young
nearby sources, the point source approximation breaks down at lower energies
and the CR spectrum depends on the size and the morphology of the source. When
applied to the nearby supernova remnants (SNRs), we find that the approximation
breaks down for some of the individual remnants like the Vela, but
interestingly it still holds good for their combined total spectrum at the
Earth. Moreover, we also find that the results obtained under this simple
approximation are quite different from those calculated under an energy
dependent escape model which is favored by diffusive shock acceleration models
inside SNRs. Our study suggests that if SNRs are the main sources of CRs in our
Galaxy, then the commonly adopted point source model (with an energy
independent escape scenario) appears flawed for CR studies from the nearby
SNRs.
