Question

Derive the expression for the electric field of half a hollow sphere which is uniformly charged on its surface.

Answer 1

$$\begin{gathered} Weconsideruniformlychargedclosedhalfhollowspherehavingcharge\sigma chargedensityperunitsurfacearea. \\ So\sigma =\frac{q}{2\pi r^2},whererisradiusofthehollowsphere. \\ ApplyingGauss\text{'}sLaw, \\ Electricfieldatapointinsidethesurfaceofhollowhalfsphere, \\ Eataninsidepoint=\frac{q}{2{\epsilon }_0\pi r^2}=\frac{\sigma \times 2\pi R^2}{2{\epsilon }_0\pi r^2}=\frac{\sigma R^2}{r^2}. \\ andEatanoutsidepoint=\frac{q}{2{\epsilon }_0\pi R^2}=\frac{\sigma }{{\epsilon }_0}. \end{gathered}$$