Question

The radii of a spherical capacitor are equal to $a$ and $b(b>a$) The space between them is filled with a dielectric constant $K$ and resistivity $\rho$ At $t=0$ the inner electrods is given a charge $q_0$ Choose the correct options

• A. Charge q on the electrode as a function of time is given by $q=q_0{e}^{-\frac{1}{\rho K{\epsilon }_0}}$
• B. In short time the charge on the inner electrode will become zero
• C. After a long time the charge on the outer sphere will become $q_0$
• D. The total amount of heat generated during the spreading of charge will be given by $H=(\frac{1}{a}-\frac{1}{b})\frac{q_0^2}{8\pi {\epsilon }_{0}K}$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A Charge q on the electrode as a function of time is given by $q=q_0{e}^{-\frac{1}{\rho K{\epsilon }_0}}$
B In short time the charge on the inner electrode will become zero
C After a long time the charge on the outer sphere will become $q_0$
D The total amount of heat generated during the spreading of charge will be given by $H=(\frac{1}{a}-\frac{1}{b})\frac{q_0^2}{8\pi {\epsilon }_{0}K}$

$C=\frac{4\pi {\epsilon }_{0}abK}{b-a}$

$R={\int }_b^{a}p\frac{dr}{4\pi r^2}=\frac{\rho }{4\pi }\frac{(b-a)}{ab}$

$tourque=RC=\rho K{ϵ}_0$

$q=q_{0e^{-tt}}$

$t=\infty ,$ q = 0

Amount of heat generated

$H=(\frac{1}{a}-\frac{1}{b})\frac{q_0^2}{8\pi {ϵ}_{0}K}$