formula

$F=-2\pi a^{2}\int_{0}^{1} x\sigma_{z}(x,0)dx=\frac{3\pi a K}{4}\int_{0}^{1}\chi(t)dt\\=\frac{3aK}{2}\left[\delta-\int_{0}^{1}\frac{xf(x)}{\sqrt{1-x^{2}}}dx\right]$