Consider the shaded part (S) of a hemispherical surface which is isolated from
the rest of the part. If the part \( S \) is charged with a uniform surface charge density \( \sigma \), then the electric field \( E \) due to \( S \) at the center of the curvature \( O \) is:
(A) \( \frac{\sigma}{2 \varepsilon_{o}} \sin \alpha \)
(B) \( \frac{\sigma}{4 \varepsilon_{o}} \sin \left(\frac{\alpha}{2}\right) \)
(C) \( \frac{\sigma}{\varepsilon_{o}} \frac{\sin (\alpha / 2)}{(\alpha / 2)} \)
(D) \( \frac{\sigma}{2 \varepsilon_{o}} \frac{\sin (\alpha / 2)}{(\alpha / 2)} \)
