Question
The electric field intensity at the centre of a uniformly charged hemispherical shell is $${E_0}.$$ Now two portions of the hemisphere are cut from either side, and the remaining portion is shown in Fig. If $$\alpha = \beta = \frac{\pi }{3},$$ then the electric field intensity at the centre due to the remaining portion is
The electric field intensity at the centre of a uniformly charged hemispherical shell is $${E_0}.$$ Now two portions of the hemisphere are cut from either side, and the remaining portion is shown in Fig. If $$\alpha = \beta = \frac{\pi }{3},$$ then the electric field intensity at the centre due to the remaining portion is
A.
$$\frac{{{E_0}}}{3}$$
B.
$$\frac{{{E_0}}}{6}$$
C.
$$\frac{{{E_0}}}{2}$$
D.
information insufficient
Answer :
$$\frac{{{E_0}}}{2}$$
Solution :
The magnitude of electric field intensity due to each part of the hemispherical surface at the centre $$'O'$$ is same.
Suppose it is $$E.$$
$$\eqalign{ & E + \frac{E}{2} + \frac{E}{2} = {E_0} \cr & {\text{or}}\,\,2E = {E_0}\,{\text{or}}\,E = \frac{{{E_0}}}{2} \cr} $$
The magnitude of electric field intensity due to each part of the hemispherical surface at the centre $$'O'$$ is same.
Suppose it is $$E.$$
$$\eqalign{ & E + \frac{E}{2} + \frac{E}{2} = {E_0} \cr & {\text{or}}\,\,2E = {E_0}\,{\text{or}}\,E = \frac{{{E_0}}}{2} \cr} $$
