The nuclear charge (`Ze`) is non uniformlly distribute with in a nucleus of radius r. The charge densilty `rho(r)` (charge per unit volume) is dependent only on the radial distance r form the centre of the nucleus s shown in figure. The electric field is only along the radial direction.

The electric field within the nucleus is generaly observed to be linearly dependent on r. This implies

Options

A. `a=0`
B. `a=R/2`
C. `a=R`
D. `a=(2R)/3`

Answer

C

Explanation

In case of sphere of charge of uniform volume density
`E=1/(4piepsilon_0).q/R^3.r` or `E propr`
Thus, for E to be linearly dependent on r volume charge density should be constant.
or a=R