Question

In the figure, the inner (shaded) region $A$ represents a sphere of radius $r_A=1$, within which the electrostatic charge density varies with the radial distance $r$ from the center as $\rho_A=k r$, where $k$ is positive. In the spherical shell $B$ of outer radius $r_B$, 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.

Which of the following statement(s) is(are) correct?

• A. If $r_B=\sqrt{\frac{3}{2}}$, then the electric field is zero everywhere outside $B$.
• B. If $r_B=\frac{3}{2}$, then the electric potential just outside $B$ is $\frac{k}{\epsilon_0}$.
• C. If $r_B=2$, then the total charge of the configuration is $15 \pi k$.
• D. If $r_B=\frac{5}{2}$, then the magnitude of the electric field just outside $B$ is $\frac{13 \pi k}{\epsilon_0}$.

Answer 1

Answer: (A)

If $r_B=\sqrt{\frac{3}{2}}$, then the electric field is zero everywhere outside $B$.

Answer 2

The correct answer is (B): If $r_B=\frac{3}{2}$, then the electric potential just outside $B$ is $\frac{k}{\epsilon_0}$.