question_answer

The electric field intensity at the center of a uniformly charged hemispherical shell is \[{{E}_{0}}.\]Now two portions of the remaining portion is shown in Fig. If \[\alpha =\beta =\pi /3\], then the electric field intensity at the center due to the remaining portion is

A) \[{{E}_{0}}/3\]

B)        \[{{E}_{0}}/6\]

C) \[{{E}_{0}}/2\]

D)        Information incomplete

Correct Answer: C

Solution :

[c] The magnitude of electric field intensity due to each part of the hemispherical surface at the center ?O? is same. Suppose it is E. \[E+\frac{E}{2}+\frac{E}{2}={{E}_{0}}\] or \[2E={{E}_{0}}\text{ or }E=\frac{{{E}_{0}}}{2}\]