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

Answer

A

Explanation

At `r=R` , from Gauss’ law `E(4piR^(2))=(q_("net"))_(epsi_(0))=(ze)/(epsi_(0))` or `=1/(4piepsi_(0)).(Ze)/(R^(2))`
E is independent of a. Hence, option (A) is correct.