Electric field intensity due to a semi- infinite wire at a point A as shown is :

Question

$(A)\;\frac{\lambda}{4 \pi \in _0 a} \sin \frac{\pi}{4} \hat i +\frac{\lambda}{4 \pi \in _0 a} \cos \frac{\pi}{4} \hat j \\ (B)\;\frac{\lambda}{4 \pi \in _0 a} (1+\sin \frac{\pi}{4}) \hat i +\frac{\lambda}{4 \pi \in _0 a} \cos \frac{\pi}{4} \hat j \\ (C)\; \frac{\lambda}{4 \pi \in _0 a} (1-\sin \frac{\pi}{4}) \hat i +\frac{\lambda}{4 \pi \in _0 a} \cos \frac{\pi}{4} \hat j \\ (D)\;\frac{\lambda}{4 \pi \in _0 a} \sin \frac{\pi}{4} \hat i +\frac{\lambda}{4 \pi \in _0 a} \cos \frac{\pi}{4} \hat j$