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  4. The nuclear charge (Z e) is non-uniformly distributed within a nucleus of radius R. The charge density ρ(r) [charge per unit volume is dependent only on the radial distance r from the centre of the nucleus as shown in figure. The electric field is only along the radial direction. <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/physics/9d009c367b7ed03ac8f56ec779edc2be-.png /> The electric field at r=R is

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Q. The nuclear charge $(Z e)$ is non-uniformly distributed within a nucleus of radius $R$. The charge density $\rho(r)$ [charge per unit volume is dependent only on the radial distance $r$ from the centre of the nucleus as shown in figure. The electric field is only along the radial direction.
image
The electric field at $r=R$ is

Electric Charges and Fields

Solution:

Electric field at $r=R$
image
$E=\frac{K Q}{R^{2}} ; Q=$ Total charge within the nucleus $=Z e$
So, $E=\frac{K Z e}{R^{2}}$
So, electric field is independent of $a . .$