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We write the electromagnetic self-force of a Lorentz-contractible sphericalshell of radius $R$ in arbitrary rectilinear motion as a series expansion inpowers of $R$, and calculate the first two terms of this series. The method weuse, which is based on the description of the particle in terms of avelocity-dependent volume charge density, avoids some important difficulties ofthe previous approaches from the literature. We compare our results with theresults obtained by other authors. The whole calculation is done in thelaboratory frame of reference.

The electromagnetic self-force of a Lorentz-contractible spherical shell  of radius $R$ in rectilinear arbitrary motion: the terms of order $1/R$ and  $R^0$