A semicircular wire is uniformly charged with linear charge density dependent on the angle $\mathrm{\theta }$ from y-direction as $\mathrm{\lambda }={\mathrm{\lambda }}_0|\sin \mathrm{\theta }|$, where ${\mathrm{\lambda }}_0$ is a constant. The electric field intensity at the centre of the arc is

• A

  $\frac{{\mathrm{\lambda }}_0}{2{\mathrm{\pi \epsilon }}_0\mathrm{R}}(-\widehat{\mathrm{j}})$

• B

  $\frac{{\mathrm{\lambda }}_0}{4{\mathrm{\pi \epsilon }}_0\mathrm{R}}(-\widehat{\mathrm{j}})$

• C

  $\frac{{\mathrm{\lambda }}_0}{6{\mathrm{\pi \epsilon }}_0\mathrm{R}}(-\widehat{\mathrm{j}})$

• D

  $\frac{{\mathrm{\lambda }}_0}{2\sqrt{2}{\mathrm{\pi \epsilon }}_0\mathrm{R}}(-\widehat{\mathrm{j}})$