Question

The electric field intensity at the center 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 figure. 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 insufficient

Answer 1

Answer: (C)

$E_0/2$

The magnitude of electric field intensity due to each part of the hemipsherical surface at the center 'O' is same. Suppose it is E.

$E+\frac{E}{2}+\frac{E}{2}=E_0$

or $2E=E_0$

or $E=\frac{E_0}{2}$