Question

The radii of the inner and outer spheres of a condenser are 9 cm and 10 cm 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

Answer 1

The correct option is B

30 volts

Given system is a spherical capacitor

So, capacitance of system $C=K\times 4\pi {ϵ}_{\circ }\left[\frac{r_1{r}_2}{r_2-r_1}\right]=\frac{6}{9\times {10}^9}\left[\frac{9\times 10}{1}\right]\times {10}^{-2}=6\times {10}^{-10}F$

Now, potential of inner sphere will be equal to potential difference of the capacitor. So $V=\frac{q}{C}=\frac{18\times {10}^{-9}}{6\times {10}^{-10}}=30V$