A wire, of length L (=20 cm ), is bent into a semi-circular arc. If the two equal halves, of the arc, were each to be uniformly charged with charges…

A wire, of length $\displaystyle \mathrm{L}(=20 \mathrm{~cm})$, is bent into a semi-circular arc. If the two equal halves, of the arc, were each to be uniformly charged with charges $\displaystyle \pm \mathrm{Q},\left[|\mathrm{Q}|=10^3 \varepsilon_0\right.$ Coulomb where $\displaystyle \varepsilon_0$ is the permittivity (in SI units) of free space] the net electric field at the centre O of the semi-circular arc would be :