A cylindrical portion of radius r is removed from a solid sphere of radius R and uniform volume charge density `rho` in such a way that the axis of the hollow cylinder coincides with one of the diameters of the sphere. (r is negligible compared to R). Then the electric field intensity at point A is

Options

A. `(rhor)/(3epsilon_(0))hati`
B. `-(rhor)/(3epsilon_(0))hati`
C. `(rhor)/(6epsilon_(0))hati`
D. `-(rhor)/(6epsilon_(0))hati`

Explanation

Field at A
Due at A due the cylinder of length 2R (which can assumed to be inifinite, since `r lt lt R`)
`E_(2)=(2K(rhopir^(2)))/(r)(-hati)=-(rho)/(2epsilon_(0))rhati`
`therefore` net field `E=E_(1)+E_(2)=(rhor)/(6epsilon_(0))hati`