The nuclear charge (`Ze`) is non uniformlly distribute with in a nucleus of radius r. The charge density `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 at `r=R` is

Options

A. independent of a
B. directly proportional to a
C. directly proportional to `a^2`
D. inversely proportional to a

Explanation

Net charge within `rltR` is constant, hence , electric field is independent of a.
`q=int_(0)^(R)(d)/(R)(R-x)4pix^(2)dx=Ze`
`d=(3Ze)/(piR^(3))`
if within a phere `rho` is constant then `Epropr`