We have a thin non conducting spherical shell of radius R with one half of the sphere carrying surface charge density ${\sigma }_1$ and rest half carrying ${\sigma }_2$ . Magnitude of force of electrostatic interaction between hemispherical part carrying surface charge density ${\sigma }_1$  and the other hemispherical portion carrying ${\sigma }_2$  is $F_0=\alpha \times {10}^4$ Newton. What will be the value of $\alpha$  ?   
$(given{\sigma }_1=\sqrt{{\epsilon }_0}\times {10}^{2}C/m^2,{\sigma }_2=4{\sigma }_1,R=\sqrt{\frac{3}{\pi }}m)$