Q. The radii of the inner and outer spheres of a condenser are $9cm$ and $10cm$ respectively. If the dielectric constant of the medium between the two spheres is 6 and charge on the inner sphere is $18 \times 10^{- 9}\ coulomb,$ then the potential of inner sphere will be, if the outer sphere is earthed
A) $180\ volts$
B) $30\ volts$
C) $18\ volts$
D) $90\ volts$
Explanation
(b) Given system is a spherical capacitor
So capacitance of system $C = K \times 4\pi\varepsilon_{0}\left( \frac{r_{1}r_{2}}{r_{2} - r_{1}} \right)$
$= \frac{6}{9 \times 10^{9}}\left( \frac{9 \times 10}{1} \right) \times 10^{- 2} = 6 \times 10^{- 10}Farad$
Now potential of inner sphere will be equal to potential difference of the capacitor. So $V = \frac{q}{C} = \frac{18 \times 10^{- 9}}{6 \times 10^{- 10}} = 30V$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.