Paragraph: The nuclear charge $(\mathrm{Ze})$ is non-uniformly distributed within a nucleus of radius $R$.…
Paragraph:
The nuclear charge $(\mathrm{Ze})$ 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. Question:
The electric field within the nucleus is generally observed to be linearly dependent on $r$. This implies
$a=0$
$a=\frac{R}{2}$
$a=R$
$a=\frac{2 R}{3}$
Solution
In case of solid sphere of charge of uniform volume density.
$
E=\frac{1}{4 \pi \varepsilon_0} \cdot \frac{q}{R^3} \cdot r \text { or } E \propto r
$
Thus, for $E$ to be linearly dependent on $r$, volume charge density should be constant.
or $\quad a=R$
$\therefore$ correct option is (c).
:
