Electric field at the center of circular arc is given by the formula
[tex]E = \frac{2k\lambda sin\frac{\theta}{2}}{R}[/tex]
here we know that
[tex]\lambda = 5nC/m[/tex]
[tex]k = 9 \times 10^9 Nm^2/C^2[/tex]
[tex]\frac{\pi}{2}R = L = 2m[/tex]
[tex]R = \frac{4}{\pi}[/tex]
also we know that
[tex]\theta = \frac{\pi}{2}[/tex]
now from above formula
[tex]E = \frac{2(9\times 10^{-9})(5\times 10^{-9})sin45}{4/\pi}[/tex]
[tex]E = 50 N/C[/tex]
