In the figure, the inner (shaded) region $A$ represents a sphere of radius $\mathrm{r}_{\mathrm{A}}=1$, within which the electrostatic charge density varies with the radial distance $r$ from the center as $\rho_A=k d$, where $k$ is positive. In the spherical shell $B$ of outer radius $r^{\mathrm{r} B}$, the electrostatic charge density varies as $\rho_B=\frac{2 k}{r}$. Assume that dimensions are taken care of. All physical quantities are in their SI units.
Select the correct option:
A
If $\mathrm{r}_{\mathrm{B}}=\sqrt{\frac{3}{2}}$, then the electric field is zero everywhere outside B .
B
If $\mathrm{r}_{\mathrm{B}}=\frac{3}{2}$, then the electric potential just outside B is $\frac{\mathrm{k}}{\varepsilon_0}$
C
If $\mathrm{rg}=2$, then the total charge of the configuration is $15 \pi \mathrm{k}$.
D
If $\mathrm{r}_{\mathrm{B}}=\frac{5}{2}$ then the magnitude of the electric field just outside B is $\frac{13 \pi \mathrm{k}}{\varepsilon_0}$
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