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A circular wire of radius \( R \) carries a total charge \( Q \) distributed uniformly over its circumference. A small length of the wire subtending angle \( \theta \) at the
\( \mathrm{P} \) centre is cut off. Find the electric field at the centre due to the remaining

W. portion .
(A) \( \quad=\frac{Q}{4 \pi^{2} \varepsilon_{0} R^{2}} \sin (\theta) \)
(B) \( =\frac{Q}{4 \pi^{2} \varepsilon_{0} R^{2}} \sin \left(\frac{\theta}{2}\right) \)
(C) \( =\frac{Q}{4 \pi^{2} \varepsilon_{0} R^{2}} \sin \left(\frac{\theta}{4}\right) \)
(D) \( =\frac{Q}{4 \pi^{2} \varepsilon_{0} R^{2}} \sin \left(\frac{\theta}{8}\right) \)
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