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 $18 \times 10^{-9}\, C$, then the potential of inner sphere will be, if the outer sphere is earthed

• A. 180 V
• B. 30 V
• C. 18 V
• D. 90 V

Answer 1

Answer: (B)

30 V

Answer 2

Given system is a spherical capacitor so, capacitance of system, $C=K \times 4 \pi \varepsilon_{0}\left[\frac{r_{1} r_{2}}{r_{2}-r_{1}}\right]$ $=\frac{6}{9 \times 10^{9}}\left[\frac{9 \times 10}{1}\right] \times 10^{-2}$ $=6 \times 10^{-10} F$ Now, potential of inner sphere will be equal to potential difference of the capacitor. So, $V=\frac{q}{C}=\frac{18 \times 10^{-9}}{6 \times 10^{-10}}=30\, V$