Question

The space between two concentric metallic spheres of radius R and 2R is filled up with a uniform poorly conducting medium of resistivity $\rho$. At the moment t=0, the inside sphere obtains a certain charge Q.[Dielectric constant of medium is 1].

• A. Charge on inside sphere at any time is $Q{e}^{\frac{-t}{\rho {\epsilon }_0}}$.
• B. Heat generated in system in long time is $\frac{Q^2}{16\pi {\epsilon }_{0}R}$.
• C. Electric field at r=3R changes exponentially.
• D. Heat generated in system in long time is $\frac{Q^2}{8\pi {\epsilon }_{0}R}$.

Answer 1

Answer: (A), (B)

The correct options are
A Charge on inside sphere at any time is $Q{e}^{\frac{-t}{\rho {\epsilon }_0}}$.
B Heat generated in system in long time is $\frac{Q^2}{16\pi {\epsilon }_{0}R}$.


$C=4\pi {\epsilon }_0\frac{R_1{R}_2}{R_2-R_1}=8\pi {\epsilon }_{0}R$

resistance $R_{}={\int }_R^{2R}\frac{\rho dr}{4\pi r^2}$

$R_{}=\frac{\rho }{8\pi R}$


$\Rightarrow q=Q{e}^{\frac{-t}{RC}}$

$q=Q{e}^{\frac{-t}{P{\epsilon }_0}}$


Heat=$\frac{Q^2}{2C}=\frac{Q^2}{2\times 8\pi {\epsilon }_{0}R}$