There is one non-conducting uniformly charged hemispherical body, which carries a total charge Q which is kept in such a manner that Y-axis divides it symmetrically.

The net electric field intensity at point A(d,0,0) is

Options

A. `Q/(4piepsilon_0d^2)`
B. `(2Q)/(4piepsilon_0d^2)`
C. `lt (2Q)/(4piepsilon_0d^2)` and ` gt Q/(4piepsilon_0d^2)`
D. gt `(2Q)/(4piepsilon_0d^2)`

Answer

C

Explanation

If we visualise the identical half in the negative y-direction then the total charge on it will be 2Q. Net electric field due to this spherical body is
`E_0=(2Q)/(4piepsilon_0d^2)`
We can see that the charge is doubled and effective distance of the centre of charge from point A (d, 0, 0) has also decreased. We can easily say that if E is the net electric field intensity due to given hemisphere then `E lt E_0`. Let us assume that E is at an angle `theta` with X-axis then the resultant of both halves will be 2E cos `theta`. This resultant should be equal to the electric field intensity due to completed sphere .
`2E cos theta =(2Q)/(4piepsilon_0d^2) rArr E=Q/(4piepsilon_0d^2 cos theta)`
We know that cos `theta` is less than one , hence `E > Q/(4piepsilon_0d^2)`