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# An infinite long semicircular tube is given as shown below one half is given a surface charge density $+\sigma$ and other half is given charge density $-,\sigma$ . Electric field at a point on axis would be

$(A)\;\frac {\sigma}{\pi \in _0} \hat j \\ (B)\;\frac {\sigma}{\pi \in _0} \hat i \\ (C)\; \frac {-\sigma}{\pi \in _0} \hat i \\ (D)\;\frac {\sigma}{\pi \in _0} \hat j$

$dE_j=0$
$dE_x=2 dE \sin \theta$
$dE=\large\frac{\sigma \times R d \theta}{2 \pi \in _0R}$
$\qquad= \large\frac{\sigma d \theta}{2 \pi \in _0}$
$E_x=\int d E_x$